General Interface for Exponential Smoothing State Space Models

exp_smoothing() is a way to generate a specification of an Exponential Smoothing model before fitting and allows the model to be created using different packages. Currently the only package is forecast. Several algorithms are implemented:

ETS - Automated Exponential Smoothing
CROSTON - Croston's forecast is a special case of Exponential Smoothing for intermittent demand
Theta - A special case of Exponential Smoothing with Drift that performed well in the M3 Competition

Usage

exp_smoothing(
  mode = "regression",
  seasonal_period = NULL,
  error = NULL,
  trend = NULL,
  season = NULL,
  damping = NULL,
  smooth_level = NULL,
  smooth_trend = NULL,
  smooth_seasonal = NULL
)

Arguments

mode: A single character string for the type of model. The only possible value for this model is "regression".
seasonal_period: A seasonal frequency. Uses "auto" by default. A character phrase of "auto" or time-based phrase of "2 weeks" can be used if a date or date-time variable is provided. See Fit Details below.
error: The form of the error term: "auto", "additive", or "multiplicative". If the error is multiplicative, the data must be non-negative.
trend: The form of the trend term: "auto", "additive", "multiplicative" or "none".
season: The form of the seasonal term: "auto", "additive", "multiplicative" or "none".
damping: Apply damping to a trend: "auto", "damped", or "none".
smooth_level: This is often called the "alpha" parameter used as the base level smoothing factor for exponential smoothing models.
smooth_trend: This is often called the "beta" parameter used as the trend smoothing factor for exponential smoothing models.
smooth_seasonal: This is often called the "gamma" parameter used as the seasonal smoothing factor for exponential smoothing models.

Details

Models can be created using the following engines:

"ets" (default) - Connects to forecast::ets()
"croston" - Connects to forecast::croston()
"theta" - Connects to forecast::thetaf()
"smooth_es" - Connects to smooth::es()

Engine Details

The standardized parameter names in modeltime can be mapped to their original names in each engine:

modeltime	forecast::ets	forecast::croston()	forecast::thetaf()	smooth::es()
seasonal_period()	ts(frequency)	ts(frequency)	ts(frequency)	ts(frequency)
error(), trend(), season()	model ('ZZZ')	NA	NA	model('ZZZ')
damping()	damped (NULL)	NA	NA	phi
smooth_level()	alpha (NULL)	alpha (0.1)	NA	persistence(alpha)
smooth_trend()	beta (NULL)	NA	NA	persistence(beta)
smooth_seasonal()	gamma (NULL)	NA	NA	persistence(gamma)

Other options can be set using set_engine().

ets (default engine)

The engine uses forecast::ets().

Function Parameters:

#> function (y, model = "ZZZ", damped = NULL, alpha = NULL, beta = NULL, gamma = NULL, 
#>     phi = NULL, additive.only = FALSE, lambda = NULL, biasadj = FALSE, 
#>     lower = c(rep(1e-04, 3), 0.8), upper = c(rep(0.9999, 3), 0.98), opt.crit = c("lik", 
#>         "amse", "mse", "sigma", "mae"), nmse = 3, bounds = c("both", "usual", 
#>         "admissible"), ic = c("aicc", "aic", "bic"), restrict = TRUE, allow.multiplicative.trend = FALSE, 
#>     use.initial.values = FALSE, na.action = c("na.contiguous", "na.interp", 
#>         "na.fail"), ...)

The main arguments are model and damped are defined using:

error() = "auto", "additive", and "multiplicative" are converted to "Z", "A", and "M"
trend() = "auto", "additive", "multiplicative", and "none" are converted to "Z","A","M" and "N"
season() = "auto", "additive", "multiplicative", and "none" are converted to "Z","A","M" and "N"
damping() - "auto", "damped", "none" are converted to NULL, TRUE, FALSE
smooth_level(), smooth_trend(), and smooth_seasonal() are automatically determined if not provided. They are mapped to "alpha", "beta" and "gamma", respectively.

By default, all arguments are set to "auto" to perform automated Exponential Smoothing using in-sample data following the underlying forecast::ets() automation routine.

Other options and argument can be set using set_engine().

