NxConv - Time Series Convolution Operator

Returns an array of cells for the convolution operator of two-time series.

Syntax

X

is the univariate time series data (one-dimensional array of cells (e.g., rows or columns)).

Y

is the second time series function (e.g., filter) values (one dimensional array of cells (e.g., rows or columns)).

Remarks

1. The time series must be homogeneous or equally spaced.
2. The two-time series can have different sizes.
3. Presample values of $X_t$ and $Y_t$ are assumed to be zero.
4. The convolution operator is described as follows:
   
   $$Z_t=\sum_{j=\mathrm{max}\left ( 1,t-M+1 \right )}^{\mathrm{min}\left ( N,t+M-1 \right )}X_jY_{M-t+j}$$
   
   Where:
   
   • $Z_t$ is the convolution time series.
   • $X_t$ is the first time series, with $N$ observations.
   • $Y_t$ is the second time series, with $M$ observations.
   • $t\in \left[ 1,N+M \right]$, i.e., $1\leq t \leq N+M$.
5. The function was added in version 1.62 DEWDROP. 

Files Examples

Related Links

• Wikipedia - Convolution

References

• Hamilton, J .D.. Time Series Analysis. Princeton University Press. (1994). ISBN 0-691-04289-6
• Tsay, Ruey S.. Analysis of Financial Time Series . John Wiley & SONS. (2005). ISBN 0-471-690740