R: Time Series Decomposition (Seasonal Adjustment) by...

decomp {timsac} | R Documentation

## Time Series Decomposition (Seasonal Adjustment) by Square-Root Filter

### Description

Decompose a nonstationary time series into several possible components by square-root filter.

### Usage

      decomp(y, trend.order=2, ar.order=2, frequency=12,
             seasonal.order=1, log=FALSE, trade=FALSE, diff=1,
             year=1980, month=1, miss=0, omax=99999.9, plot=TRUE)

### Arguments

`y` | a univariate time series.
`trend.order` | trend order (0, 1, 2 or 3).
`ar.order` | AR order (less than 11, try 2 first).
`frequency` | number of seasons in one period.
`seasonal.order` | seasonal order (0, 1 or 2).
`log` | log transformation of data (if `log` = TRUE).
`trade` | trading day adjustment (if `trade` = TRUE).
`diff` | numerical differencing (1 sided or 2 sided).
`year` | the first year of the data.
`month` | the first month of the data.
`miss` | missing data flag.
= 0 : | no consideration
> 0 : | values which are greater than `omax` are treated as missing data
< 0 : | values which are less than `omax` are treated as missing data
`omax` | maximum or minimum data value (if `miss` > 0 or `miss` < 0).
`plot` | logical. If TRUE (default) `trend`, `seasonal`, `ar` and `trad` are plotted.

### Details

The Basic Model
y(t) = T(t) + AR(t) + S(t) + TD(t) + W(t)
where T(t) is trend component, AR(t) is AR process, S(t) is seasonal component, TD(t) is trading day factor and W(t) is observational noise.

Component Models

Trend component (trend.order m1)
m1= 1 : T(t) = T(t-1) + V1(t)
m1= 2 : T(t) = 2T(t-1) - T(t-2) + V1(t)
m1= 3 : T(t) = 3T(t-1) -3T(t-2) + T(t-2) + V1(t)

AR component (ar.order m2)
AR(t) = a(1)AR(t-1) + ... + a(m2)AR(t-m2) + V2(t)

Seasonal component (seasonal.order k, frequency f)
k=1 : S(t) = -S(t-1) - ... - S(t-f+1) + V3(t)
k=2 : S(t) = -2S(t-1) - ... -f S(t-f+1) - ... - S(t-2f+2) + V3(t)

Trading day effect
TD(t) = b(1) TRADE(t,1) + ... + b(7) TRADE(t,7)
where TRADE(t,i) is the number of i-th days of the week in t-th data and b(1) + ... + b(7) = 0.

### Value

`trend` | trend component.
`seasonal` | seasonal component.
`ar` | AR process.
`trad` | trading day factor.
`noise` | observational noise.
`aic` | AIC.
`lkhd` | likelihood.
`sigma2` | sigma^2.
`tau1` | system noise variances tau2(1).
`tau2` | system noise variances tau2(2).
`tau3` | system noise variances tau2(3).
`arcoef` | vector of AR coefficients.
`tdf` | trading day factor. `tdf(i)` (i=1,7) are from Sunday to Saturday sequentially.

### References

G.Kitagawa (1981) A Nonstationary Time Series Model and Its Fitting by a Recursive Filter Journal of Time Series Analysis, Vol.2, 103-116.

W.Gersch and G.Kitagawa (1983) The prediction of time series with Trends and Seasonalities Journal of Business and Economic Statistics, Vol.1, 253-264.

G.Kitagawa (1984) A smoothness priors-state space modeling of Time Series with Trend and Seasonality Journal of American Statistical Association, VOL.79, NO.386, 378-389.

### Examples

      data(Blsallfood)
      z <- decomp(Blsallfood, trade=TRUE, year=1973)
      z$aic
      z$lkhd
      z$sigma2
      z$tau1
      z$tau2
      z$tau3

[Package timsac version 1.3.5 Index]