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A $k\times k$ matrix of covariances between all pairs of $k$ random variables. It is also called variance-covariance matrix or simply the covariance matrix.
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Generate Multivariate Log-Normal Variables with given Covariance and Mean
Let ${\bf X}=(X_1,...,X_n)$ be an $n$-dimensional log-normal random variable.
I want to $force$ my random variables to be such that $Cov(X_i,X_j)=\Sigma_{i,j}$ and $E(X_i)=\mu_i$ where $\Sigma_{i,j}$ …
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Covariance Estimation of time series with mixed frequencies
I have three times series $x_{1,t}$, $x_{2,t}$ and $x_{3,t}$.
For the first two time series ($x_{1,t}$ and $x_{2,t}$) I have daily data, but for the last one, I have monthly data (let us assume that i …
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Covariance Linear Shrinkage Estimator : Implied Data
I have been using linear shrinkage to better estimate the covariance matrix when I do not have enough data.
Let $\bf X$ be a $T\times n$ matrix representing the data (previously centered) and
$${\bf S …