FORECASTING TIME SERIES AND REGRESSION

Section 2
BASIC STATISTICAL CONCEPTS
A parameter is a descriptive measure of the population .
Some population parameters :
1. The population mean, denoted μ, is the average of the values in the population. 2. The population range, denoted RNG, is the difference between the largest value and the smallest value in the population. 3. The population variance ,denoted a Ϭ2 ,is the average of the squared deviations of the
然后，对模型进行延伸，对未 来进行预测。
Section 1 AN INTRODUCTION TO FORECASTING
Cross-sectional data &
交叉数据是在一个时间点一些观察值
time series
• Cross-sectional data are values observed at one point in time. • A time series is a chronological sequence of observations on a particular variable.
An Introduction to Forecasting
1.1 Cross-sectional and series data 1.2 Forecasting methods 1.3 Forecasting errors 1.4 Choosing A Forecasting Technique 1.5 Overview of the Quantitative Forecasting Techniques
Section 1
AN INTRODUCTION TO FORECASTING
1.1 Forecasting and Data
问题：什么是预测？ and conditions Predictions of future events
are called forecasts ,and the act of making such predictions is called forecasting.
Section 2
BASIC STATISTICAL CONCEPTS
2.2 Probability
• We define an experiment to be any process of observation that has an uncertain outcome. • An event is an experimental outcome that may or may not take place. • The probability of an event is a number that measures the chance, or likelihood, that the event will occur when the experiment is performed.
Section 1
AN INTRODUCTION TO FORECASTING
1.3 Errors in forecasting
Two types of forecast：
• The point forecast
is a single number that represents our best prediction of the actual value of the
Section 2
BASIC STATISTICAL CONCEPTS
2.1 Population
We define a population to be the entire collection of elements about which information is desired.
• finite population • infinite population
Section 1
AN INTRODUCTION TO FORECASTING
Section 1
AN INTRODUCTION TO FORECASTING
1.2 Forecasting methods
• Subjective curve fitting Qualitative forecasting methods : generally use the opinions of experts to predict future events subjectively. • Delphi method • Technological comparisons
1.5 An overview of quantitative forecasting techniques
• Regression analysis
• Univariate time series : time series regression ,classical decomposition , exponential smoothing • Box-jenkins methods
2. The pattern of data
3. The cost of forecasting
4. The accuracy of desired
5. The availability of data
6. The ease of operation and understanding
Section 1 AN INTRODUCTION TO FORECASTING
时间序列是对一个特定的变量的按时间顺序的观察值
Section 1
AN INTRODUCTION TO FORECASTING
The components of a time serise
1.Trend
refers to the upward movement that characterize a time serises 2.Cycle over a to recurring up and down movements around trend levels. refers period of time. 3.Seasonal variations are Irregular fluctuations series that complete themselves 4. periodic patterns in a time are erratic movements in are then repeated on a no recognizable within a calendar year anda time series that followyearly basis. or regular pattern.
identify a pattern that can be used to describe it.
• Then this pattern is extrapolated ,or extended,into 首先，预测者对数据进行分析，得
到可以用来描述的模型 the future in order to prepare a forecast.
values in the population from the population mean μ.
4. The population standard deviation, denoted Ϭ , is the positive square root of the population variance.
variable being forecasted.
• The prediction interval forecast
is an interval of number that is calculated so that we are very confident that the actual value will be contained in the interval.
• Process control
• Strategic management
Section 1
AN INTRODUCTION TO FORECASTING
How to use past data ?
• First the forecaster analyzes the data in order to
Section 1
AN INTRODUCTION TO FORECASTING
BASIC STATISTICAL CONCEPTS
• 2.1 Populations
• 2.2 Probability • 2.3 Random samples and sample statistics • 2.4 Continuous probability distributions • 2.5 The normal probability distributions
Quantitative forecasting techniques : involve the analysis of historical data in an attempt to predict future values of a variable of interest.
• Univariate forecasting model • Causal forecasting models
Section 1
AN INTRODUCTION TO FORECASTING
Measuring forecast errors The forecast error for a particular forecast yt* is et= yt - yt*
1. Absolute deviation= |et |= | yt - yt*| 2. Mean absolute deviation(MAD) 3. Squared error 4. Mean squared error(MSE) 5. Absolute percentage error 6. Mean absolபைடு நூலகம்te percentage error(MAPE)
• 2.6 The t-distribution ,the F-distribution ,and the CHI-SQUARE
distribution • 2.7 Confidence intervals for a population mean • 2.8 Hypothesis testing for a population mean
Section 1
AN INTRODUCTION TO FORECASTING
1.4 Choosing a forecasting technique
We must consider the following factors:
1. The time frame
Immediate : less than one month Short term : one to three months Medium ：more than three months to less than two years Long term : two years or more
Section 1
AN INTRODUCTION TO FORECASTING
The Important of Forecast
• In marketing departments • In finance
• In personnel management
• In production scheduling