| Version: | 2.1-1 |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Title: | Time Series Autoregressive-Based Decomposition |
| Description: | Autoregressive-based decomposition of a time series based on the approach in West (1997). Particular cases include the extraction of trend and seasonal components. |
| Author: | Susana Barbosa |
| Maintainer: | Susana Barbosa <sabarbosa@fc.ul.pt> |
| Date: | 2022-05-31 |
| NeedsCompilation: | no |
| Packaged: | 2022-05-31 17:41:06 UTC; susana |
| Repository: | CRAN |
| Date/Publication: | 2022-05-31 22:20:26 UTC |
Time series autoregressive decomposition
Description
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 |
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.
Value
A list with components:
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.
Examples
data(tempEng)
coef=ardec.lm(tempEng)$coefficients
# warning: running the next command can be time comsuming!
decomposition=ardec(tempEng,coef)
Fit an autoregressive model as a linear regression
Description
Function ardec.lm fits an autoregressive model of order p, AR(p) to a time series through a linear least squares regression.
Usage
ardec.lm(x)
Arguments
x |
time series |
Value
For ardec.lm, an object of class "lm".
Author(s)
S. M. Barbosa
References
West, M. (1995), Bayesian inference in cyclical component dynamic linear models.Journal of the American Statistical Association, 90, 1301-1312.
See Also
Examples
data(tempEng)
model=ardec.lm(tempEng)
Extraction of individual periodic components from a monthly time series
Description
Function ardec.periodic extracts a periodic component from the autoregressive decomposition of a monthly time series.
Usage
ardec.periodic(x, per, tol = 0.95)
Arguments
x |
time series |
per |
period of the component to be extracted |
tol |
tolerance for the period of the component |
Value
A list with components:
period |
period for the anual component |
modulus |
damping factor for the annual component |
component |
extracted component |
Author(s)
S. M. Barbosa
Examples
data(tempEng)
ardec.periodic(tempEng,per=12)
Estimation of the trend component from a monthly time series
Description
Function ardec.trend extracts the trend component from the autoregressive decomposition of a monthly time series.
Usage
ardec.trend(x)
Arguments
x |
time series |
Value
A list with components:
modulus |
damping factor for the annual component |
trend |
trend component |
Author(s)
S. M. Barbosa
Examples
data(co2)
ardec.trend(co2)
Time series of monthly temperature values
Description
Monthly temperature in Central England from 1723-1970
Usage
data(tempEng)Format
Time-Series [1:2976] from 1723 to 1971
Source
Hipel, K. W. and Mcleod, A. (1994) Time Series Modelling of Water Resources and Environmental Systems, Elsevier
Examples
data(tempEng)