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Use CONSUMP for this exercise.(i) Let $y_{t}$ be real per capita disposable income. Use the data through 1989 to estimate the model$y_{t}=\alpha+\beta t+\rho y_{t-1}+u_{t}$and report the results in the usual form.(ii) Use the estimated equation from part (i) to forecast $y$ in $1990 .$ What is the forecast error?(iii) Compute the mean absolute error of the one-step-ahead forecasts for the 1990 s, using the parameters estimated in part (i).(iv) Now, compute the MAE over the same period, but drop $y_{t-1}$ from the equation. Is it better to $\quad$ include $y_{t-1}$ in the model or not?

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(i) see video (ii) 177.66 (iii) 371.76 (iv) see video, AR(1) with time trend

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Chapter 18

Advanced Time Series Topics

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part one. We estimate an a. R. one model with a linear time trend. Using the data up through 1989. This is what we get. We have 30 observations and The centered errol of the regression is 200 23.9. The r square is very high, very close to you one but it is not a meaningful measure of goodness of fit of the model because it is likely that the time series Y. T. Has the trend and possibly a unit rate. Let's move way down to part three, part 2. In part two, we need to calculate the forecast for 1990. The Time Index is 32. We plug t equals 32 and Why 17 -1 equals 17,800 and four one oh nine Into the estimated equation. And we get the forecast of 18,000 122 point three. The actual value is 17,000 944, 1 64. And so subtract from the actual value, the predictive value. We have the forecast error Of -177.66. Yeah. Yeah. The mean absolute error for the 1990s, using the model, estimated in part one is 371.76. Hard for without the first leg of why we get these results. The mean absolute error or the forecast in the 1990s is about 700 18 coin 26. This is much higher than for the model with Why 17 -1. So we should use a R. One model with a linear time train, As in Part one.

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