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forecast的用法及固定搭配
预测在我们日常生活中扮演着重要的角色，无论是个人规划还是商业决策，都需要对未来进行一定程度的预测。
在英语中，“forecast”是一个常用的动词，我们可以用它来表示预测未来的事物或者事件。
除了常规的用法外，它还有一些固定搭配，通过这些固定搭配，我们可以更准确地表达预测的内容和方式。
我们来看看“forecast”这个词在英语中的基本用法。
作为动词，“forecast”通常意味着预测或者预告。
在日常生活中，我们经常可以听到一些天气预报员使用这个词来预测未来的天气情况。
在商业和经济领域，“forecast”也被广泛使用，用来表示对未来市场走势、销售额等方面的预测。
我们可以看到，“forecast”这个词在不同的领域中都有着广泛的应用。
我们来看看“forecast”这个词在固定搭配中的运用。
在英语中，“forecast”常常和其他词语搭配在一起，形成一些固定的短语，来表示不同的预测情况。
“weather forecast”就是天气预报的意思，通过预测未来天气的变化，人们可以提前做好准备。
“economic forecast”则表示经济预测，这对政府决策和商业规划都具有重要意义。
除了这些常见的固定搭配外，“forecast”还可以和不同的名词组合，来形成更加专业和具体的预测内容。
在个人看来，预测具有一定的风险和不确定性，但在适当的情况下，它可以帮助我们做出更加明智的决策。
通过预测未来的趋势和发展，我们可以更好地规划自己的生活和工作。
作为一名文章写手，我认为对于“forecast”这个主题的深入理解和分析，可以帮助我们更好地把握未来的方向，从而提升我们的写作质量和深度。
总结而言，“forecast”作为一个动词，在英语中有着广泛的应用和丰富的固定搭配。
通过对这些固定搭配的学习和掌握，我们可以更加准确地表达自己对未来的预测和观点。
预测是一项具有挑战性的任务，但只有通过不断的学习和实践，我们才能够提升自己的预测能力和准确性。
9What do consumers believe about future gasoline prices
What do consumers believe about future gasoline prices?Soren T.Anderson a,Ryan Kellogg b,James M.Sallee c,na Michigan State University,NBER,United Statesb University of Michigan,NBER,United Statesc University of Chicago,NBER,United Statesa r t i c l e i n f oArticle history:Received26November2012Available online27July2013Keywords:Gasoline pricesConsumer beliefsAutomobile demandEnergy efficiencya b s t r a c tA full understanding of how gasoline prices affect consumer behavior frequently requiresinformation on how consumers forecast future gasoline prices.We provide the firstevidence on the nature of these forecasts by analyzing two decades of data on gasolineprice expectations from the Michigan Survey of Consumers.We find that averageconsumer beliefs are typically indistinguishable from a no-change forecast,justifying anassumption commonly made in the literature on consumer valuation of energy efficiency.We also provide evidence on circumstances in which consumer forecasts are likely todeviate from no-change and on significant cross-consumer forecast heterogeneity.&2013Elsevier Inc.All rights reserved.1.IntroductionThe price of gasoline is important for the economy and for economic research.Gas prices are particularly salient to consumers,and motor fuels account for5%of all consumer expenditures.Moreover,oil price shocks are strongly correlated with recessions,even more than gasoline's expenditure share would explain(Hamilton,2008).Consumer reactions to gasoline prices have been used to study a broad array of economic phenomena,ranging from the demand for automobiles(Busse et al.,2013;Li et al.,2009;Allcott,2012;Gillingham,2011;Linn and Klier,2010)and driving choices(Small and Van Dender,2007;Knittel and Sandler,2012;Davis and Kilian,2011;Li et al.,2012),to the consumption of leisure(West and Williams,2007),search behavior (Lewis and Marvel,2011),and mental accounting(Hastings and Shapiro,2011).Understanding how consumers respond to gasoline prices today requires information about what consumers believe about future gasoline prices.For example,if an increase in today's price causes consumers to expect an even higher price tomorrow,the effect of current price shocks on the macroeconomy could be amplified,perhaps by enough to explain the stronger-than-expected correlation between current prices and economic growth.Unfortunately,little to no evidence exists regarding consumers'beliefs about future gasoline prices.What does the average consumer believe the future price of gasoline will be,and how does this belief vary with the current price?How varied are beliefs across individuals?Are consumers'beliefs reasonable?Do beliefs respond differently to different types of gasoline price shocks?How should researchers model consumer beliefs?In the absence of direct evidence,prior research has been left to make assumptions that are often guided by convenience.In this paper,we take first steps toward answering these questions by analyzing data from a high-quality survey that directly elicits consumer beliefs.Contents lists available at ScienceDirectjournal homepage:/locate/jeemJournal ofEnvironmental Economics and Management0095-0696/$-see front matter&2013Elsevier Inc.All rights reserved./10.1016/j.jeem.2013.07.002n Corresponding author.Fax:+17737022286.E-mail addresses:sta@(S.T.Anderson),kelloggr@(R.Kellogg),sallee@(J.M.Sallee).URLS:/$sta(S.T.Anderson),/$kelloggr(R.Kellogg),/$sallee(J.M.Sallee).Journal of Environmental Economics and Management66(2013)383–403When consumers buy energy-using durable goods,they must forecast the future price of energy to determine their willingness to pay for energy efficiency.In turn,research that attempts to estimate or control statistically for consumers 'valuation of energy efficiency must explicitly model consumers 'beliefs about future energy prices and may draw biased inferences if these beliefs are mis-specified.This issue is most relevant for studies using identification strategies that rely on time-series variation in energy prices to identify demand —a strategy that is particularly common in automobile research (Kahn,1986;Goldberg,1998;Kilian and Sims,2006;Li et al.,2009;Allcott and Wozny,2011;Bento et al.,2012;Klier and Linn,2010;Sallee et al.,2009;Whitefoot et al.,2011;Langer and Miller,2011;Linn and Klier,2010;Busse et al.,2013).These studies frequently assume that consumers adopt no-change forecasts for future gasoline prices in real terms;that is,they assume that the expected future price is the current price.1If consumer beliefs deviate significantly from this assumption,then researchers may under-estimate or over-estimate consumers 'valuation of fuel economy (and other important attributes)depending on the direction of the deviation.2In lieu of direct evidence,there is perhaps little reason to believe that consumer expectations will align conveniently with the no-change hypothesis favored by applied researchers.Future crude oil and gasoline prices are notoriously difficult to predict,and there is substantial controversy among academic and industry experts about what the future price of oil will be and how best to predict future prices (Hamilton,2009;Alquist and Kilian,2010;Alquist et al.,2013).The main goal of our paper is therefore to test directly whether consumers forecast the future price of gasoline to equal the current price.We conduct our analysis using high-frequency data on consumer beliefs about future gasoline prices from the Michigan Survey of Consumers (MSC).Every month,the MSC asks a nationally representative sample of about 500respondents to report their beliefs about the current state of the economy and to forecast several economic variables.Since 1993,the MSC has regularly asked respondents to report whether they think gasoline prices will be higher or lower (or the same)in five year 's time and then to forecast the exact price change.To the best of our knowledge,we (along with Richard Curtin,our collaborator on a related paper (Anderson et al.,2011))are the first researchers to use this unique cache of information on gasoline price expectations,and very little existing work directly measures consumer beliefs about future energy prices in any context.3Our analysis indicates that in normal economic climates the average consumer expects the future real price of gasoline to equal the current price.That is,we generally cannot reject the hypothesis,commonly assumed in the automobile demand literature,that the average consumer 's forecast of future gasoline prices moves one-for-one with changes in the current price.While a no-change gasoline price forecast is obviously not perfect,we believe it is a good benchmark for determining whether consumer forecasts are reasonable.4We do identify some specific settings in which the average consumer 's forecast deviates from no-change.The first such case is the 2008financial crisis,during which consumers predicted that gasoline prices would rebound following their sharp decline.In a companion paper,Anderson et al.(2011),we show that this prediction turned out to be prescient.The second case deals with state-specific price shocks,such as those that might arise from local refinery outages,which tend to be short lived and for which a no-change forecast is therefore clearly inaccurate.We find that consumer forecasts do change less than one-for-one with state-specific gasoline price movements,but they nevertheless predict more persistence in state-specific shocks than is actually present in the historical data.Two recent papers,Davis and Kilian (2011)and Li et al.