Consider the MA(1) process:
$$ y_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} $$
where $\varepsilon$ is a white noise process with $\mathbb{E}(\varepsilon_t) = 0$ and $\operatorname{Var}(\varepsilon_t) = \sigma^2$, and $t=1,2,\dotsc,T$. Assume now that given a realization of the MA(1) process you estimate instead an AR(1) model:
$$ y_t = \varphi_1 y_{t-1} + \varepsilon_t $$
where $0<\varphi_1<1$ is an unknown parameter, $\varepsilon$ is a white noise process, and $t=1,2,\dotsc,T$.
Derive the (large sample) bias in the OLS estimator $\varphi_1$.
self-study
tag and read its Wiki. (You will need to remove one of the current tags, I suggest you may removetime-series
.) $\endgroup$ – Richard Hardy Mar 12 '16 at 10:58