# Stationarity of $\ y_t = c_1 +c_2t +u_t$

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?

• 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 $t$. Jan 12, 2017 at 19:48
• It is not stationary because the mean increases with time. If you remove the trend you will have an approximate white nose (stationary) proess. Jan 12, 2017 at 19:49
• Can you show me each step: how to exactly do it? many thanks Jan 12, 2017 at 19:59
• Don't I have to detrend the series first by substracting c_2t? Jan 13, 2017 at 12:09

Expected value of $\ y_ t$ = $\ c_1 + c_2 * t$
given that $\ E(u_t) = 0$