(2012),find that gasoline consumption is much more responsive to changes in gasoline taxes than to changes in pre-tax gasoline prices.One explanation for this result,emphasized by both papers,is that consumers might perceive changes in gasoline tax policy to be more persistent than price fluctuations caused by shifts in supply and demand.We use our data to directly test this hypothesis,but we find no evidence that consumer forecasts respond more strongly to tax changes than to pre-tax price changes.We also find substantial heterogeneity in forecasts across consumers.In our sample,the standard deviation in the price forecast across respondents each month averages 62cents (in 2010dollars).Using a simple simulation,we find that this heterogeneity may generate as much variation in consumers 'willingness to pay for fuel economy as is generated by heterogeneity across consumers in vehicle miles traveled or discount rates.We also find that the degree of heterogeneity in consumers 'forecasts co-varies with gasoline prices and that,when we study consumers who are surveyed twice (six months apart),this heterogeneity is mostly accounted for by individual fixed effects.We believe these results will be valuable for a1Equivalently,consumers are assumed to believe that gasoline prices follow a martingale process.Throughout the paper,we use the “no-change ”terminology as it accords with the literature on oil price forecasting (see for example Alquist et al.,2013).We do not use the term “random walk ”because a random walk process further implies that the price innovations are iid.2This issue is a specific instance of the broader empirical problem,discussed by Manski (2004),that preferences and expectations are generally not both identified from choice data alone.3One recent exception is Allcott (2012),which estimates automobile demand using a specially designed survey instrument that asks consumers to report (among other things)their beliefs about future gasoline prices in real terms.We compare our results to Allcott 's below.4A no-change forecast for crude oil is theoretically sensible because rapidly rising or falling prices would induce storage and extraction arbitrage (Hamilton,2009).In addition,no-change forecasts predict future crude oil prices as well as or better than forecasts based on futures markets and surveys of experts (Alquist and Kilian,2010;Alquist et al.,2013).This argument is based on the crude oil literature.Retail gasoline prices may behave differently on short time horizons,but they will be tethered to crude prices over a five-year horizon.Likewise,retail prices may spike in specific locations due to refinery outages or supply disruptions,at which time it is reasonable to expect mean reversion in prices in those specific locations,but we believe such occurrences will be too rare to influence our aggregate statistics.S.T.Anderson et al./Journal of Environmental Economics and Management 66(2013)383–403384nascent strand of research —such as Allcott et al.(2012)and Bento et al.(2012)—that seeks to understand the policy and econometric implications of heterogeneity in consumers 'valuation of fuel economy.Anderson et al.(2011)present results that are auxiliary to our main findings here.In that paper,we ask the relatively narrow question of how well consumer forecasts predict future gasoline prices and price volatility.We calculate the mean squared prediction error of the MSC forecast,showing that it is generally similar to that of the no-change benchmark but that it actually out-performed this benchmark during the financial crisis (as did futures prices).We also document a correlation between forecast heterogeneity and measures of future gasoline price volatility,but note that this correlation is driven entirely by the financial crisis.In contrast,in the present paper we ask what consumers believe about future gasoline prices,how these beliefs respond to changes in the current price of gasoline,and what these beliefs imply for research on consumer demand for automobiles.We test directly whether or not the average MSC forecast is consistent with consumers adopting a no-change forecast based on the current price of gasoline and find that it is.We also provide additional results on state panel variation,the impact of taxes on forecasts,and forecast heterogeneity.Thus,while the two papers both involve statistical tests comparing MSC forecasts to the current price of gasoline,they ask and attempt to answer a distinct set of questions.The paper proceeds as follows.In Section 2we discuss a model of consumer demand for fuel economy that highlights the importance of gasoline price expectations.In Section 3we describe the MSC data and detail our transformation of the raw data into aggregate measures.Section 4provides graphical evidence regarding the relationship between current gasoline prices and average consumer forecasts;we verify this evidence with regression-based tests in Section 5.Section 6discusses the response of consumer forecasts to state-level price variation,and Section 7examines the hypothesis that forecasts respond differently to tax and pre-tax price changes.Section 8then examines cross-consumer forecast heterogeneity.Section 9concludes.2.Estimating the demand for automobile fuel economyConsumer beliefs about future gasoline prices are important for understanding behavior in a variety of contexts.Here,we emphasize one key example —estimation of the demand for automobiles and automobile fuel economy —to make clear the importance of future beliefs in economic modeling.Consider the following standard expression for household utility that serves as the basis for many models of automobile demand:u ijt ¼Àαp jt ÀγE it ∑T s ¼0ð1þr i ÞÀs g t þs m ij ;t þs GPM j þβX j þξj þεijt :ð1ÞHere,u ijt is the utility that household i derives from purchasing vehicle j at time t ;p jt is the purchase price of this vehicle;E it ½Á and its contents,detailed below,are consumer i 's expected fuel costs over the lifetime of the vehicle,in present-value terms;X j is a vector of observable vehicle characteristics,such as interior volume and horsepower;ξj is unobservable (to the econometrician)vehicle quality;and εijt is the idiosyncratic utility that an individual consumer derives from the vehicle.5Households are assumed to choose the vehicle model (if any)that gives them the highest utility,facilitating estimation of utility parameters using data on vehicle attributes and household choices.Similar utility models have been used in other energy-intensive durable goods settings,such as purchases of household appliances (Dubin and McFadden,1984).In any given future time period t +s ,fuel costs equal the number of miles m ij ;t þs the vehicle is driven,multiplied by the vehicle 's fuel consumption rate in gallons per mile GPM j ,multiplied by the future real price of gasoline g t þs .Discounting at rate r i and summing over the full,T -period lifetime of the vehicle gives total lifetime fuel costs in brackets.The expectations operator is required because the vehicle 's lifetime,future miles driven,and the future real price of gasoline (which embodies expectations about future gasoline prices and inflation)are not known with certainty at the time of purchase.6Thus,when trading off the purchase price of a vehicle (and other vehicle attributes)against expected lifetime fuel costs,a consumer must consider the fuel efficiency of the vehicle,the number of miles she plans to drive,and the future price of gasoline in real terms.In this model,testing whether consumers fully value the benefits of fuel economy is equivalent to testing the null hypothesis that α¼γ.Empirically implementing this test requires that a researcher populate the expected fuel costs term with each of its underlying es traveled,fuel consumption per mile,discount rates,and time horizons (or close approximations thereof)are all readily observable to researchers,if not for individual vehicles and consumers,then at least for broad classes of vehicles and consumers.7In contrast,expected future gasoline prices have not been directly5εijt is typically modeled as iid logit or generalized extreme value.Random coefficients logit models that allow for heterogeneity in γhave generally not been used in the energy efficiency valuation literature,though a recent paper (Bento et al.,2012)has begun to explore the implications of such an approach.6Of course,variation in other parameters may also be important.Technically,the vehicle 's future fuel consumption per mile (which varies with driving conditions and can degrade over time)and the real rate of discounting from one future period to the next are not known with certainty either.Moreover,miles driven in any future period may depend on the price of gasoline.Beliefs about future gasoline prices,however,are