R: Exponential smoothing forecasts

ses {forecast} | R Documentation

## Exponential smoothing forecasts

### Description

Returns forecasts and other information for exponential smoothing forecasts applied to `y`.

### Usage

    ses(y, h = 10, level = c(80, 95), fan = FALSE, initial = c("optimal",
      "simple"), alpha = NULL, lambda = NULL, biasadj = FALSE, x = y, ...)

    holt(y, h = 10, damped = FALSE, level = c(80, 95), fan = FALSE,
      initial = c("optimal", "simple"), exponential = FALSE, alpha = NULL,
      beta = NULL, phi = NULL, lambda = NULL, biasadj = FALSE, x = y, ...)

    hw(y, h = 2 * frequency(x), seasonal = c("additive", "multiplicative"),
      damped = FALSE, level = c(80, 95), fan = FALSE, initial = c("optimal",
      "simple"), exponential = FALSE, alpha = NULL, beta = NULL,
      gamma = NULL, phi = NULL, lambda = NULL, biasadj = FALSE, 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.
`initial` | Method used for selecting initial state values. If `optimal`, the initial values are optimized along with the smoothing parameters using `ets`. If `simple`, the initial values are set to values obtained using simple calculations on the first few observations. See Hyndman & Athanasopoulos (2014) for details.
`alpha` | Value of smoothing parameter for the level. If `NULL`, it will be estimated.
`lambda` | Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated. When `lambda=TRUE`, `additive.only` is set to FALSE.
`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.
`x` | Deprecated. Included for backwards compatibility.
`...` | Other arguments passed to `forecast.ets`.
`damped` | If TRUE, use a damped trend.
`exponential` | If TRUE, an exponential trend is fitted. Otherwise, the trend is (locally) linear.
`beta` | Value of smoothing parameter for the trend. If `NULL`, it will be estimated.
`phi` | Value of damping parameter if `damped=TRUE`. If `NULL`, it will be estimated.
`seasonal` | Type of seasonality in `hw` model. "additive" or "multiplicative"
`gamma` | Value of smoothing parameter for the seasonal component. If `NULL`, it will be estimated.

### Details

ses, holt and hw are simply convenient wrapper functions for `forecast(ets(...))`.

### 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 `ets` and associated functions.

An object of class `"forecast"` is a list containing at least 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`).
`residuals` | Residuals from the fitted model.
`fitted` | Fitted values (one-step forecasts)

### Author(s)

Rob J Hyndman

### References

Hyndman, R.J., Koehler, A.B., Ord, J.K., Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer-Verlag: New York. http://www.exponentialsmoothing.net.

Hyndman, R.J., Athanasopoulos (2014) Forecasting: principles and practice, OTexts: Melbourne, Australia. http://www.otexts.org/fpp.

### See Also

`ets`, `HoltWinters`, `rwf`, `arima`.

### Examples

    fcast <- holt(airmiles)
    plot(fcast)
    deaths.fcast <- hw(USAccDeaths,h=48)
    plot(deaths.fcast)

[Package forecast version 8.2 Index]