timsac (version 1.3.8)

canoca: Canonical Correlation Analysis of Vector Time Series

Description

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

Usage

canoca(y)

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.

Arguments

y

a multivariate time series.

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