uniquely without empirical support in the existing literature.7Fuel consumption per mile for virtually every vehicle sold in the last several decades is readily available to consumers and researchers alike from the Environmental Protection Agency (EPA)based on standardized testing procedures.Estimates for expected vehicle lifetimes (or rather,the probability that a vehicle survives a given number of years)and the number of miles that vehicles are driven are available directly from the National Highway Transportation S.T.Anderson et al./Journal of Environmental Economics and Management 66(2013)383–403385observable to researchers in any form.In lieu of direct evidence,applied researchers frequently assume that consumers use a no-change forecast (Busse et al.,2013;Sallee et al.,2009).That is,researchers assume that the expected future real price of gasoline equals the current price,simply replacing future gasoline prices g t þs in the expression above with the current price g t .Less frequently,researchers estimate their own econometric forecast models to predict future gasoline prices as a function of current and lagged macroeconomic variables,sometimes specifying a probability distribution for the evolution of future prices (Kilian and Sims,2006).More recently,Allcott and Wozny (2011)assume that expected future gasoline prices equal the price of crude oil in futures markets plus an add-on to account for refining costs,distribution,marketing,and taxes.Because fuel consumption per mile is highly correlated with a vehicle 's other attributes,such as engine size,weight,horsepower,and interior volume,the variation in expected fuel costs needed to identify these models comes largely (and often exclusively,to the extent that vehicle-specific fixed effects are used)through time-series variation in expected gasoline prices.Thus,correct specification of consumer beliefs about future gasoline prices is crucial to identification of the ratio γ=α.Suppose,for instance,that the researcher models consumers as having a no-change forecast.Under this assumption,whenever the current gasoline price increases by $1,consumer beliefs about the future price will also increase by $1.If,however,consumer beliefs about the future price actually increase by less than $1,then the no-change assumption will lead to an estimate of γthat is biased toward zero:consumers will seem under-responsive to lifetime fuel costs.If,on the other hand,consumer beliefs increase by more than $1,then conventional estimates of γwill be biased upward.This strong dependence of inferences about consumers 'valuation of fuel economy on assumptions about gasoline price expectations is the main motivation for our study.While we have emphasized here the subset of the automobile demand literature focused specifically on consumer valuation of fuel economy,misspecification of consumer beliefs about future gasoline prices has the potential to contaminate econometric estimates of consumer preferences for other key attributes,including vehicle price,size,and horsepower,in any study that uses time-series variation in gasoline prices to aid in identification (for example,Berry et al.,1995).3.Data3.1.Data sourcesOur expectations data come from the Michigan Survey of Consumers (MSC),which every month asks a nationally representative random sample of about 500respondents to state their beliefs about the current state of the economy and to forecast several economic variables.A subset of these questions are aggregated into a single measure known as the University of Michigan Consumer Sentiment Index,which is widely followed as a leading indicator of economic performance.The survey has a short panel component:about one-third of respondents each month are repeat respondents from six months earlier,another third are new respondents that will be surveyed again in six months,and the final third are new respondents that will never be surveyed again.A core set of questions appears in every survey,but the survey has added and discontinued and even restarted various questions over time,so not all information is available in every time period.We are primarily interested in two questions related to expected future gasoline prices that appear in nearly every survey dating back to 19938:Question:“Do you think that the price of gasoline will go up during the next five years,will gasoline prices go down,or will they stay about the same as they are now?”If respondents answer “stay about the same,”their expected price change is recorded as zero.If respondents answer “go up ”or “go down,”they are asked a follow-up question:Question:“About how many cents per gallon do you think gasoline prices will (increase/decrease)during the next five years compared to now?”If consumers report a range of price changes,they are asked to pick a single number.If they refuse or are unable to pick a single number,then the median of their reported range is recorded instead.If consumers respond that they “don 't know ”or refuse to respond at any stage of the questioning,then their non-response is noted as such,but only after being prompted several times to give a response.Less than 1%of respondents are coded as non-response.The survey has also asked an identical set of questions about expected twelve-month future gasoline prices since 2006and occasionally during (footnote continued )Safety Administration,can be calculated from the National Household Travel Survey or other surveys,or can be obtained from state administrative datasets,as in Knittel and Sandler (2012).Lastly,discount rates for vehicle purchase decisions can be inferred from market interest rates,including rates on new and used car loans (after adjusting for expected inflation),which are available at the micro level in some vehicle transaction data sets and in aggregate from the Federal Reserve.8There are several short gaps in the data availability:November 1993–February 1994,December 1999–February 2000,and January –April 2004.S.T.Anderson et al./Journal of Environmental Economics and Management 66(2013)383–403386S.T.Anderson et al./Journal of Environmental Economics and Management66(2013)383–403387 1982–1992.We focus here on the five-year forecast because this time horizon is more relevant for automobile demand and because the data coverage is significantly better.9The survey was designed to elicit expectations about gasoline price changes in nominal terms,and there are several compelling reasons to believe that respondents answer in nominal rather than real dollars.First,experienced survey practitioners generally believe that respondents answer in nominal terms unless they are specifically coaxed into a real-price calculation(Curtin,2004).Second,because the questions about gasoline prices follow a series of questions about expected inflation and prices in general,we suspect that consumers are primed to answer in nominal terms.Third,the question asks for gasoline price changes in cents per gallon,so that answering in real terms would require the respondent to make an inflation adjustment calculation.Finally,should respondents ask for clarification,interviewers are instructed to tell respondents to answer in nominal values.Thus,we assume from here on that consumers respond in nominal terms.Our belief that consumers respond in nominal terms may explain a difference between our results and those in Allcott (2012),which finds that consumers expect a real price increase on average,whereas we find a no-change forecast.Allcott draws on a single cross section of data from October2010.In that month,the MSC series also predicts a small increase in real prices and an even larger increase in nominal prices—one that is roughly equivalent to the increase in Allcott's survey.Thus, the discrepant results are reconciled if respondents in the Allcott survey answer in nominal terms,contrary to instructions (our favored interpretation),or if respondents in the MSC series answer in real rather than nominal terms(Allcott's favored interpretation).In addition to the MSC data,from the U.S.Energy Information Administration(EIA)we collected the monthly,sales-weighted average retail price of gasoline(including taxes)by regional Petroleum for Administration of Defense District (PADD)for all grades(regular,midgrade,and premium)and formulations(conventional,oxygenated,and reformulated).10 We match MSC respondents by state to each of the seven PADD regions contained in the EIA data.Because we believe that consumers are reporting expected future gasoline prices in nominal terms,we need to deflate these prices by a measure of expected inflation to facilitate comparison to current gasoline prices in real terms.Fortunately, the MSC asks a series of questions that allow us to deflate each respondent's gasoline price forecast using his or her stated beliefs about future inflation.The first question is:“What about the outlook for prices over the next5–10years?Do you think prices will be higher,about the same,or lower,5–10years from now?”If respondents answer“about the same,”their expected inflation rate is recorded as zero.If respondents answer“higher”or“lower,”then they are asked a follow-up question:“By about what percent per year do you expect prices to go(up/down)on the average,during the next5–10 years?”