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=1, 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 trade 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 (m1:trend.order)

T(t) = T(t-1) + V1(t) : m1 = 1

T(t) = 2T(t-1) - T(t-2) + V1(t) : m1 = 2

T(t) = 3T(t-1) -3T(t-2) + T(t-2) + V1(t) : m1 = 3

AR component (m2:ar.order)

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

Seasonal component (k:seasonal.order, f:=frequency)

S(t) = -S(t-1) - ... - S(t-f+1) + V3(t) : k=1

S(t) = -2S(t-1) - ... -f*S(t-f+1) - ... - S(t-2f+2) + V3(t) : k=2

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).

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(y=Blsallfood, trade=TRUE, year=1973)
  z$aic
  z$lkhd
  z$sigma2
  z$tau1
  z$tau2
  z$tau3

[Package timsac version 1.2.1 Index]