Function forecasting::ExponentialSmoothingTrendSeasonality(dataValues, estimates, noObservations, noAveragingPeriods, alpha, beta, gamma, periodLength, ErrorMeasures, Residuals)

# forecasting::ExponentialSmoothingTrendSeasonality

The exponential smoothing with trend and seasonality procedure is a time series forecasting procedure. This procedure is an extension from the exponential smoothing whereby the forecast also captures both a trend and a seasonality. The reader interested in the mathematical background is referred to:

## Function Prototype

To provide the error measures and residuals only when you need them, there are three flavors of the ExponentialSmoothingTrendSeasonality procedure provided:

forecasting::ExponentialSmoothingTrendSeasonality(
! Provides the estimates, but not the error measures nor the residuals
dataValues,      ! Input, parameter indexed over time set
estimates,       ! Output, parameter indexed over time set
noObservations,  ! Scalar input, length history
alpha,           ! Scalar input, weight of observation
beta,            ! Scalar input, weight of change in observation
gamma,           ! Scalar input, weight of seasonality
periodLength)    ! Scalar input, length of season

forecasting::ExponentialSmoothingTrendSeasonalityEM(
! Provides estimates and error measures, but not the residuals
dataValues,      ! Input, parameter indexed over time set
estimates,       ! Output, parameter indexed over time set
noObservations,  ! Scalar input, length history
alpha,           ! Scalar input, weight of observation
beta,            ! Scalar input, weight of change in observation
gamma,           ! Scalar input, weight of seasonality
periodLength,    ! Scalar input, length of season
ErrorMeasures)   ! Output, indexed over forecasting::ems

forecasting::ExponentialSmoothingTrendSeasonalityEMR(
! Provides estimates, error measures, and residuals
dataValues,      ! Input, parameter indexed over time set
estimates,       ! Output, parameter indexed over time set
noObservations,  ! Scalar input, length history
alpha,           ! Scalar input, weight of observation
beta,            ! Scalar input, weight of change in observation
gamma,           ! Scalar input, weight of seasonality
periodLength,    ! Scalar input, length of season
ErrorMeasures,   ! Output, indexed over forecasting::ems
Residuals)       ! Output, parameter indexed over time set


## Arguments

dataValues

A one dimensional parameter containing the observations for the first $$T$$ elements of the time set.

estimates

A one dimensional parameter containing the estimates for all elements in the time set.

noObservations

Specifies the number of elements that belong to the history of the time set. This parameter corresponds to $$T$$ in the notation presented in Time Series Forecasting Notation.

noAveragingPeriods

Specifies the number of values used to compute a single average. This parameter corresponds to $$N$$ in the mathematical notation above.

alpha

Specifies the weighting factor for the observation. This parameter corresponds to $$\alpha$$ in the mathematical notation above.

beta

Specifies the weighting factor for the change in observation.

gamma

Specifies the weighting factor for the seasonality.

periodLength

Specifies the period length.

ErrorMeasures

The error measures as presented in Time Series Forecasting Notation.

Residuals

The residuals as presented in Time Series Forecasting Notation.

Note

In order to use this function, the Forecasting system library needs to be added to the application.