KFKSDS (version 1.6)

predict.stsmSS: Kalman Filter for State Space Models

Description

These functions run the iterative equations of the Kalman filter for a state space model.

Usage

"predict"(object, y, n.ahead = 12L, ...)

Arguments

object

a list containing the matrices of the state space model.

y

a numeric time series.

n.ahead

a numeric. The number of steps ahead to predict.

...

further arguments. Currently omitted.

Value

A list containing the following elements: itempreda time series containing n.ahead predictions. itemsea time series containing the standard errors of pred. itemaa univariate or multivariate time series object containing n.ahead predictions for the state vector. itemPa univariate or multivariate time series object containing the square of the standard errors of a.

Details

This function computes the same values as the function predict.StructTS from the stats package but the predictions of the components are also returned.

References

Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.

Examples

## local level model
## Nile time series
require("stsm")
y <- Nile
m <- stsm::stsm.model(model = "local-level", y = y, transPars = "StructTS")
fit <- StructTS(y, "level")
m <- stsm::set.pars(m, as.vector(fit$coef[c(2,1)]) * 100 / var(y))
ss <- stsm::char2numeric(m, P0cov = TRUE)
res <- predict(ss, y, 5)

# display forecasts and confidence intervals
plot(cbind(y, res$pred), type = "n", plot.type = "single")
lines(y)
lines(res$pred, col = "blue")
lines(res$pred + 2 * res$se, col = "red", lty = 2)
lines(res$pred - 2 * res$se, col = "red", lty = 2)

# for the whole series, the above is the same as "predict.StructTS" 
all.equal(res$pred, predict(fit, 5)$pred)
all.equal(res$se, predict(fit, 5)$se)

## basic Structural model
## AirPassengers time series (in logarithms)
y <- log(AirPassengers)
m <- stsm::stsm.model(model = "BSM", y = y, transPars = "StructTS")
fit <- StructTS(y, "BSM")
m <- stsm::set.pars(m, as.vector(fit$coef[c(4,1:3)]) * 100 / var(y))
ss <- stsm::char2numeric(m, P0cov = TRUE)
res <- predict(ss, y, 12)

all.equal(res$pred, predict(fit, 12)$pred)
all.equal(res$se, predict(fit, 12)$se)

# forecasts and confidence intervals for the series
# scaled back to original scale
expy <- exp(y)
plot(cbind(expy, exp(res$pred + 2 * res$se)), type = "n", plot.type = "single")
lines(expy)
lines(exp(res$pred), col = "blue")
lines(exp(res$pred + 2 * res$se), col = "red", lty = 2)
lines(exp(res$pred - 2 * res$se), col = "red", lty = 2)

# forecasts for the trend component
# the aproach in StructTS() seems to seasonal fluctuations in the trend
# see the "stsm" package for a more flexible interface for maximum likelihood 
# procedures to fit a structural time series model
trend <- exp(fitted(fit)[,1])
plot(cbind(trend, AirPassengers), type = "n", plot.type = "single")
lines(AirPassengers, col = "gray")
lines(trend)
lines(exp(res$a[,1]), col = "blue")
lines(exp(res$a[,1] + 2 * sqrt(res$P[,1])), col = "red", lty = 2)
lines(exp(res$a[,1] - 2 * sqrt(res$P[,1])), col = "red", lty = 2)

# forecasts for the seasonal component
seas <- exp(fitted(fit)[,3])
plot(cbind(seas, exp(res$a[,3]) + 2 * sqrt(res$P[,3])), 
  type = "n", plot.type = "single")
lines(seas)
lines(exp(res$a[,3]), col = "blue")
lines(exp(res$a[,3] + 2 * sqrt(res$P[,3])), col = "red", lty = 2)
lines(exp(res$a[,3] - 2 * sqrt(res$P[,3])), col = "red", lty = 2)