R: Bayesian Seasonal Adjustment Procedure

baysea {timsac} | R Documentation

## Bayesian Seasonal Adjustment Procedure

### Description

Decompose a nonstationary time series into several possible components.

### Usage

      baysea(y, period = 12, span = 4, shift = 1, forecast = 0, trend.order = 2,
             seasonal.order = 1, year = 0, month = 1, out = 0, rigid = 1,
             zersum = 1, delta = 7, alpha = 0.01, beta = 0.01, gamma = 0.1,
             spec = TRUE, plot = TRUE, separate.graphics = FALSE)

### Arguments

`y` | a univariate time series.
`period` | number of seasonals within a period.
`span` | number of periods to be processed at one time.
`shift` | number of periods to be shifted to define the new span of data.
`forecast` | length of forecast at the end of data.
`trend.order` | order of differencing of trend.
`seasonal.order` | order of differencing of seasonal. `seasonal.order` is smaller than or equal to `span`.
`year` | trading-day adjustment option.
= 0 : | without trading day adjustment
> 0 : | with trading day adjustment
| (the series is supposed to start at this `year`)
`month` | number of the month in which the series starts. If `year`=0 this parameter is ignored.
`out` | outlier correction option.
0 : | without outlier detection
1 : | with outlier detection by marginal probability
2 : | with outlier detection by model selection
`rigid` | controls the rigidity of the seasonal component. more rigid seasonal with larger than rigid.
`zersum` | controls the sum of the seasonals within a period.
`delta` | controls the leap year effect.
`alpha` | controls prior variance of initial trend.
`beta` | controls prior variance of initial seasonal.
`gamma` | controls prior variance of initial sum of seasonal.
`spec` | logical. If `TRUE` (default), estimate spectra of irregular and differenced adjusted.
`plot` | logical. If `TRUE` (default), plot `trend`, `adjust`, `smoothed`, `season` and `irregular`.
`separate.graphics` | logical. If `TRUE`, a graphic device is opened for each graphics display.

### Details

This function realized a decomposition of time series `y` into the form

y(t) = T(t) + S(t) + I(t) + TDC(t) + OCF(t)

where T(t) is trend component, S(t) is seasonal component, I(t) is irregular, TDC(t) is trading day factor and OCF(t) is outlier correction factor. For the purpose of comparison of models the criterion ABIC is defined

ABIC = -2 log (maximum likelihood of the model).

Smaller value of ABIC represents better fit.

### Value

`outlier` | outlier correction factor.
`trend` | trend.
`season` | seasonal.
`tday` | trading day component if `year` > 0.
`irregular` | = `y` - `trend` - `season` - `tday` - `outlier`.
`adjust` | = `trend` - `irregular`.
`smoothed` | = `trend` + `season` + `tday`.
`aveABIC` | averaged ABIC.
`irregular.spec` | a list with components `acov` (autocovariances), `acor` (normalized covariances), `mean`, `v` (innovation variance), `aic` (AIC), `parcor` (partial autocorrelation) and `rspec` (rational spectrum) of irregular if `spec` = `TRUE`.
`adjusted.spec` | a list with components `acov`, `acor`, `mean`, `v`, `aic`, `parcor` and `rspec` of differenced adjusted series if `spec` = `TRUE`.
`differenced.trend` | a list with components `acov`, `acor`, `mean`, `v`, `aic` and `parcor` of differenced trend series if `spec` = `TRUE`.
`differenced.season` | a list with components `acov`, `acor`, `mean`, `v`, `aic` and `parcor` of differenced seasonal series if `spec` = `TRUE`.

### References

H.Akaike, T.Ozaki, M.Ishiguro, Y.Ogata, G.Kitagawa, Y-H.Tamura, E.Arahata, K.Katsura and Y.Tamura (1985) Computer Science Monograph, No.22, Timsac84 Part 1. The Institute of Statistical Mathematics.

### Examples

    data(LaborData)
    baysea(LaborData, forecast = 12)

[Package timsac version 1.3.6 Index]