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Results tagged with covariance
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user 52295
A measure of the degree of linear association between a pair of random variables.
2
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109
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Help understanding the step $\sum_{j=0}^n\sum_{k=0}^ng_jg_k\text{Cov}(\epsilon_{n-1},\epsilo...
I understand that the sum over $k$ gets removed and that we want to avoid zero covariance, but how does $+h\sigma^2$ pop up? … Doing the substitution $k=h+j$ then the covariance is just the variance which is onl $\sigma^2$ (no $h$), and then it's multiplied to the sum and not added. …
- 221
0
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1
answer
82
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Show that $\text{Cov}[X_r,X_s]=\text{Cov}[X_{r+h},X_{s+h}]$ for $X_t=a+bZ_t+cZ_{t-2}.$
Problem: Let $\{Zt\}$ be a sequence of independent normal random variables, each with mean $0$ and variance $\sigma^2$, and let $a$,
$b$, and $c$ be constants. Is $X_t=a+bZ_t+cZ_{t-2}$ a (weakly)
sta …
- 221
1
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1
answer
119
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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