(underlining in the original survey codebook).We use the responses to these questions to deflate nominal price forecasts by expected inflation,as described in Section3.2.11Lastly,we collected data on the Consumer Price Index(CPI)from the Bureau of Labor Statistics to put all prices into a common unit.12We have complete data on all of these variables—actual gasoline prices,inflation expectations,and CPI—for our study period of January1993to December2009(except for several short gaps due to missing MSC data).Before proceeding,we pause to discuss the relevance of five-year forecasts for vehicle demand.Expected gasoline prices over a vehicle's entire lifetime are potentially relevant for predicting demand.Even if a new buyer expects to sell a vehicle after,say,3years,she should consider gasoline prices beyond that time horizon because used car resale values correlate strongly with gasoline prices(Allcott and Wozny,2011;Busse et al.,2013;Kilian and Sims,2006;Sallee et al.,2009).While a five-year forecast is incomplete,we believe it is still relevant for several reasons.First,according to MSC administrators, the questions about gasoline prices were added at the behest of a major domestic automaker,which suggests that automakers view the five-year horizon as relevant to demand.Second,five years is the approximate midpoint of an average vehicle's lifetime,measured in terms of expected discounted miles driven(authors'calculations based on survival probabilities and miles driven at each age reported in Lu2006).Finally,according to the Federal Reserve Board,13the average new car loan lasts about five years—a fact that government regulators have used in the past to justify (perhaps inappropriately)a five-year planning horizon when calculating the benefits to consumers of fuel economy regulation.149Note that even if consumers expect to own a vehicle for fewer than five years,future gasoline prices still determine valuation of fuel economy because they influence resale value.10According to EIA data,regular gasoline's share of total gasoline consumption rose gradually from67%to83%during our sample period,while midgrade's share fell from20%to9%and premium's share fell from12%to5%.We use the“all grades”price in our analysis because it most closely reflects the price faced by the“average”gasoline buyer at any given time during our sample period.Consumers of different grades face nearly identical month-to-month variation in gasoline prices,however,with monthly changes that differ by less than half a penny on average.Thus,our choice of gasoline grade likely has a trivial effect on our main results.11The average inflation expectation in the survey is quite stable over time,with the mean forecast ranging only between2.5%and5.9%and the median forecast ranging only between3%and4%.To some extent,this variation over time appears to be influenced by gasoline prices,a regularity noted by van der Klaauw et al.(2008).To verify the robustness of our results to this variation,we have used inflation forecasts from the Philadelphia Federal Reserve's survey of experts,rather than MSC inflation forecasts,to deflate respondents'nominal gasoline price forecasts.Our results are qualitatively unaffected by this change.12We use series CUUR0000SA0LE,which is the non-seasonally adjusted index for all urban consumers,all items less energy.13Federal Reserve numbers available at /releases/g19/Current/.14See page63103of NHTSA's latest CAFE rule published in the Federal Register,available here:/staticfiles/rulemaking/pdf/cafe/ 2017-25_CAFE_Final_Rule.pdf.。
麦肯锡公司价值评估经典模型
A Tutorial on the Discounted Cash FlowModel for Valuation of CompaniesL.Peter Jennergren∗Sixth revision,August25,2006SSE/EFI Working Paper Series in Business Administration No.1998:1AbstractAll steps of the discounted cashflow model are outlined.Essential steps are: calculation of free cashflow,forecasting of future accounting data(income state-ments and balance sheets),and discounting of free cashflow.There is particularemphasis on forecasting those balance sheet items which relate to Property,Plant,and Equipment.There is an exemplifying valuation included(of a company calledMcKay),as an illustration.A number of other valuation models(abnormal earn-ings,adjusted present value,economic value added,and discounted dividends)arealso discussed.Earlier versions of this working paper were entitled“A Tutorial onthe McKinsey Model for Valuation of Companies”.Key words:Valuation,free cashflow,discounting,accounting dataJEL classification:G31,M41,C60∗Stockholm School of Economics,Box6501,S-11383Stockholm,Sweden.The author is indebted to Tomas Hjelstr¨o m,Joakim Levin,Per Olsson,Kenth Skogsvik,and Ignacio Velez-Pareja for discussions and comments.1IntroductionThis tutorial explains all the steps of the discounted cashflow model,prominently featured in a book by an author team from McKinsey&Company(Tim Koller,Marc Goedhart,and David Wessels:Valuation:Measuring and Managing the Value of Compa-nies,Wiley,Hoboken,New Jersey;4th ed.2005).The purpose is to enable the reader to set up a complete valuation model of his/her own,at least for a company with a simple structure.The discussion proceeds by means of an extended valuation example.The company that is subject to the valuation exercise is the McKay company.1 The McKay example in this tutorial is somewhat similar to the Preston example (concerning a trucking company)in thefirst two editions of Valuation:Measuring and Managing the Value of Companies(Copeland et al.1990,Copeland et al.1994).How-ever,certain simplifications have been made,for easier understanding of the model.In particular,the capital structure of McKay is composed only of equity and debt(i.e., no convertible bonds,etc.).Also,McKay has no capital leases or capitalized pension liabilities.2McKay is a single-division company and has no foreign operations(and con-sequently there are no translation differences).There is no goodwill and no minority interest.The purpose of the McKay example is merely to present all essential aspects of the discounted cashflow model as simply as possible.Some of the historical income statement and balance sheet data have been taken from the Preston example.However, the forecasted income statements and balance sheets are totally different from Preston’s. All monetary units are unspecified in this tutorial(in the Preston example in Copeland et al.1990,Copeland et al.1994,they are millions of US dollars).This tutorial is intended as a guided tour through one particular implementation of the discounted cashflow model and should therefore be viewed only as exemplifying:This is one way to set up a valuation model.Some modelling choices that have been made will be pointed out later on.However,it should be noted right away that the specification given below of net Property,Plant,and Equipment(PPE)as driven by revenues agrees with Koller et al.2005.Thefirst two editions of Valuation:Measuring and Managing the Value of Companies contain two alternative model specifications relating to investment1Previous versions of this tutorial were entitled“A Tutorial on the McKinsey Model for Valuation of Companies”,since they focused on the McKinsey implementation of the discounted cashflow model. However,after several revisions of the McKinsey book as well as of this tutorial,there are now some differences in emphasis and approach between the two,motivating the title change.Otherwise,the most important changes in the sixth revision of this tutorial are as follows:The working capital items inventories and accounts payable are now driven by operating expenses,rather than by revenues.Section 15and Appendix2are new.2Pension contributions in McKay may hence may be thought of as paid out to an outside pension fund concurrently with the salaries generating those contributions,so no pension debt remains on the company’s books.in PPE(cf.Levin and Olsson1995).In the following respect,this tutorial is an extension of Koller et al.2005:It contains a more detailed discussion of capital expenditures,i.e.,the mechanism whereby cash