How can I determine if

$\ y_t = c_1 +c_2t +u_t$

is stationary?

$\ c_1$ and $\ c_2 $ are known constants and $\ u_t $ is a white noise process with variance $\sigma^2 $.

I do not understand the role of the t.

Am I right to describe this as a trend stationary process?

How can I show the mean of the moving average?

  • 3
    $\begingroup$ Hint: compute the expected value of $y_t$. If a time series is stationary, its marginal distribution, and specifically its expected value, must not vary with $t$. $\endgroup$
    – J. Virta
    Jan 12, 2017 at 19:48
  • 1
    $\begingroup$ It is not stationary because the mean increases with time. If you remove the trend you will have an approximate white nose (stationary) proess. $\endgroup$ Jan 12, 2017 at 19:49
  • $\begingroup$ Can you show me each step: how to exactly do it? many thanks $\endgroup$ Jan 12, 2017 at 19:59
  • $\begingroup$ Don't I have to detrend the series first by substracting c_2t? $\endgroup$ Jan 13, 2017 at 12:09

1 Answer 1


Expected value of $\ y_ t$ = $\ c_1 + c_2 * t $

given that $\ E(u_t) = 0 $

It is not stationary, since the expected value varies with t.


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