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

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 Number of periods for forecasting Confidence level for prediction intervals. If TRUE, level is set to seq(51,99,by=3). This is suitable for fan plots. Box-Cox transformation parameter. Ignored if NULL. Otherwise, forecasts back-transformed via an inverse Box-Cox transformation. 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 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. Deprecated. Included for backwards compatibility.

## 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.

## 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.

## 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/.

smooth.spline, arima, holt.

## Examples

fcast <- splinef(uspop,h=5)
plot(fcast)summary(fcast)#>
#> Forecast method: Cubic Smoothing Spline
#>
#> Model Information:
#> $beta #> [1] 9.280668e-14 #> #>$call
#> splinef(y = uspop, h = 5)
#>
#>
#> Error measures:
#>                     ME     RMSE      MAE       MPE     MAPE       MASE
#> Training set 0.7288723 4.643268 3.247273 -1.379552 9.580963 0.04654289
#>                    ACF1
#> Training set -0.4369553
#>
#> Forecasts:
#>      Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
#> 1980       225.6523 219.6912 231.6133 216.5356 234.7689
#> 1990       248.1045 233.3293 262.8798 225.5077 270.7013
#> 2000       270.5568 244.8162 296.2974 231.1900 309.9236
#> 2010       293.0091 254.5045 331.5136 234.1214 351.8967
#> 2020       315.4613 262.6160 368.3067 234.6413 396.2814