timsac (version 1.3.0)

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)

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.

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 $b(i) (i = 1,...,q)$.

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