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=1, 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 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. |
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.
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). |
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(y=Blsallfood, trade=TRUE, year=1973) z$aic z$lkhd z$sigma2 z$tau1 z$tau2 z$tau3