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

## 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. 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.- biasadj
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
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.

## 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/.

## Examples

```
fcast <- splinef(uspop,h=5)
plot(fcast)
summary(fcast)
#>
#> Forecast method: Cubic Smoothing Spline
#>
#> Model Information:
#> $beta
#> [1] 0.0006859
#>
#> $call
#> splinef(y = uspop, h = 5)
#>
#>
#> Error measures:
#> ME RMSE MAE MPE MAPE MASE
#> Training set 0.7704553 4.572546 3.165298 -0.6110405 8.174722 0.04536795
#> ACF1
#> Training set -0.4363661
#>
#> Forecasts:
#> Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
#> 1980 225.6937 219.8454 231.5419 216.7496 234.6378
#> 1990 248.1814 233.7246 262.6382 226.0717 270.2912
#> 2000 270.6692 245.5023 295.8361 232.1798 309.1586
#> 2010 293.1569 255.5241 330.7897 235.6025 350.7113
#> 2020 315.6447 264.0068 367.2826 236.6713 394.6181
```