For questions about strictly stationary or stationary in the wide sense sequences or processes. Questions about deterministic stationary processes (in the case of discrete dynamical systems) are welcome.
Questions tagged [stationary-processes]
434 questions
6
votes
1 answer
Proving stationarity of AR(1) process
I would like to prove that the AR(1) process: $X_t=\phi X_{t-1}+u_t$, where ${u_t}$ is white noise $(0,\sigma^2)$ and $\vert\phi\vert<1$, is covariance stationary. One requirement is that $\mathbb{E}(X_t)$ is a constant (in this case should be…
SemiMetrics
- 61
1
vote
0 answers
When do weakly stationary processes have positive spectral density?
Let $\boldsymbol{X} = (X_n)_{n\in \mathbb{Z}}$ be a zero-mean real valued stationary process. Denote $\gamma$ its autocovariance function, i.e.:
\begin{equation}
\gamma(h) = \mathbb{E}X_nX_{n+h}
\end{equation}
Suppose $\gamma$ is summable, i.e.…
Alfred F.
- 386
1
vote
0 answers
Stationary processes
I'm still learning English so I'm already sorry for what's going to happen.
I don't know if I am right about the strictly stationary.
Let's suppose a process is strictly stationary: does that mean $X_t$ and $X_{t+h}$ (for all $h>0$) have the same…
Benco016
- 11
0
votes
0 answers
Invariant distributions of transition matrices
Please note down all invariant distributions for each of the following transition matrices.
$\begin{pmatrix} 0&\frac{1}{2}&\frac{1}{2}\\ \frac{1}{3}&\frac{1}{3}&\frac{1}{3}\\ \frac{1}{2}&\frac{1}{2}&0 \end{pmatrix}$, $\begin{pmatrix} 1&0&0&0&\dots\\…
Tino
- 137
- 7
0
votes
1 answer
Clarifying the following concepts: renewal processes, stationary processes, counting processes and point processes
Is it true that a renewal process is a stationary process on $\mathbb{R}^+$ and a counting process is a point process on $\mathbb{R}^+$?
So the latter concepts are the generalization of the former ones?
newbie
- 3,441