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1、,Business and Economic Forecasting Chapter 5,Demand Forecasting is a critical managerial activity which comes in two forms: Qualitative Forecasting Gives the Expected DirectionQuantitative Forecasting Gives the precise Amount,2.7654 %,2002 South-Western Publishing,Time-Series Characteristics: Secula
2、r Trend and Cyclical Variation in Womens Clothing Sales,Time-Series Characteristics: Seasonal Pattern and Random Fluctuations,Microsoft Corp. Sales Revenue, 19842001,Figure 6.2,White Noise and MA(1) Time Series,A MA(1) Process,A moving average process of order one MA(1) can be characterized as one w
3、here xt = et + a1et-1, t = 1, 2, with et being an iid sequence with mean 0 and variance This is a stationary, weakly dependent sequence as variables 1 period apart are correlated, but 2 periods apart they are not,Three Stationary AR(1) Time Series,An AR(1) Process,An autoregressive process of order
4、one AR(1) can be characterized as one where yt =yt-1 + et , t = 1, 2, with et being an iid sequence with mean 0 and variance2 For this process to be weakly dependent, it must be the case that | 1Corr(yt ,yt+h) = Cov(yt ,yt+h)/(y y) = 1h which becomes small as h increases,Three Stationary AR(1) Time
5、Series,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 1Thus, stationarity implies that the xts are identically distributed and that the nature of any c
6、orrelation between adjacent terms is the same across all periods,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 tThus, this weaker form of stationarity requires only
7、that the mean and variance are constant across time, and the covariance just depends on the distance across time,Three Non-Stationary AR(1) Time Series,A Random Walk and A Random Walk With Drift,Random Walks,A random walk is an AR(1) model where 1 = 1, meaning the series is not weakly dependentWith
8、a random walk, the expected value of yt is always y0 it doesnt depend on tVar(yt) = et , so it increases with tWe say a random walk is highly persistent since E(yt+h|yt) = yt for all h 1,Random Walks (continued),A random walk is a special case of whats known as a unit root processNote that trending
9、and persistence are different things a series can be trending but weakly dependent, or a series can be highly persistent without any trendA random walk with drift is an example of a highly persistent series that is trending,Random Walk with Drift vs. Trend Stationary AR(1),Trending Time Series,Econo
10、mic time series often have a trendJust because 2 series are trending together, we cant assume that the relation is causalOften, both will be trending because of other unobserved factorsEven if those factors are unobserved, we can control for them by directly controlling for the trend,A trending seri
11、es cannot be stationary, since the mean is changing over timeA trending series can be weakly dependentIf 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 “detren
12、ded” series in a regressionDetrending a series involves regressing each variable in the model on tThe residuals form the detrended seriesBasically, the trend has been partialled out,Why Forecast Demand?,Both public and private enterprises operate under conditions of uncertainty. Management wishes to
13、 limit this uncertainty by predicting changes in cost, price, sales, and interest rates. 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, th
14、e uncertainty that all managers feel.,Hierarchy of Forecasting,The selection of forecasting techniques depends in part on the level of economic aggregation involved. The hierarchy of forecasting is: National Economy (GDP, interest rates, inflation, etc.) sectors of the economy (durable goods)industr
15、y forecasts (automobile manufacturers) firm forecasts ( Ford Motor Company ),Forecasting Criteria,The choice of a particular forecasting method depends on several criteria: costs of the forecasting method compared with its gains complexity of the relationships among variables time period involved ac
16、curacy needed in forecast the lead time between receiving information and the decision to be made,Significance of Forecasting,The accuracy of a forecasting model is measured by how close the actual variable, Y, ends up to the forecasting variable, Y. Forecast error is the difference. (Y - Y) Models differ in accuracy, which is often based on the square root of the average squared forecast error over a series of N forecasts and actual figures Called a root mean square error, RMSE. RMSE = (Y - Y)2 / N ,
