管理经济学--生意和经济的预测(1)-文档资料

Detrending a series involves regressing each variable in the model on t
The residuals form the detrended series
Basically, the trend has been partialled out
If a series is weakly dependent and is stationary about its trend, we will call it a trend-stationary process
Detrending
Adding a linear trend term to a regression is the same thing as using “detrended” series in a regression
Gives the Expected Direction
Quantitative Forecasting 2.7654 %
Gives the precise Amount
2002 South-Western Publishing
Time-Series Characteristics: Secular Trend and Cyclical Variation in Women’s Clothing Sales
Thus, this weaker form of stationarity requires only that the mean and variance are constant across time, and the covariance just depends on the distance across time
A random walk with drift is an example of a highly persistent series that is trending
Random Walk with Drift vs. Trend Stationary AR(1)
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National Economy (GDP, interest rates, inflation,
etc.) sectors of the economy (durable goods)
industry forecasts (automobile manufacturers)
• firm forecasts ( Ford Motor Company )
sequence as variables 1 period apart are
correlated, but 2 periods apart they are not
Three Stationary AR(1) Time Series
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control for them by directly controlling for the trend
A trending series cannot be stationary, since the mean is changing over time
A trending series can be weakly dependent
Hierarchy of Forecasting
The selection of forecasting techniques depends in part on the level of economic aggregation involved. The hierarchy of forecasting is:
Thus, stationarity implies that the xt’s are identically distributed and that the nature of any correlation between adjacent terms is the same across all periods
Accurate forecasting can help develop strategies to promote profitable trends and to avoid unprofitable ones.
A forecast is a prediction concerning the future. Good forecasting will reduce, but not eliminate, the uncertainty that all managers feel.
Covariance Stationary Process
A stochastic process is covariance stationary if E(xt) is constant, Var(xt) is constant and for any t, h ≥ 1, Cov(xt, xt+h) depends only on h and not on t
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rho=.5
rho=.9
An AR(1) Process
An autoregressive process of order one [AR(1)] can be characterized as one where yt =ρyt-1 + et , t = 1, 2,… with et being an iid sequence with mean 0 and varianceσ2 For this process to be weakly dependent, it must be the case that |ρ| < 1
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-1.5 White Noise
MA(1)
A MA(1) Process
A moving average process of order one
since E(yt+h|yt) = yt for all h ≥ 1
Random Walks (continued)
A random walk is a special case of what’s known as a unit root process
Note that trending and persistence are different things – a series can be trending but weakly dependent, or a series can be highly persistent without any trend
Corr(yt ,yt+h) = Cov(yt ,yt+h)/(σy σy) = ρ1h which becomes small as h increases
Three Stationary AR(1) Time Series
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With a random walk, the expected value of yt is always y0 – it doesn’t depend on t
Var(yt) = σet , so it increases with t We say a random walk is highly persistent
Why Forecast Demand?
Both public and private enterprises operate under conditions of uncertainty.
Management wishes to limit this uncertainty by predicting changes in cost, price, sales, and interest rates.
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rho=-.5
rho=-.9
Stationary Stochastic Process
A stochastic process is stationary if for every collection of time indices 1 ≤ t1 < …< tm the joint distribution of (xt1, …, xtm) is the same as that of (xt1+h, … xtm+h) for h ≥ 1
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Trend Stationary AR(1)
Trending Time Series
Economic time series often have a trend Just because 2 series are trending together,
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Random Walk With Drift
Random Walks
A random walk is an AR(1) model where ρ1 = 1, meaning the series is not weakly dependent
Time-Series Characteristics: Seasonal Pattern and Random Fluctuations
Microsoft Corp. Sales Revenue, 1984–2001
Figure 6.2
White Noise and MA(1) Time Series
we can’t assume that the relation is causal Often, both will be trending because of other
unobserved factors Even if those factors are unobserved, we can
[MA(1)] can be characterized as one where
xt = et + a1et-1, t = 1, 2, … with et being an iid
sequence with mean 0 and variance
2 e
This is a stationary, weakly dependent
Three Non-Stationary AR(1) Time Series
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rho=1.25
rho=-1.25
A Random Walk and A Random Walk With Drift
管理经济学--生意和经济的预测(1)-文档资料
Business and Economic Forecasting
Chapter 5
Demand Forecasting is a critical managerial activity which comes in two forms:
Qualitative Forecasting