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Econ 427 lecture 14 slides

Econ 427 lecture 14 slides. Forecasting with MA Models. Optimal forecast. One which, given the available information, has the smallest average loss. This will normally be the conditional mean (the mean given that we are a particular time period, t; i.e. given an “information set”):.

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Econ 427 lecture 14 slides

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  1. Econ 427 lecture 14 slides Forecasting with MA Models

  2. Optimal forecast • One which, given the available information, has the smallest average loss. • This will normally be the conditional mean (the mean given that we are a particular time period, t; i.e. given an “information set”): • The best linear forecast will then be the linear approximation to this, called the linear projection, • Remember the info set will generally be current and past values of y and innovations (epsilons).

  3. Optimal forecast for MA • Like before (Chs. 5 and 6), we calculate the optimal point forecast by writing down the process at period T+h and then “projecting it” on the information available at time T. • Book’s MA(2) example: • Write out the process at time T+1: • Projecting this on the time T info set, (remember that expectations of future innovs are zero)

  4. Optimal forecast for MA • For period T+2: • Projecting this on the time T info set, • And so forth… So for periods beyond T+2, Why is that? an MA(q) process is not forecastable more than q steps ahead. Why? Recall Autocorr function drops to 0 after q steps

  5. Uncertainty around optimal forecast • We would like to know how much uncertainty there will be around point estimates of forecasts. • To see that, let’s look at the forecast errors, • Same for all forecasts T+h, h>2 Why are errors serially correlated? Why can’t we use this info to improve forecast?

  6. Uncertainty around optimal forecast • forecast error variance is the variance of eT+h,T Notice that the error variance is less than the underlying variability of the series yt for h < q. Note that because of its MA(2) form, the variance of yt equals • We can use these conditional variances to construct confidence intervals. What will they look like?

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