Lecture 13 – Modeling Trends
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چکیده
We say that a time series yt has a (time) trend if the s-step ahead forecast, i.e., ,...) , ( 1 − + t t s t y y y E has a time-dependent component that does not go to zero as s gets large. For instance, if yt = a + bt + ut , b ≠ 0 where ut is a zero-mean stationary and ergodic process, then ,...) , ( 1 − + t t s t y y y E = a + b(t+s) + E(ut+s │yt, yt-1,...) The last term goes to zero as s goes to infinity, but a+b(t+s) is increasing linearly with s. That is, ,...) , ( 1 − + t t s t y y y E ≈ a + b(t+s) for sufficiently large s.
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تاریخ انتشار 2005