decomp {timsac} | R Documentation |
Decompose a nonstationary time series into several possible components by square-root filter.
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)
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 | ||||||
trade |
trading day adjustment (if | ||||||
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.
| ||||||
omax |
maximum or minimum data value (if | ||||||
plot |
logical. If |
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 eqnt-th data and b(1) + … + b(7) = 0.
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. |
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.
data(Blsallfood) z <- decomp(Blsallfood, trade = TRUE, year = 1973) z$aic z$lkhd z$sigma2 z$tau1 z$tau2 z$tau3