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]