is absorbed by investments in PPE.This mechanism centers on two particular forecast assumptions,[this year’s net PPE/revenues]and[depreciation/last year’s net PPE].3It is explained below how those assumptions can be specified consistently.On a related note, the treatment of deferred income taxes is somewhat different,and also more detailed, compared to Koller et al.2005.In particular,deferred income taxes are related to a forecast ratio[timing differences/this year’s net PPE],and it is suggested how to set that ratio.There is also another extension in this tutorial:Alternative valuation models are also discussed.In fact,in the end McKay is valued throughfive different models.The McKay valuation is set up as a spreadsheetfile in Excel named MCK.XLS.That file is an integral part of this tutorial.The model consists of the following parts(as can be seen by downloading thefile):Table1.Historical income statements,Table2.Historical balance sheets,Table3.Historical free cashflow,Table4.Historical ratios for forecast assumptions,Table5.Forecasted income statements,Table6.Forecasted balance sheets,Table7.Forecasted free cashflow,Table8.Forecast assumptions,Value calculations.Tables in the spreadsheetfile and in thefile printout that is included in this tutorial are hence indicated by numerals,like Table1.Tables in the tutorial text are indicated by capital letters,like Table A.The outline of this tutorial is as follows:Section2gives an overview of essential model features.Section3summarizes the calculation of free cashflow.Section4is an introduction to forecastingfinancial statements and also discusses forecast assumptions relating to operations and working capital.Sections5,6,and7deal with the specification of the forecast ratios[this year’s net PPE/revenues],[depreciation/last year’s net PPE], and[retirements/last year’s net PPE].Section8considers forecast assumptions about taxes.Further forecast assumptions,relating to discount rates andfinancing,are discussed in Section9.Section10outlines the construction of forecastedfinancial statements and free cashflow,given that all forecast assumptions have beenfixed.Section11outlines a3Square brackets are used to indicate specific ratios that appear in tables in the spreadsheetfiles.slightly different version of the McKay example,with another system for accounting for deferred income taxes.4The discounting procedure is explained in Section12.Section13 gives results from a sensitivity analysis,i.e.,computed values of McKay’s equity when certain forecast assumptions are revised.Section14discusses another valuation model, the abnormal earnings model,and indicates how McKay’s equity can be valued by that model.Section15considers a differentfinancing policy for McKay.Under thatfinancing policy,McKay is valued byfive different models(discounted cashflow,adjusted present value,economic value added,discounted dividends,and abnormal earnings).5Section 16contains concluding remarks.Appendix1discusses how a data base from Statistics Sweden can be used as an aid in specifying parameters related to the forecast ratios[this year’s net PPE/revenues],[depreciation/last year’s net PPE]and[retirements/last year’s net PPE].Appendix2is a note on the value driver formula that is recommended for continuing value by Koller et al.2005.2Model overviewEssential features of the discounted cashflow model are the following:1.The model uses published accounting data as input.Historical income statements and balance sheets are used to derive certain criticalfinancial ratios.Those historical ratios are used as a starting point in making predictions for the same ratios in future years.2.The object of the discounted cashflow model is to value the equity of a going concern.Even so,the asset side of the balance sheet is initially valued.The value of the interest-bearing debt is then subtracted to get the value of the equity.Interest-bearing debt does not include deferred income taxes and trade credit(accounts payable and other current liabilities).Credit in the form of accounts payable is paid for not in interest but in higher operating expenses(i.e.,higher purchase prices of raw materials)and is therefore part of operations rather thanfinancing.Deferred income taxes are viewed as part of equity;cf.Sections9and10.It may seem like an indirect approach to value the assets and deduct interest-bearing debt to arrive at the equity(i.e.,it may seem more straight-forward to value the equity directly,by discounting future expected dividends). However,this indirect approach is the recommended one,since it leads to greater clarity and fewer errors in the valuation process(cf.Koller et al.2005,pp.126-128).4This version of the McKay example is contained in the Excelfile MCK B.XLS.A printout from that file is also included in this tutorial.The two versions of the McKay example are equivalent as regards cashflow and resulting value.In other words,it is only the procedure for computing free cashflow that differs(slightly)between them.5See thefile MCK EXT.XLS.A printout from thatfile is also included here.3.The value of the asset side is the value of operations plus excess marketable secu-rities.The latter can usually be valued using book values or published market values. Excess marketable securities include cash that is not necessary for operations.For valu-ation purposes,the cash account may hence have to be divided into two parts,operating cash(which is used for facilitating transactions relating to actual operations),and ex-cess cash.(In the case of McKay,excess marketable securities have been netted against interest-bearing debt at the date of valuation.Hence there are actually no excess mar-ketable securities in the McKay valuation.This is one of the modelling choices that were alluded to in the introduction.)4.The operations of thefirm,i.e.,the total asset side minus excess marketable secu-rities,are valued by the WACC method.In other words,free cashflow from operations is discounted to a present value using the WACC.There is then a simultaneity problem (actually quite trivial)concerning the WACC.More precisely,the debt and equity values enter into the WACC weights.However,equity value is what the model aims to determine.5.The asset side valuation is done in two parts:Free cashflow from operations is forecasted for a number of individual years in the explicit forecast period.After that, there is a continuing(post-horizon)value derived from free cashflow in thefirst year of the post-horizon period(and hence individual yearly forecasts must be made for each year in the explicit forecast period and for one further year,thefirst one immediately following the explicit forecast period).The explicit forecast period should consist of at least10-15years(cf.Koller et al.2005,p.230).The explicit forecast period can be thought of as a transient phase during a turn-around or after a take-over.The post-horizon period, on the other hand,is characterized by steady-state development.This means that the explicit forecast period should as a minimal requirement be sufficiently long to capture transitory effects,e.g.,during a turn-around operation.Actually,it is a requirement of the present implementation of the discounted cashflow model that the explicit forecast period should not be shorter than the economic life of the PPE.6.For any future year,free cashflow from operations is calculated from forecasted income statements and balance sheets.This means that free cashflow is derived from a consistent scenario,defined by forecastedfinancial statements.This is probably the main strength of the discounted cashflow model,since it is difficult to make reasonable forecasts of free cashflow in a direct fashion.Financial statements are forecasted in nominal terms (which implies that nominal free cashflow is discounted using a nominal discount rate).7.Continuing value is computed through an infinite discounting formula.In this tutorial,the Gordon formula is used(cf.Brealey et al.2006,pp.40,65).In other words, free cashflow in the post-horizon period increases by some constant percentage from year to year,hence satisfying a necessary condition for infinite discounting.(The Gordon formula is another one of the modelling choices made in this tutorial.)As can be inferred from this list of features,and as will be explained below,the discounted cashflow model combines three rather different tasks:Thefirst one is the production of forecastedfinancial statements.This is not trivial.In particular,it involves issues relating to capital expenditures that are fairly complex.