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Results tagged with expected-value
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user 52295
1
vote
1
answer
138
views
Show that $\mathbb{E}[(S+\xi)^2]\rightarrow 0$ as $n\rightarrow\infty$
EDIT: Showing this using Ito's lemma is easy, that's NOT what I want to do. I also realised that $2\mathbb{E}[S\xi]\neq 2\xi\mathbb{E}[S]$ since $\xi$ is also a random variable. Nontheless, if this is …
- 221
0
votes
0
answers
68
views
Is the mean of a stationary timeseries the same everywhere?
Say for example I have the white noise process $Y_t\sim\text{WN}(\mu,\sigma^2)$. Is it true that $\mathbb{E}[Y_t]=\mathbb{E}[Y_{t-h}]$, where $h\in\mathbb{N}?$
- 221
1
vote
2
answers
163
views
Question about slides in lecture note: What if we can't assume $\mu=0?$
The question popped up when I was reading these lecture notes online. Consider the MA$(1)$ process given by $X_t=W_t+bW_{t-1}$ where $W_t$ is white noise distributed with constant variance $\sigma_W^2 …
- 221
1
vote
1
answer
119
views
Show that $\text{Cov}[Z_t,Z_{t+h}]=\text{Cov}[Z_s,Z_{s+h}].$
Problem: If $X\sim\text{WN}(\mu,\sigma^2).$ Let then $Z$ be the process defined by \begin{equation}
Z_t=\sum_{i=0}^na_iX_{t-i} \end{equation} for some coefficients $a_1,...,a_n\in\mathbb{R}$ wit …
- 221