Time series decomposition using a regression model
Providing values coming from a regression on the original series, a tsd object is created using the original series, the regression model and the residuals
decreg(x, xreg, type="additive")
x |
a regular time series ('rts' under S+ and 'ts' under R) |
xreg |
a second regular time series or a vector of the same length as |
type |
the type of model, either |
a 'tsd' object
Frédéric Ibanez (ibanez@obs-vlfr.fr), Philippe Grosjean (phgrosjean@sciviews.org)
Frontier, S., 1981. Méthodes statistiques. Masson, Paris. 246 pp.
Kendall, M., 1976. Time-series. Charles Griffin & Co Ltd. 197 pp.
Legendre, L. & P. Legendre, 1984. Ecologie numérique. Tome 2: La structure des données écologiques. Masson, Paris. 335 pp.
Malinvaud, E., 1978. Méthodes statistiques de l'économétrie. Dunod, Paris. 846 pp.
Sokal, R.R. & F.J. Rohlf, 1981. Biometry. Freeman & Co, San Francisco. 860 pp.
data(marphy)
density <- ts(marphy[, "Density"])
plot(density)
Time <- time(density)
# Linear model to represent trend
density.lin <- lm(density ~ Time)
summary(density.lin)
xreg <- predict(density.lin)
lines(xreg, col=3)
density.dec <- decreg(density, xreg)
plot(density.dec, col=c(1, 3, 2), xlab="stations")
# Order 2 polynomial to represent trend
density.poly <- lm(density ~ Time + I(Time^2))
summary(density.poly)
xreg2 <- predict(density.poly)
plot(density)
lines(xreg2, col=3)
density.dec2 <- decreg(density, xreg2)
plot(density.dec2, col=c(1, 3, 2), xlab="stations")
# Fit a sinusoidal model on seasonal (artificial) data
tser <- ts(sin((1:100)/12*pi)+rnorm(100, sd=0.3), start=c(1998, 4),
frequency=24)
Time <- time(tser)
tser.sin <- lm(tser ~ I(cos(2*pi*Time)) + I(sin(2*pi*Time)))
summary(tser.sin)
tser.reg <- predict(tser.sin)
tser.dec <- decreg(tser, tser.reg)
plot(tser.dec, col=c(1, 4), xlab="stations", stack=FALSE, resid=FALSE,
lpos=c(0, 4))
plot(tser.dec, col=c(1, 4, 2), xlab="stations")
# One can also use nonlinear models (see 'nls')
# or autoregressive models (see 'ar' and others in 'ts' library)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.