Decomposition of a time series into latent subseries from a fitted autoregressive model
Usage
ardec(x, coef, ...)
Arguments
x
time series
coef
autoregressive parameters of AR(p) model
…
additional arguments for specific methods
Value
A list with components:
period
periods of latent components
modulus
damping factors of latent components
comps
matrix of latent components
Details
If an observed time series can be adequately described by an (eventually high order) autoregressive AR(p) process, a constructive result (West, 1997) yields a time series decomposition in terms of latent components following either AR(1) or AR(2) processes depending on the eigenvalues of the state evolution matrix.
Complex eigenvalues r exp(iw) correspond to pseudo-periodic oscillations as a damped sine wave with fixed period (2pi/w) and damping factor r. Real eigenvalues correspond to a first order autoregressive process with parameter r.
References
West, M. (1997), Time series decomposition. Biometrika, 84, 489-494.
West, M. and Harrisson, P.J. (1997), Bayesian Forecasting and Dynamic Models, Springer-Verlag.
# NOT RUN {data(tempEng)
coef=ardec.lm(tempEng)$coefficients
# warning: running the next command can be time comsuming!
decomposition=ardec(tempEng,coef)
# }