# splinef

##### Cubic Spline Forecast

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

- Keywords
- ts

##### 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:

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.

##### 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

##### Examples

```
# NOT RUN {
fcast <- splinef(uspop,h=5)
plot(fcast)
summary(fcast)
# }
```

*Documentation reproduced from package forecast, version 8.2, License: GPL-3*