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, ...)
```

### 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)
```

*ArDec*version 2.1-1 Index]