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I have this homework about time series econometrics and I am having some difficulty trying to solve it. Can somebody can help me understand how to start and solve it?

This is the text of the problem:

Consider the process: $$y_t= 1.2y_{t-1} - 0.4y_{t-2} + x_t + u_t,\qquad t=1,2$$ where $y_0=0$, $u_t\sim N(0,16)$ is a white noise and $x_t$ is a stochastic process with known mean $μ_x=2$ and variance $σ^2=4$. Determine the forecast of $y_{t+1}$ and its 95% confidence interval (assuming normality) conditional on $y_t=1$ and $y_{t-1}=2$. State additional assumptions on $x_t$ if you need those.


Update: I know how to determine the forecast of $y_{t+1}$ and I know the formula for the confidence interval, however, I get confused with those two conditions on $y_t=1$ and $y_{t-1}=2$. What do they mean in solving it? I do not want that some of you write the solution but I would like to understand how to solve it.

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  • $\begingroup$ Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$ – Silverfish Dec 27 '15 at 19:46
  • $\begingroup$ You need to state what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$ – gung Dec 27 '15 at 23:38
  • $\begingroup$ @gung I know how to determine the forecast of yt+1 and I know the formula for the confidence interval, however, I get confused with those two conditions on yt=1 and yt-1=2. What do they mean in solving it? I do not want that some of you write the solution but I would like to understand how to solve it. Thank you $\endgroup$ – sicecon Dec 30 '15 at 14:44

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