A time series is a set of numerical data obtained at regular periods of time.
Forecasting is the use of time series analysis and other methods for prediction. Business Forecasting is important; many economic and business datasets are time series. Areas of application include marketing, banking, finance and investment. In Operations Management, time series analysis plays an important role in forecasting demand, planning production and controlling inventory.The correlation between observations k time intervals apart is numerically measured by the lag k autocorrelation coefficient. This is just like a correlation between an X and a Y, where Y is Yt and X is Yt-k.
If one or more of the autocorrelation coefficients is high, an "autoregressive" model is fitted. A first-order autoregressive prediction equation is
^Yt+1 = b0 + b1 Yt .A second-order model would include also Yt-1; e.g., tomorrow's result would be predicted using not only today's but also yesterday's.
The Durbin-Watson statistic is approximately 2(1-r) where r is the 1st-order autoregression coefficient of the residuals. Since 0 < r < 1, DW is between 0 and 4. A value DW = 0 corresponds to r=1; DW = 4, to r = -1. DW = 2, to r = 0 . The residuals are supposed to be uncorrelated, so r = 0 (DW = 2) is ideal. If DW is too far from 2 (roughly speaking, as a rule of thumb, less than 1.5 or more than 2.5, although these limits really depend upon n ), a different model should be tried: Probably some important variable has been omitted.Statistical computer packages include the ARIMA (AutoRegressive Integrated Moving Average) command, which will fit time series models easily. Time series which are trending up or down should be differenced. Then, which model to use is indicated by the pattern of autocorrelations and the corresponding partial autocorrelations (autocorrelations with the effect of intervening lags removed).
Exponential Smoothing is included in many business software packages. The exponential smoothing forecasting scheme isSeasonal models regress, for example, this quarter's Y on that for the corresponding quarter in preceding years. Two-way tables are useful for presenting seasonal data; e.g., with the rows being months and the columns being years.
Transfer function models relate a time series of Y to that of one or more X's. For example, since steel is made from iron and coal, it makes sense to try to predict steel prices from iron and coal prices. LetHowever, one would not really want to say that I and C determined or "caused" the price of steel (S) unless one took account of the possibility of predicting St from St-1. Hence one would consider a model