Autoregressive Models and Their Estimation Leta-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 *1 = y + - + - + 1169) where y, d.d., are fixed parameters and thes, are 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. 4.dy..for which the sum of squares S- ---* -A-, 116.101 is a minimum Forecasting from Estimated Autoregressive Models Suppose that we have observations - from a time series and that an autoregressive model of order p has been fitted to these data. Write the es- timated model as follows: x = 9+-+ 116.11) Standing at times, we obtain forecasts of future values of the series from a = + dia 1 dia O , = 1,2,3...) (16.12) where for h> 0, is the forecast of standing at time, and for Is , &e it is simply the observed value of 040 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