.

Autoregressive Models and Their Estimation Let ut - 1.2... be a time series. A model that can often be used effec- tively to represent that series is the autoregressive model of order * + + + + + 116.9) where y.dd, are fixed parameters and the care random variables that have means and constant variances and are uncorrelated with one another. The parameters of the autoregressive model are estimated through a least squares algorithm, as the values of y ...for which the sum of squares Ss - - - - - de, 10.10) is a minimum. Forecasting from Estimated Autoregressive Models Suppose that we have observations 11,13, from a time series and that an autoregressive model of order y has been fitted to these data. Write the es- timated model as follows: (16.11) Standing at time we obtain forecasts of future values of the series from = 1 + drievk-1 + dist + - O = 1,2,3...) 116.12 ) where for h> 0, ia is the forecast of standing at time, and for Is Dr. It is simply the observed value ofr. u40 Example 16.2 Forecasting Sales Data (Autoregressive Model) You have been asked to develop an autoregressive model to forecast the Shiller real home price index data. This index is contained in the data file Shiller House Price Cost