Abstract
In this paper (when the input random vector consists of mutually correlated components or subvectors), techniques of the correlation analysis for a multivariate system are discussed. A multidimensional linear algebraic equation having a matrix of comparably high order can be derived.
In the case of the multivariate system, the correlation techniques may be used as in the univariate system. But there are few papers treating the case generally when the input random vector of the multivariate system has mutually correlated components or subvectors.
It is shown that the correlation techniques for univariate systems is generalized to the case of the multivariate system, and that the equations to estimate impulse responses of the system should be quite analogous to the normal equation of the regression analysis. From this result, the method estimating the accuracy of calculated impulse response functions are presented by applying some techniques of multivariate statistical analysis. It is especially pointed out that the techniques of simultaneous confidence interval estimation on regression coefficients are useful to estimate the impulse response functions.
