Relation between Vector Auto-regressive models and correlation matrix
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I am generating a multivariate time series using Vector Autoregressive Models- $$X(t) = AX(t-1) + epsilon$$ where $X in R^{n times 1}$, $A in R^{n times n}$ and $epsilon in R^{n times 1}$ is a constant. Is there a relation between $A$ matrix and correlation matrix storing the correlation information between different variables of the multivariate time series? Correlation matrix can be defined as- $$sigma _{i,j} = correlation(x_i,x_j) $$ where $correlation(x_i,x_j)$ is the correlation between $i^{th}$ and $j^{th}$ variable of the time series and $sigma _{i,j}$ is the $i,j$ element in the correlation matrix.
statistics correlation time-series vector-auto-regression
asked Nov 14 at 2:55
Dushyant Sahoo
548
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I am generating a multivariate time series using Vector Autoregressive Models- $$X(t) = AX(t-1) + epsilon$$ where $X in R^{n times 1}$, $A in R^{n times n}$ and $epsilon in R^{n times 1}$ is a constant. Is there a relation between $A$ matrix and correlation matrix storing the correlation information between different variables of the multivariate time series? Correlation matrix can be defined as- $$sigma _{i,j} = correlation(x_i,x_j) $$ where $correlation(x_i,x_j)$ is the correlation between $i^{th}$ and $j^{th}$ variable of the time series and $sigma _{i,j}$ is the $i,j$ element in the correlation matrix.
statistics correlation time-series vector-auto-regression
asked Nov 14 at 2:55
Dushyant Sahoo
548
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am generating a multivariate time series using Vector Autoregressive Models- $$X(t) = AX(t-1) + epsilon$$ where $X in R^{n times 1}$, $A in R^{n times n}$ and $epsilon in R^{n times 1}$ is a constant. Is there a relation between $A$ matrix and correlation matrix storing the correlation information between different variables of the multivariate time series? Correlation matrix can be defined as- $$sigma _{i,j} = correlation(x_i,x_j) $$ where $correlation(x_i,x_j)$ is the correlation between $i^{th}$ and $j^{th}$ variable of the time series and $sigma _{i,j}$ is the $i,j$ element in the correlation matrix.
statistics correlation time-series vector-auto-regression
asked Nov 14 at 2:55
Dushyant Sahoo
548
I am generating a multivariate time series using Vector Autoregressive Models- $$X(t) = AX(t-1) + epsilon$$ where $X in R^{n times 1}$, $A in R^{n times n}$ and $epsilon in R^{n times 1}$ is a constant. Is there a relation between $A$ matrix and correlation matrix storing the correlation information between different variables of the multivariate time series? Correlation matrix can be defined as- $$sigma _{i,j} = correlation(x_i,x_j) $$ where $correlation(x_i,x_j)$ is the correlation between $i^{th}$ and $j^{th}$ variable of the time series and $sigma _{i,j}$ is the $i,j$ element in the correlation matrix.
statistics correlation time-series vector-auto-regression
statistics correlation time-series vector-auto-regression
asked Nov 14 at 2:55
Dushyant Sahoo
548
asked Nov 14 at 2:55
Dushyant Sahoo
548
edited Nov 14 at 4:01
asked Nov 14 at 2:55
Dushyant Sahoo
548
asked Nov 14 at 2:55
Dushyant Sahoo
548
asked Nov 14 at 2:55
Dushyant Sahoo
548
548
add a comment |
add a comment |
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