ses: Exponential smoothing forecasts

In forecast: Forecasting Functions for Time Series and Linear Models

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 univariate time series of class ts
h	Number of periods for forecasting. Default value is twice the largest seasonal period (for seasonal data) or ten (for non-seasonal data).
level	Confidence levels 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. 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.
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.

forecast class

An object of class forecast is a list usually 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.

residuals

Residuals from the fitted model. For models with additive errors, the residuals will be x minus the fitted values.

fitted

Fitted values (one-step forecasts)

The function summary can be used to obtain and print a summary of the results, while the functions plot and autoplot produce plots of the forecasts and prediction intervals. The generic accessor functions fitted.values and residuals extract various useful features from the underlying model.

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. https://robjhyndman.com/expsmooth/.

Hyndman and Athanasopoulos (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. https://otexts.com/fpp2/

See Also

ets(), stats::HoltWinters(), rwf(), stats::arima().

Examples

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

forecast documentation built on March 18, 2026, 9:07 a.m.