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)



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. If lambda="auto", then a transformation is automatically selected using BoxCox.lambda. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.


Use adjusted back-transformed mean for Box-Cox transformations. If transformed data is used to produce forecasts and fitted values, a regular back transformation will result in median forecasts. If biasadj is TRUE, an adjustment will be made to produce mean forecasts and fitted values.


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.


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:


A list containing information about the fitted model


The name of the forecasting method as a character string


Point forecasts as a time series


Lower limits for prediction intervals


Upper limits for prediction intervals


The confidence values associated with the prediction intervals


The original time series (either object itself or the time series used to create the model stored as object).


One-step forecasts from the fitted model.


Smooth estimates of the fitted trend using all data.


Residuals from the fitted model. That is x minus one-step forecasts.


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.


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

See also


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