(The other valuation models use forecastedfinancial statements,just like the discounted cashflow model,so thefirst task is the same for those models as well.)The second task is deriving free cashflow from operations fromfinancial statements. At least in principle,this is rather trivial.In fairness,it is not always easy to calculate free cashflow from complicated historical income statements and balance sheets.However,all financial statements in this tutorial are very simple(and there is,in any case,no reason to forecast accounting complexities if the purpose is one of valuation).The third task is discounting forecasted free cashflow to a present value.While not exactly trivial,this task is nevertheless one that has been discussed extensively in the corporatefinance literature, so there is guidance available.This tutorial will explain the mechanics of discounting in the discounted cashflow model.However,issues relating to how the relevant discount rates are determined will largely be brushed aside.Instead,the reader is referred to standard text books(for instance,Brealey et al.2006,chapters9,17,and19).3Historicalfinancial statements and the calculation of free cashflowThe valuation of McKay is as of Jan.1year1.Historical input data are the income statements and balance sheets for the years−6to0,Tables1and2.Table1also includes statements of retained earnings.It may be noted in Table1that operating expenses do not include depreciation.In other words,the operating expenses are cash costs.At the bottom of Table2,there are a couple offinancial ratio calculations based on historical data for the given years.Short-term debt in the balance sheets(Table2)is that portion of last year’s long-term debt which matures within a year.It is clear from Tables1and 2that McKay’sfinancial statements are very simple,and consequently the forecasted statements will also have a simple structure.As already mentioned earlier,McKay has no excess marketable securities in the last historical balance sheet,i.e.,at the date of valuation.From the data in Tables1and2,historical free cashflow for the years−5to0 is computed in Table3.Each annual free cashflow computation involves two balance sheets,that of the present year and the previous one,so no free cashflow can be obtained for year−6.Essentially the same operations are used to forecast free cashflow for year1and later years(in Table7).The free cashflow calculations assume that the clean surplus relationship holds.This implies that the change in book equity(including retainedearnings)equals net income minus net dividends(the latter could be negative,if there is an issue of common equity).The clean surplus relationship does not hold,if PPE is written down(or up)directly against common equity(for instance).Such accounting operations may complicate the calculation of free cashflow from historicalfinancial statements(and if so,that calculation may not be trivial).However,there is usually no reason to forecast deviations from the clean surplus relationship in a valuation situation.EBIT in Table3means Earnings Before Interest and Taxes.NOPLAT means Net Op-erating Profits Less Adjusted Taxes.Taxes on EBIT consist of calculated taxes according to the income statement(from Table1)plus[this year’s tax rate]×(interest expense) minus[this year’s tax rate]×(interest income).Interest income and interest expense are taken from Table1.The tax rate is given in Table4.Calculated taxes according to the income statement reflect depreciation of PPE over the economic life.Change in deferred income taxes is this year’s deferred income taxes minus last year’s deferred income taxes. In the McKay valuation example,it is assumed that deferred income taxes come about for one reason only,timing differences in depreciation of PPE.That is,fiscal depreciation takes place over a period shorter than the economic life.Working capital is defined net.Hence,working capital consists of the following balance sheet items:Operating cash plus trade receivables plus other receivables plus inventories plus prepaid expenses minus accounts payable minus other current liabilities.Accounts payable and other current liabilities are apparently considered to be part of the operations of thefirm,not part of thefinancing(they are not interest-bearing debt items).Change in working capital in Table3is hence this year’s working capital minus last year’s working capital.Capital expenditures are this year’s net PPE minus last year’s net PPE plus this year’s depreciation.Depreciation is taken from Table1,net PPE from Table2.It should be emphasized that depreciation in Table1(and forecasted depreciation in Table5)is according to plan,over the economic life of the PPE.Free cashflow in Table3is hence cash generated by the operations of thefirm,after paying taxes on operations only,and after expenditures for additional working capital and after capital expenditures.(“Additional working capital”could of course be negative.If so,free cashflow is generated rather than absorbed by working capital.)Hence,free cash flow represents cash that is available for distribution to the holders of debt and equity in thefirm,and for investment in additional excess marketable securities.Stated somewhat differently,free cashflow is equal tofinancial cashflow,which is the utilization of free cashflow forfinancial purposes.Table3also includes a break-down offinancial cashflow. By definition,free cashflow must be exactly equal tofinancial cashflow.We now return briefly to thefinancial ratios at the end of Table2.Invested capi-tal is equal to working capital plus net PPE.Debt at the end of Table2in the ratio [debt/invested capital]is interest-bearing(short-term and long-term).Thefinancial ratio[NOPLAT/invested capital]is also referred to as ROIC(Return on Invested Capital).It is a better analytical tool for understanding the company’s performance than other return measures such as return on equity or return on assets,according to Koller et al.(2005,p. 183).Invested capital in the ratio[NOPLAT/invested capital]is the average of last year’s and this year’s.It is seen that McKay has provided a decreasing rate of return in recent years.It can also be seen from Table3that the free cashflow has been negative,and that the company has handled this situation by increasing its debt.It is evident from the bottom of Table2that the ratio of interest-bearing debt to invested capital has increased substantially from year−6to year0.Table4contains a set of historicalfinancial ratios.Those ratios are important,since forecasts of the same ratios will be used to produce forecasted income statements and balance sheets.Most of the items in Table4are self-explanatory,but a few observations are called PPE(which is taken from Table2)enters into four ratios.In two of those cases,[depreciation/net PPE]and[retirements/net PPE],the net PPE in question is last year’s.In the other two cases,[net PPE/revenues]and[timing differences/net PPE],the net PPE in question is this year’s.Retirements are defined as depreciation minus change in accumulated depreciation between this year and last year(accumulated depreciation is taken from Table2).This must hold,since last year’s accumulated de-preciation plus this year’s depreciation minus this year’s retirements equals this year’s accumulated depreciation.The timing differences for a given year are measured between accumulatedfiscal depre-ciation of PPE and accumulated depreciation according to PPE economic life.For a given piece of PPE that is about to be retired,accumulatedfiscal depreciation and accumulated depreciation according to economic life are both equal to the original acquisition value. Consequently,non-zero timing differences are related to non-retired PPE only.The ratio [timing differences/net PPE]in Table4has been calculated byfirst dividing the deferred income taxes for a given year by the same year’s corporate tax rate(also given in Table 4).This gives that year’s timing differences.After that,there is a second division by that year’s net PPE.4Forecast assumptions relating to operations and working capitalHaving recorded the historical performance of McKay in Tables1-4,we now turn to the task of forecasting free cashflow for years1and later.Individual free cashflow forecasts are produced for each year1to12.The free cashflow amounts for years1to11 are discounted individually to a present value.The free cashflow for year12and all later years is discounted through the Gordon formula,with the free cashflow in year12as astarting value.Years1to11are therefore the explicit forecast period,and year12and all later years the post-horizon period.As required,the explicit forecast period is longer than the economic life of the PPE(the latter is assumed to be10years in Section7).Tables5-8have