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Results tagged with stationarity
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user 241962
A strictly stationary process (or time series) is one whose joint distribution is constant over time shifts. A weakly stationary (or covariance stationary) process or series is one whose mean and covariance function (variance and autocorrelation function) do not change over time.
0
votes
0
answers
23
views
$ E(f(X_0)f'(X_l)) = E(f'(X_0) f(X_l)) $ for a stationary process?
Do I need strict stationarity or does weak stationarity suffice for the equation to hold?
I tried to show
$$
P(f(X_0)f'(X_l) > x) = P(f'(X_0)f(X_l) > x)
$$
but didn't succeed so far. …
- 153
1
vote
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Is a weakly stationary AR(p) process also strictly stationary if the noise is i.i.d.?
There is a unique solution to these equations which fulfills weak stationarity and causality. … I believe that $X_t$ is a strictly stationary process due to the $\epsilon_t$ being iid, but in the literature I can't find a proof for this claim (all proofs that I saw are about weak stationarity). …
- 153
5
votes
2
answers
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Is the MA($\infty$) process with i.i.d. noise strictly stationary?
I have a MA($\infty$) process defined by
$$
X_t = \sum_{k=0}^\infty \alpha_{k} \epsilon_{t-k}, \qquad t\in\mathbb{Z}
$$
where the sums converge a.s. and the $\epsilon_t$ are i.i.d. centered noise wit …
- 153