ardec {ArDec}R Documentation

Time series autoregressive decomposition

Description

Decomposition of a time series into latent subseries from a fitted autoregressive model

Usage

ardec(x, coef, th = 0.95, ...)

Arguments

x time series
coef autoregressive parameters of AR(p) model
th value of damping threshold
... additional arguments for specific methods

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.

For time series with missing observations, using ardec can give unreliable results (in case the autoregressive model for the longest consecutive stretch of non-missing values given by na.contiguous is not able to capture successfully the temporal structure of the data). Depending on the application / data, interpolation of the missing observations before applying ardec might be preferable.

Value

An object of the class "ardec", which is a list with components:

start start time of the time series
frequency frequency of the time series
period periods of latent components
modulus damping factors of latent components
comps matrix of latent components

Author(s)

S. M. Barbosa

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.

Barbosa, SM, Silva, ME, Fernandes, MJ (2008), Changing seasonality in North Atlantic coastal sea level from the analysis of long tide gauge records. Tellus, 60A, 165-177.

Examples

data(tempEng)
coef=ardec.lm(tempEng)$coefficients
decomposition=ardec(tempEng,coef)

[Package ArDec version 1.2-3 Index]