This function applies a linear filter to some vector time series.
filter.process(X, A)X %c% A
A matrix. Row \(t\) corresponds to \(Y_t\).
vector time series given in matrix form. Each row corresponds to a timepoint.
an object of class timedom.
filter.process: Multivariate convolution (filter) in the time domain
%c%: Convenience operator for filter.process function
Let \([X_1,\ldots, X_T]^\prime\) be a \(T\times d\) matrix corresponding to a vector series \(X_1,\ldots,X_T\). This time series is transformed to the series \(Y_1,\ldots, Y_T\), where $$ Y_t=\sum_{k=-q}^p A_k X_{t-k},\quad t\in\{p+1,\ldots, T-q\}.$$ The index \(k\) of \(A_k\) is determined by the lags defined for the time domain object. When index \(t-k\) falls outside the domain \(\{1,\ldots, T\}\) we set \(X_t=\frac{1}{T}\sum_{k=1}^T X_k\).
timedom