Autoregression model with a time trend term. Statistically valid?

Question

Assume we have a time-series with a deterministic trend.

I'm wondering if the following model is well specified as an AR model:

$y_{t} = b_{0} + b_{1}t + b_{2}y_{t-1} + \epsilon_{t} \ \ \ \ \ \ $

Specifically, I'm interested in knowing if it's OK to put a time term and auto-regressive terms in the same model.

If it is not, what would be the better way of specifying the model?

Well, it's not "an AR model", it's more complicated than that; it's a model with an AR component - but such a model can be written down - indeed you just did it. I imagine you mean to ask something else. — Glen_b, Commented Apr 11, 2013 at 10:01
Thank you for your comment. I'm not asking whether it can be written down or not. I'm asking whether it is statistically well specified -i.e. if it has reliable statistical properties. Will the t and F-tests be biased? Will multicollinearity or serial correlation be introduced as a result of having both AR terms and the time term? That sort of thing. — J4y, Commented Apr 11, 2013 at 10:39
"Will ... serial correlation be introduced as a result of having both AR terms and the time term?" -- clearly, since AR is already serially correlated; the time trend introduces an additional source of 'dependence'. Often this sort of thing can be identified, but there can be a number of issues. A couple of relevant papers - no.1 no.2 — Glen_b, Commented Apr 11, 2013 at 11:24

vinux · Accepted Answer · 2013-04-11 11:26:16Z

2

It's OK to put a time term and auto-regressive terms in the same model. But, the model may not be meaningful when $\epsilon_t$ is non stationary.

If the series is stationary after removing deterministic part, one can add deterministic part in the time series analysis.

In your case if $y_t$ is stationary after removing the time trend, you can proceed with your model.

answered Apr 11, 2013 at 11:26

vinux

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