the same format as Tables1-4.In fact,Table5may be seen as a continuation of Table1,Table6as a continuation of Table2,and so on.We start the forecasting job by setting up Table8,the forecast ing assumptions (financial ratios and others)in that table,and using a couple of further direct forecasts of individual items,we can set up the forecasted income statements,Table5,and the forecasted balance sheets,Table6.From Tables5and6,we can then in Table7derive the forecasted free cashflow(just like we derived the historical free cashflow in Table3, using information in Tables1and2).Consider now the individual items in Table8.It should be noted in Table8that all items are the same for year12,thefirst year of the post-horizon period,as for year11,the last year of the explicit forecast period.Since thefirst year in the post-horizon period is representative of all subsequent post-horizon period years,all items are the same for every post-horizon period year as for the last year of the explicit forecast period.This is actually an important condition(cf.Levin and Olsson1995,p.38;Lundholm and O’Keefe2001, pp.321-322):If that condition holds,then free cashflow increases by the same percentage (the nominal revenue growth rate for year12in Table8,cell T135)between all successive years in the post-horizon period.This means that a necessary condition for discounting by means of the Gordon formula in the post-horizon period is satisfied.The revenue growth in each future year is a combination of inflation and real growth. More precisely,nominal revenue growth is“one plus real growth multiplied by one plus expected inflation minus one”.Actually,in years10and11there is no real growth,and the same assumption holds for all later years as well(in the application of the Gordon formula).The underlying assumption in Table8is apparently that real operations will initially expand but will eventually(in year10)settle down to a steady state with no further real growth.Inflation,on the other hand,is assumed to be3%in all coming years(including after year12).The ratio of operating expenses to revenues is assumed to improve immediately,e.g.,as a consequence of a determined turn-around effort.Ap-parently,it is set to90%year1and all later years.To avoid misunderstandings,this forecast assumption and the other ones displayed in Table8are not necessarily intended to be the most realistic ones that can be imagined.The purpose is merely to demonstrate the mechanics of the discounted cashflow model for one particular scenario.A table in Levin and Olsson1995(p.124;based on accounting data from Statistics Sweden)contains information about typical values of the ratio between operating expenses and revenues in various Swedish industries(cf.also Appendix1for a further discussion of the Statistics Sweden data base).A number of items in the forecasted income statements and balance sheets are directly driven by revenues.That is,those items are forecasted as percentages of revenues.In particular,this holds for most of the working capital items.It is thus assumed that as revenues increase,the required amounts of working capital for these items increase correspondingly.It is not important whether revenues increase due to inflation or real growth,or a combination of both.Working capital turns over very quickly,and therefore it is a reasonable assumption that these working capital items are simply proportional to revenues.The ratios between the different working capital items and revenues for future years in Table8have been set equal to the average values of the corresponding historical percentages in Table4.Again,this is only for illustrative purposes.Another table in Levin and Olsson1995(p.125),again based on data from Statistics Sweden, reports average values of the ratio between(aggregate)working capital and revenues in different Swedish industries.Two of the working capital items,inventories and accounts payable,are forecasted as percentages of operating expenses rather than as percentages of revenues.This is actually not a very important distinction(i.e.,one may perhaps just as well forecast all working capital items as percentages of revenues;cf.Koller et al.2005, pp.243-244).The ratios between these two working capital items and operating expenses for future years are also set as average historical values.5Forecast assumptions relating to property,plant, and equipmentThe forecast assumptions relating to PPE will be considered next(this section and the following two).The equations that determine capital expenditures may be stated as follows(subscripts denote years):(capital expenditures)t=(net PPE)t−(net PPE)t−1+depreciation t,(net PPE)t=revenues t×[this year’s net PPE/revenues],depreciation t=(net PPE)t−1×[depreciation/last year’s net PPE].To this set of equations,we may add three more that are actually not necessary for the model:retirements t=(net PPE)t−1×[retirements/last year’s net PPE],(accumulated depreciation)t=(accumulated depreciation)t−1+depreciation t−retirements t, (gross PPE)t=(net PPE)t+(accumulated depreciation)t.In particular,this second set of three equations is needed only if one wants to produce forecasted balance sheets showing how net PPE is related to gross PPE minus accumulated depreciation.It should be noted that such detail is not necessary,since thefirst set ofthree equations suffices for determining net PPE,depreciation,and consequently also capital expenditures.6It is clear from thefirst three equations that forecasts have to be made for two partic-ular ratios,[this year’s net PPE/revenues]and[depreciation/last year’s net PPE].Setting those ratios in a consistent fashion involves somewhat technical considerations.In this section and the following one,one way of proceeding,consistent with the idea of the company developing in a steady-state fashion in the post-horizon period,will be outlined.To begin with,the idea of the company developing in a steady-state fashion has to be made more precise.As indicated in Section4,the forecast assumptions should be specified in such a manner that nominal free cashflow increases by a constant percentage every year in the post-horizon period.This is a necessary condition for infinite discounting by the Gordon formula.But if so,capital expenditures must also increase by the same constant percentage in every post-horizon period year.For this condition on capital expenditures to hold,there must be an even age distribution of nominal acquisition values of successive PPE cohorts.More precisely,it must hold that the acquisition value of each PPE cohort develops in line with the assumed constant growth percentage that is applicable to the post-horizon period.As also mentioned in Section4,that constant percentage is the same as the assumed nominal revenue growth in the post-horizon period,3%in the McKay example.The general idea is now to set steady-state values of the two ratios[this year’s net PPE/revenues]and[depreciation/last year’s net PPE]for the last year of the explicit forecast period(year11in the McKay example).Those steady-state values will then also hold for every year in the post-horizon period(since all forecast assumptions have to be the same in thefirst year of the post-horizon period as in the last year of the explicit forecast period,as already explained in Section4).During the preceding years of the explicit forecast period,steady-state values of[this year’s net PPE/revenues]and[depreciation/last year’s net PPE]are not assumed.Values for these two ratios in the preceding explicit forecast period years arefixed in the following heuristic fashion in the McKay example:For thefirst year of the explicit forecast period, they are set as averages of the corresponding values for the historical years.7Values for6If the historicalfinancial statements do not show gross PPE and accumulated depreciation,only net PPE,then it seems pointless to try to include these items in the forecastedfinancial statements.If so, the second set of three equations is deleted.In the McKay case,the historical statements do indicate gross PPE and accumulated depreciation.For that(aesthetic)reason,those items will also be included in the forecasted statements.7The value for the last year of the explicit forecast period of[retirements/last year’s net PPE]is also set as a steady-state value.For thefirst year of the explicit forecast period,that ratio is set equal to the corresponding value for the last historical year.An average of corresponding values for all historical years is not used in this case,since[retirements/last year’s net PPE]appears to have been unstable during。
excel中的forecast函数
