COVLAG Function

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COVLAG Function

computes autocovariance estimates for a vector time series

COVLAG( x, k)

The inputs to the COVLAG function are as follows:

x: is an n ×nv matrix of time series values; n is the number of observations, and nv is the dimension of the random vector.
k: is a scalar, the absolute value of which specifies the number of lags desired. If k is positive, a mean correction is made. If k is negative, no mean correction is made.

The COVLAG function computes a sequence of lagged crossproduct matrices. This function is useful for computing sample autocovariance sequences for scalar or vector time series.

The value returned by the COVLAG function is an nv ×(k*nv) matrix. The ith nv ×nv block of the matrix is the sum

$\frac{1}n \sum_{j=i}^n x_j^' x_{j-i+1} {if } k\lt$

where x_j is the jth row of x. If k>0, then the ith nv ×nv block of the matrix is

$\frac{1}n \sum_{j=i}^n (x_j-\bar{x})^'(x_{j-i+1}-\bar{x})$

where $\bar{x}$ is a row vector of the column means of x. For example, the statements

   x={-9,-7,-5,-3,-1,1,3,5,7,9};
   cov=covlag(x,4);

produce the matrix

              COV           1 row       4 cols    (numeric)

                        33      23.1      13.6       4.9

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