predict.nlar {tsDyn}

Predict method for objects of class ‘nlar’.

Description

Forecasting a non-linear model object of general class ‘nlar’, including ‘setar’ and ‘star’.

Usage

## S3 method for class 'nlar'
predict(
  object,
  newdata,
  n.ahead = 1,
  type = c("naive", "MC", "bootstrap", "block-bootstrap"),
  nboot = 100,
  ci = 0.95,
  block.size = 3,
  boot1Zero = TRUE,
  seed = NULL,
  ...
)

Arguments

object

An object of class ‘nlar’; generated by setar() or lstar().

newdata

Optional. A new data frame to predict from.

n.ahead

An integer specifying the number of forecast steps.

type

Type of forecasting method used. See details.

nboot

The number of replications for type MC or bootstrap.

ci

The forecast confidence interval (available only with types MC and bootstrap).

block.size

The block size when the block-bootstrap is used.

boot1Zero

Whether the first innovation for MC/bootstrap should be set to zero.

seed

optional, the seed for the random generation.

...

Further arguments passed to the internal ‘oneStep’ function. Mainly argument ‘thVar’ if an external threshold variable was provided

Details

The forecasts are obtained recursively from the estimated model. Given that the models are non-linear, ignoring the residuals in the 2- and more steps ahead forecasts leads to biased forecasts (so-called naive). Different resampling methods, averaging n.boot times over future residuals, are available:

naive

No residuals

MC

Monte-Carlo method, where residuals are taken from a normal distribution, with a standard deviation equal to the residuals sd.

bootstrap

Residuals are resampled from the empirical residuals from the model.

block-bootstrap

Same as bootstrap, but residuals are resampled in block, with size block.size

The MC and bootstrap methods correspond to equations 3.90 and 3.91 of Franses and van Dijk (2000, p. 121). The bootstrap/MC is initiated either from the first forecast, n.ahead=1 (set with boot1zero to TRUE), or from the second only.

When the forecast method is based on resampling, forecast intervals are available. These are obtained simply as empirical ci quantiles of the resampled forecasts (cf Method 2 in Franses and van Dijk, 2000, p. 122).

Value

A ‘ts’ object, or, in the case of MC/bootstrap, a list containing the prediction (pred) and the forecast standard errors (se).

Author(s)

Matthieu Stigler

References

Non-linear time series models in empirical finance, Philip Hans Franses and Dick van Dijk, Cambridge: Cambridge University Press (2000).

See Also

The model fitting functions setar, lstar.

A more sophisticated predict function, allowing to do sub-sample rolling predictions: predict_rolling.

Examples

x.train <- window(log10(lynx), end = 1924)
x.test <- window(log10(lynx), start = 1925)


### Use different forecasting methods:
mod.set <- setar(x.train, m=2, thDelay=0)
pred_setar_naive <- predict(mod.set, n.ahead=10)
pred_setar_boot <- predict(mod.set, n.ahead=10, type="bootstrap", n.boot=200)
pred_setar_Bboot <- predict(mod.set, n.ahead=10, type="block-bootstrap", n.boot=200)
pred_setar_MC <- predict(mod.set, n.ahead=10, type="bootstrap", n.boot=200)

## Plot to compare results:
pred_range <- range(pred_setar_naive, pred_setar_boot$pred, pred_setar_MC$pred, na.rm=TRUE)
plot(x.test, ylim=pred_range, main="Comparison of forecasts methods from same SETAR")
lines(pred_setar_naive, lty=2, col=2)
lines(pred_setar_boot$pred, lty=3, col=3)
lines(pred_setar_Bboot$pred, lty=4, col=4)
lines(pred_setar_MC$pred, lty=5, col=5)

legLabels <- c("Observed", "Naive F", "Bootstrap F","Block-Bootstrap F", "MC F")
legend("bottomleft", leg=legLabels, lty=1:5, col=1:5)