timsac (version 1.3.0)

canoca: Canonical Correlation Analysis of Vector Time Series

Description

Analyze canonical correlation of a d-dimensional multivariate time series.

Usage

canoca(y)

Arguments

y

a multivariate time series.

Value

• aic
  AIC.
• aicmin
  minimum AIC.
• order.maice
  MAICE AR model order.
• v
  innovation variance.
• arcoef
  autoregressive coefficients. arcoef[i,j,k] shows the value of $i$-th row, $j$-th column, $k$-th order.
• nc
  number of cases.
• future
  number of variable in the future set.
• past
  number of variables in the past set.
• cweight
  future set canonical weight.
• canocoef
  canonical R.
• canocoef2
  R-squared.
• chisquar
  chi-square.
• ndf
  N.D.F.
• dic
  DIC.
• dicmin
  minimum DIC.
• order.dicmin
  order of minimum DIC.
• matF
  the transition matrix $F$.
• vectH
  structural characteristic vector $H$ of the canonical Markovian representation.
• matG
  the estimate of the input matrix $G$.
• vectF
  matrix $F$ in vector form.

Details

First AR model is fitted by the minimum AIC procedure. The results are used to ortho-normalize the present and past variables. The present and future variables are tested successively to decide on the dependence of their predictors. When the last DIC (=chi-square - 2.0*N.D.F.) is negative the predictor of the variable is decided to be linearly dependent on the antecedents.

References

H.Akaike, E.Arahata and T.Ozaki (1975) Computer Science Monograph, No.5, Timsac74, A Time Series Analysis and Control Program Package (1). The Institute of Statistical Mathematics.

Examples

ar <- array(0,dim=c(3,3,2))
  ar[,,1] <- matrix(c(0.4,  0,   0.3,
                      0.2, -0.1, -0.5,
                      0.3,  0.1, 0),3,3,byrow=TRUE)
  ar[,,2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3),3,3,byrow=TRUE)
  x <- matrix(rnorm(1000*3),1000,3)
  y <- mfilter(x,ar,"recursive")
  z <- canoca(y)
  z$arcoef