Exponential smoothing forecasts

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.

Value

An object of class forecast.

Details

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

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 accessors functions fitted.values and residuals extract various useful features from the underlying model.

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

Author

Rob J Hyndman

Examples


fcast <- holt(airmiles)
plot(fcast)

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