canoca {timsac}

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.

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.

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.

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