timsac (version 1.3.8)

canarm: Canonical Correlation Analysis of Scalar Time Series

Description

Fit an ARMA model to stationary scalar time series through the analysis of canonical correlations between the future and past sets of observations.

Usage

canarm(y, lag = NULL, max.order = NULL, plot = TRUE)

Value

arinit

AR coefficients of initial AR model fitting by the minimum AIC procedure.

v

innovation vector.

aic

AIC.

aicmin

minimum AIC.

order.maice

order of minimum AIC.

parcor

partial autocorrelation.

nc

total number of case.

future

number of present and future variables.

past

number of present and past variables.

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.

arcoef

AR coefficients \(a(i) (i = 1,...,p)\).

macoef

MA coefficients \(b(i) (i = 1,...,q)\).

Arguments

y

a univariate time series.

lag

maximum lag. Default is \(2 \sqrt{n}\), where \(n\) is the length of the time series y.

max.order

upper limit of AR order and MA order, must be less than or equal to lag. Default is lag.

plot

logical. If TRUE (default), parcor is plotted.

Details

The ARMA model of stationary scalar time series \(y(t) (t=1,...,n)\) is given by $$y(t) - a(1)y(t-1) - ...- a(p)y(t-p) = u(t) - b(1)u(t-1) - ... - b(q)u(t-q),$$ where \(p\) is AR order and \(q\) is MA order.

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

# "arima.sim" is a function in "stats".
# Note that the sign of MA coefficient is opposite from that in "timsac".
y <- arima.sim(list(order=c(2,0,1), ar=c(0.64,-0.8), ma=c(-0.5)), n = 1000)
z <- canarm(y, max.order = 30)
z$arcoef
z$macoef