excel中的forecast函数摘要：一、Excel 简介二、FORECAST 函数的概述三、FORECAST 函数的参数及用法1.参数一：known_y"s2.参数二：known_x"s3.参数三：constant4.参数四：linear_trend5.参数五：seasonal_periods6.参数六：seasonal_index四、FORECAST 函数的实例应用1.实例一：简单线性趋势预测2.实例二：多项式趋势预测3.实例三：季节性预测五、FORECAST 函数与其他时间序列预测函数的比较六、总结正文：Excel 是一款广泛应用于数据处理和分析的软件，其内置的函数库为用户提供了丰富的数据分析工具。
在Excel 中，FORECAST 函数是一个强大的时间序列预测函数，可以用于对一组数据进行预测。
FORECAST 函数的概述如下：`=FORECAST(known_y"s, known_x"s, constant, linear_trend, seasonal_periods, seasonal_index)`1.参数一：known_y"sKnown_y"s 是一个数组，表示已知的因变量（响应）值。
这些值通常是按时间顺序排列的。
2.参数二：known_x"sKnown_x"s 是一个数组，表示已知的自变量（预测）值。
这些值通常是按时间顺序排列的，且与known_y"s 中的值相对应。
3.参数三：constantConstant 是一个可选参数，表示常数项。
如果需要添加常数项，请将其值设置为1。
4.参数四：linear_trendLinear_trend 是一个可选参数，表示线性趋势。
如果需要添加线性趋势，请将其值设置为1。
5.参数五：seasonal_periodsSeasonal_periods 是一个可选参数，表示季节性周期的数量。
简单一次平均需求预测代码
简单一次平均需求预测代码全文共四篇示例，供读者参考第一篇示例：随着市场竞争的加剧和消费者需求的日益多样化，企业需要对产品需求进行准确的预测，以便制定合理的生产计划和库存控制策略。
简单一次平均需求预测是一种常用的预测方法，通过对历史数据的分析来预测未来的需求。
本文将介绍一份关于简单一次平均需求预测的代码，帮助读者快速实现需求预测的功能。
我们需要准备相关的数据集。
一般来说，数据集应包括历史销售数据，以及需要预测的时间范围。
接下来，我们将使用Python编程语言来实现简单一次平均需求预测的代码。
```pythonimport numpy as np# 定义简单一次平均需求预测函数def simple_average_demand_forecast(data):forecast = np.mean(data)return forecast# 准备数据集sales_data = [100, 150, 120, 130, 110]print("预测的需求量为：", forecast)```在上面的代码中，我们首先导入了NumPy库，然后定义了一个简单一次平均需求预测的函数simple_average_demand_forecast。
这个函数接收一个包含历史销售数据的数组作为参数，然后计算这些数据的平均值作为预测值。
我们准备了一个包含历史销售数据的列表sales_data，并调用了简单一次平均需求预测函数，将预测结果打印出来。
通过这份代码，我们可以快速实现对需求量的预测，并且可以根据实际情况对预测模型进行调整和优化。
简单一次平均需求预测只是一种基本的预测方法，还有很多更复杂的预测模型可以尝试。
希望读者可以通过这份代码对需求预测有一个初步的了解，并且能够根据自己的需求进行进一步的学习和实践。
祝各位在预测工作中取得好结果！第二篇示例：需求预测在企业的经营中起着至关重要的作用，通过对未来需求的合理预测可以帮助企业更好地进行生产计划、库存管理以及市场营销等方面的决策。
sampleforecast 解析
sampleforecast 解析样例预测（sample forecast）是指利用过去同类数据的历史记录和趋势，通过统计学或机器学习等方法，预测未来同类数据的发展趋势和表现。
具体来讲，它是指对于某一时序数据集，我们以其中一部分数据为训练集，另一部分数据为验证集，通过对训练集的学习，得出对验证集的预测值，用预测值和实际值进行比较来评价和优化模型，最终可以得到对未来同类数据的预测。
样例预测被广泛应用于金融、医疗、气象、航空、电力等多个领域，以为决策者提供重要的参考和支持。
样例预测主要分为时间序列预测和面板数据预测两类。
时间序列预测是指对观测到的时间序列数据进行预测，例如股票价格、空气质量指数、天气、人口数量等；面板数据预测是指对某一时间点的同类数据进行预测，例如某一省份的经济增长率、某一地区的人口迁移等。
更为具体来说，时间序列预测可以用自回归模型（AR）、移动平均模型（MA）、自回归移动平均模型（ARMA）、自回归积分滑动平均模型（ARIMA）来实现预测。
而面板数据预测可以通过面板数据模型（Panel Data Model）、差分面板数据模型（Diff-in-Diff Model）、固定效应模型（Fixed-Effects Model）、随机效应模型（Random-Effects Model）等方法来实现。
在样例预测过程中，数据的选取十分重要。
因为一个好的样本数据能够更加准确地反映未来的发展趋势。
一般来讲，我们需要选择那些历史数据足够长、包含的变量足够全、具有代表性的数据作为样本，例如，股票价格预测中常常选取与该股票相关的行业指数、国际市场情况等数据作为样本，从而更好的预测该股票的未来走势。
除了数据的选取外，模型的选择也是影响预测效果的重要因素。
不同的预测问题，会需要不同的预测方法和算法。
例如，对于时间序列的预测问题，我们需要对时间序列的特性（如趋势、季节性、周期性、噪声）进行分析，结合建模的目标和限制、采用适当的预测算法和模型来进行建模；而对于面板数据的预测问题，则需要结合数据的时空特性、面板数据模型中的基本假设、回归项的引入等因素进行综合考虑。
excel中的forecast函数
excel中的forecast函数【实用版】目录1.Excel 中的 FORECAST 函数概述2.FORECAST 函数的基本语法3.FORECAST 函数的用法示例4.FORECAST 函数的优点和局限性正文1.Excel 中的 FORECAST 函数概述FORECAST 函数是 Excel 中一个十分实用的函数，主要用于预测某个值在一个序列中的趋势。
它可以根据一组已知的数据点，预测未来某个值可能是多少。
FORECAST 函数在各种领域都有广泛的应用，例如财务分析、市场营销和工程项目等。
2.FORECAST 函数的基本语法FORECAST 函数的基本语法如下：```=FORECAST(x, known_y"s, known_x"s)```其中，x 表示我们要预测的值，known_y"s 表示已知的因变量值，known_x"s 表示已知的自变量值。
3.FORECAST 函数的用法示例假设我们有一家公司的销售额数据，如下所示：日期 | 销售额（万元）----|-------------2021-01-01 | 102021-01-02 | 122021-01-03 | 152021-01-04 | 18现在，我们想要预测 2021-01-05 的销售额。
可以使用 FORECAST 函数，已知的因变量值（销售额）和自变量值（日期）如下：已知销售额：{10, 12, 15, 18}已知日期：{2021-01-01, 2021-01-02, 2021-01-03, 2021-01-04} 我们将这些值代入 FORECAST 函数，得到预测结果：```=FORECAST(5, {10, 12, 15, 18}, {2021-01-01, 2021-01-02, 2021-01-03, 2021-01-04})```计算结果为：21.75（万元）这意味着，根据历史数据，预测 2021-01-05 的销售额为 21.75 万元。
excel线性回归涉及的两个函数：trend和forecast函数，同时也可以使用四种运算。。。
excel线性回归涉及的两个函数：trend和forecast函数，同时也可以使⽤四种运算。
excel线性回归相对来说⽤得⽐较少，但对于做统计和建筑分析预测的朋友来说，有时会涉及到。
下⾯讲讲excel线性回归的具体⽤法，可以使⽤四种运算和Excel内置函数：trend和forecast函数来完成。
⽐如下⾯所⽰Excel⼯作表，就是⼀个典型的线性内插值的实例。
已知两点确定⼀条直线，通过斜率相等求出对应的Y值。
分别使⽤了forecast函数和TREND函数完成。
⽤Excel线性回归计算出4对应的值为 5.8。
第三种⽅法，就是纯粹的四则运算，借助EXCEL的⾃动计算功能完成结果。
forecast函数的帮助说明：根据已有的数值计算或预测未来值。
此预测值为基于给定的 x 值推导出的 y 值。
已知的数值为已有的 x 值和 y 值，再利⽤线性回归对新值进⾏预测。
可以使⽤该函数对未来销售额、库存需求或消费趋势进⾏预测。
forecast函数语法为：FORECAST(x, known_y's, known_x's) X 必需。
需要进⾏值预测的数据点。
Known_y's 必需。
因变量数组或数据区域。
Known_x's 必需。
⾃变量数组或数据区域。
TREND函数的帮助说明：返回⼀条线性回归拟合线的值。
即找到适合已知数组 known_y's和 known_x's 的直线（⽤最⼩⼆乘法），并返回指定数组 new_x's 在直线上对应的 y 值。
TREND函数的语法：TREND(known_y's, [known_x's], [new_x's], [const]) trend和forecast函数区别，都可以完成Excel线性回归分析，它们都是返回沿线性趋势的值。
两个都是根据已知的两列数据，得到线性回归⽅程，并根据给定的新的X值，得到相应的预测值。
excel中的forecast函数
excel中的forecast函数
摘要：
1.介绍Excel 中的FORECAST 函数
2.FORECAST 函数的语法和参数
3.FORECAST 函数的使用方法及示例
4.FORECAST 函数在实际应用中的优势和局限性
正文：
Excel 中的FORECAST 函数是一种用于预测未来趋势的函数，它可以根据现有数据点预测未来值。
该函数属于统计学中的线性回归分析，可以用于预测销售趋势、库存需求等。
FORECAST 函数的语法为：`=FORECAST(x, known_y"s, known_x"s)` 其中，x 为需要预测的自变量值；known_y"s 为已知的因变量值；known_x"s 为已知的自变量值。
使用FORECAST 函数时，需要先提供一组现有的数据点，然后函数将根据这组数据点预测未来的值。
例如，假设我们想要预测某个产品的未来销售量，我们可以提供过去一段时间内的销售数据作为已知数据点，然后使用FORECAST 函数预测未来的销售量。
FORECAST 函数在实际应用中有很多优势，例如它可以快速、简单地预测未来趋势，帮助企业制定合理的销售策略和库存计划。
然而，这种预测方法也存在一定的局限性，例如它假设未来的趋势将遵循过去的趋势，没有考虑到可能出现的突发事件或市场变化。
总之，Excel 中的FORECAST 函数是一个实用的预测工具，可以在一定程度上帮助我们预测未来趋势。
excel的forecast函数
excel的forecast函数Excel的Forecast函数Excel是一款广泛应用于数据处理和分析的软件，其中的Forecast函数是一种非常实用的工具。
Forecast函数可以根据已有的数据，预测未来的趋势和结果，为企业和个人的决策提供重要的参考依据。
本文将从使用方法、应用场景和注意事项三个方面，详细介绍Excel的Forecast 函数。
一、使用方法Forecast函数的语法如下：=FORECAST(x,known_y’s,known_x’s)其中，x表示要预测的值，known_y’s表示已知的y值，known_x’s表示已知的x值。
这三个参数都是必须的，且已知的y值和x值必须是相对应的。
例如，如果已知的y值是销售额，已知的x值是时间，则销售额和时间必须是一一对应的关系。
在使用Forecast函数时，需要注意以下几点：1.已知的y值和x值必须是相对应的，且数量相等。
2.已知的x值必须是数值型数据，不能是文本或日期。
3.已知的y值和x值必须按照x值的大小顺序排列。
4.要预测的值x必须在已知的x值的范围内。
二、应用场景Forecast函数可以应用于各种领域，例如：1.销售预测：根据历史销售数据，预测未来的销售趋势和销售额。
2.股票预测：根据历史股票价格，预测未来的股票价格走势。
3.人口预测：根据历史人口数据，预测未来的人口增长趋势和人口规模。
4.气象预测：根据历史气象数据，预测未来的天气情况和气温变化。
5.其他预测：还可以应用于各种其他领域的预测，例如房价预测、交通流量预测等。
三、注意事项在使用Forecast函数时，需要注意以下几点：1.预测结果只是一种可能性，不一定准确。
2.预测结果受到多种因素的影响，例如市场环境、政策变化、自然灾害等。
3.预测结果应该结合实际情况进行分析和判断，不能完全依赖于预测结果。
4.如果已知的数据不够充分或者不够准确，预测结果可能会出现较大误差。
总之，Excel的Forecast函数是一种非常实用的工具，可以帮助我们预测未来的趋势和结果，为企业和个人的决策提供重要的参考依据。
决定活动持续时间的重要参数
决定活动持续时间的重要参数1、最早开始时间和最早结束时间最早开始时间（Earliest Start Time，ES）是指某项活动能够开始的最早时间，最早结束时间（Earliest Finish Time，EF）是指某项活动能够完成的最早时间。
通常认为，最早结束时间等于最早开始时间加上该活动的估算时间，即EF=ES+活动时间估值。
2、最迟开始时间和最迟结束时间最迟开始时间（Latest Start Time，LS）是指为了使项目在完工时间内完成，某项活动最迟必须在什么时候开始；最迟结束时间（Latest Finish Time，LF）是指为了使项目在要求完工的时间内完成，某项活动最迟必须在什么时候结束。
最迟开始时间，可以用该项活动的最迟结束时间减去该活动的估算时间，即LS=LF-活动估算时间。
3、总时差如果最迟开始时间与最早开始时间不同，那么该活动的开始时间就可以浮动，称之为总时差（Float or Slack）；同理，如果最迟结束时间与最早结束时间不同，那么该活动的结束时间也可以是浮动，同样称之为总时差。
总时差是指在不推迟整个项目的最迟结束时间的前提下，一个活动可能的最早开始时间的推迟时间量。
对同一个活动来说，以下两个公式计算出来的总时差是相等的。
即：总时差（TS）=最迟开始时间（LS）-最早开始时间（ES）总时差（TS）=最迟结束时间（LF）-最早结束时间（EF）4、自由时差自由时差（Free Float），简称FF，指一项工作在不影响其紧后工作最早开始时间的条件下，本工作可以利用的机动时间。
用紧后工作的最早开始时间与该工作的最早完成时间之差表示。
即：自由时差（FFi-j）=（ESj-k）-（EFi-j）式中，ESj-k表示紧后工作j-k的最早开始时间，EFi-j表示工作i-j的最早结束时间。
5、活动计时方式（1）正推法（Forward Pass）。
正推法是指按照网络逻辑关系从项目开始的那一刻正向（一般从左至右）对所有网络活动中为完成部分最早开始时间和最早结束时间的计算。
yearfrac函数逻辑
yearfrac函数逻辑yearfrac函数是一种金融函数，用于计算两个日期之间的年份差异。
它的逻辑是根据所选的日计数方法来确定两个日期之间的天数，然后将天数除以选择的基准天数（通常是一年的天数）来确定年份差异。
yearfrac函数的一般形式如下：yearfrac(start_date, end_date, basis)其中，start_date是开始日期，end_date是结束日期，basis是用于确定计算方法的参数。
在yearfrac函数中，通过选择basis参数的不同值来确定日计数方法。
下面是一些常用的basis参数及其对应的日计数方法：- 0：美国（NASD）30/360方法这种方法假设每个月都是30天，每年都是360天。
- 1：实际/实际方法这种方法使用实际的天数来计算，并且将年份差异调整为要计算的年份的实际长度。
这是一种最常用的基准方法。
- 2：实际/360方法这种方法将每个月都视为30天，每年都是360天，并使用实际的天数来计算。
- 3：实际/365方法这种方法将每个月都视为30.436875天（365.25/12），每年都是365.25天，并使用实际的天数来计算。
值得注意的是，在使用yearfrac函数时，需要确保日期的格式正确，以及正确设置了日期格式。
另外，yearfrac函数通常返回一个小数，表示两个日期之间的年份差异。
如果需要将结果格式化为百分比或其他形式，可以使用其他函数对yearfrac函数的结果进行进一步处理。
下面是yearfrac函数的一些示例：- 示例1：start_date = 2021-01-01end_date = 2022-01-01basis = 1使用实际/实际方法来计算2021年到2022年之间的年份差异。
根据实际天数计算，结果为1年。
- 示例2：start_date = 2021-01-01end_date = 2022-01-01basis = 0使用美国（NASD）30/360方法来计算2021年到2022年之间的年份差异。
筛选年份的函数
筛选年份的函数摘要：1.筛选年份的函数概述2.筛选年份的函数实现方法3.筛选年份的函数应用实例4.总结正文：1.筛选年份的函数概述筛选年份的函数是一种用于筛选特定年份数据的函数，通常在数据分析、统计和可视化等领域中被广泛应用。
通过筛选年份的函数，我们可以更方便地对数据进行时间序列分析，了解各年份的数据特征和趋势。
2.筛选年份的函数实现方法筛选年份的函数可以通过多种编程语言实现，这里以Python 语言为例，介绍如何使用Python 中的Pandas 库实现筛选年份的函数。
首先，需要导入Pandas 库，并创建一个包含年份和数据的DataFrame。
然后，通过使用DataFrame 的`query`方法或布尔索引筛选特定年份的数据。
示例代码如下：```pythonimport pandas as pd# 创建一个包含年份和数据的DataFramedata = {"年份": [2010, 2011, 2012, 2013, 2014, 2015],"数据": [10, 20, 30, 40, 50, 60]}df = pd.DataFrame(data)# 使用query 方法筛选2010 年至2014 年的数据filtered_data = df.query("年份>= 2010 & 年份<= 2014")# 使用布尔索引筛选2010 年至2014 年的数据filtered_data = df[(df["年份"] >= 2010) & (df["年份"] <= 2014)]```3.筛选年份的函数应用实例假设我们有一份关于某城市各年份降水量的数据，希望通过筛选年份的函数分析2010 年至2015 年降水量的变化趋势。
```python# 创建一个包含年份和降水量的DataFramedata = {"年份": [2010, 2011, 2012, 2013, 2014, 2015],"降水量": [100, 120, 150, 180, 200, 220]}df = pd.DataFrame(data)# 使用筛选年份的函数筛选2010 年至2015 年的降水量数据filtered_data = df.query("年份>= 2010 & 年份<= 2015")# 计算2010 年至2015 年降水量的平均值和标准差mean_降水= filtered_data["降水量"].mean()std_降水= filtered_data["降水量"].std()print("2010 年至2015 年降水量平均值：", mean_降水)print("2010 年至2015 年降水量标准差：", std_降水)```4.总结筛选年份的函数是一种实用的数据处理方法，可以帮助我们快速地筛选特定年份的数据，便于进行时间序列分析和趋势研究。