R: Cubic Spline Forecast

splinef {forecast} | R Documentation

## Cubic Spline Forecast

### Description

Returns local linear forecasts and prediction intervals using cubic smoothing splines.

### Usage

    splinef(y, h = 10, level = c(80, 95), fan = FALSE, lambda = NULL,
      biasadj = FALSE, method = c("gcv", "mle"), x = y)

### Arguments

`y` | a numeric vector or time series of class `ts`
`h` | Number of periods for forecasting
`level` | Confidence level for prediction intervals.
`fan` | If TRUE, level is set to seq(51,99,by=3). This is suitable for fan plots.
`lambda` | Box-Cox transformation parameter. Ignored if NULL. Otherwise, forecasts back-transformed via an inverse Box-Cox transformation.
`biasadj` | Use adjusted back-transformed mean for Box-Cox transformations. If TRUE, point forecasts and fitted values are mean forecast. Otherwise, these points can be considered the median of the forecast densities.
`method` | Method for selecting the smoothing parameter. If `method="gcv"`, the generalized cross-validation method from `smooth.spline` is used. If `method="mle"`, the maximum likelihood method from Hyndman et al (2002) is used.
`x` | Deprecated. Included for backwards compatibility.

### Details

The cubic smoothing spline model is equivalent to an ARIMA(0,2,2) model but with a restricted parameter space. The advantage of the spline model over the full ARIMA model is that it provides a smooth historical trend as well as a linear forecast function. Hyndman, King, Pitrun, and Billah (2002) show that the forecast performance of the method is hardly affected by the restricted parameter space.

### Value

An object of class "`forecast`".

The function `summary` is used to obtain and print a summary of the results, while the function `plot` produces a plot of the forecasts and prediction intervals.

The generic accessor functions `fitted.values` and `residuals` extract useful features of the value returned by `splinef`.

An object of class `"forecast"` containing the following elements:

`model` | A list containing information about the fitted model
`method` | The name of the forecasting method as a character string
`mean` | Point forecasts as a time series
`lower` | Lower limits for prediction intervals
`upper` | Upper limits for prediction intervals
`level` | The confidence values associated with the prediction intervals
`x` | The original time series (either `object` itself or the time series used to create the model stored as `object`).
`onestepf` | One-step forecasts from the fitted model.
`fitted` | Smooth estimates of the fitted trend using all data.
`residuals` | Residuals from the fitted model. That is x minus one-step forecasts.

### Author(s)

Rob J Hyndman

### References

Hyndman, King, Pitrun and Billah (2005) Local linear forecasts using cubic smoothing splines. Australian and New Zealand Journal of Statistics, 47(1), 87-99. https://robjhyndman.com/publications/splinefcast/.

### See Also

`smooth.spline`, `arima`, `holt`.

### Examples

    fcast <- splinef(uspop,h=5)
    plot(fcast)
    summary(fcast)

[Package forecast version 8.2 Index]