Parameter Notes:

xreg - This model is not set up to use exogenous regressors. Only univariate models will be fit.

croston

The engine uses forecast::croston().

Function Parameters:

#> function (y, h = 10, alpha = 0.1, x = y)

The main arguments are defined using:

smooth_level(): The "alpha" parameter

Parameter Notes:

xreg - This model is not set up to use exogenous regressors. Only univariate models will be fit.

theta

The engine uses forecast::thetaf()

Parameter Notes:

xreg - This model is not set up to use exogenous regressors. Only univariate models will be fit.

smooth_es

The engine uses smooth::es().

Function Parameters:

#> function (y, model = "ZZZ", lags = c(frequency(y)), persistence = NULL, 
#>     phi = NULL, initial = c("optimal", "backcasting", "complete"), initialSeason = NULL, 
#>     ic = c("AICc", "AIC", "BIC", "BICc"), loss = c("likelihood", "MSE", 
#>         "MAE", "HAM", "MSEh", "TMSE", "GTMSE", "MSCE"), h = 10, holdout = FALSE, 
#>     bounds = c("usual", "admissible", "none"), silent = TRUE, xreg = NULL, 
#>     regressors = c("use", "select"), initialX = NULL, ...)

The main arguments model and phi are defined using:

error() = "auto", "additive" and "multiplicative" are converted to "Z", "A" and "M"
trend() = "auto", "additive", "multiplicative", "additive_damped", "multiplicative_damped" and "none" are converted to "Z", "A", "M", "Ad", "Md" and "N".
season() = "auto", "additive", "multiplicative", and "none" are converted "Z", "A","M" and "N"
damping() - Value of damping parameter. If NULL, then it is estimated.
smooth_level(), smooth_trend(), and smooth_seasonal() are automatically determined if not provided. They are mapped to "persistence"("alpha", "beta" and "gamma", respectively).

By default, all arguments are set to "auto" to perform automated Exponential Smoothing using in-sample data following the underlying smooth::es() automation routine.

Other options and argument can be set using set_engine().

Parameter Notes:

xreg - This is supplied via the parsnip / modeltime fit() interface (so don't provide this manually). See Fit Details (below).

Fit Details

Date and Date-Time Variable

It's a requirement to have a date or date-time variable as a predictor. The fit() interface accepts date and date-time features and handles them internally.

fit(y ~ date)

Seasonal Period Specification

The period can be non-seasonal (seasonal_period = 1 or "none") or seasonal (e.g. seasonal_period = 12 or seasonal_period = "12 months"). There are 3 ways to specify:

seasonal_period = "auto": A period is selected based on the periodicity of the data (e.g. 12 if monthly)
seasonal_period = 12: A numeric frequency. For example, 12 is common for monthly data
seasonal_period = "1 year": A time-based phrase. For example, "1 year" would convert to 12 for monthly data.

Univariate:

For univariate analysis, you must include a date or date-time feature. Simply use:

Formula Interface (recommended): fit(y ~ date) will ignore xreg's.
XY Interface: fit_xy(x = data[,"date"], y = data$y) will ignore xreg's.

Multivariate (xregs, Exogenous Regressors)

Just for smooth engine.

The xreg parameter is populated using the fit() or fit_xy() function:

Only factor, ordered factor, and numeric data will be used as xregs.
Date and Date-time variables are not used as xregs
character data should be converted to factor.

Xreg Example: Suppose you have 3 features:

y (target)
date (time stamp),
month.lbl (labeled month as a ordered factor).

The month.lbl is an exogenous regressor that can be passed to the arima_reg() using fit():

fit(y ~ date + month.lbl) will pass month.lbl on as an exogenous regressor.
fit_xy(data[,c("date", "month.lbl")], y = data$y) will pass x, where x is a data frame containing month.lbl and the date feature. Only month.lbl will be used as an exogenous regressor.

Note that date or date-time class values are excluded from xreg.

Examples

library(dplyr)
library(parsnip)
library(rsample)
library(timetk)
library(smooth)

# Data
m750 <- m4_monthly %>% filter(id == "M750")
m750
#> # A tibble: 306 × 3
#>    id    date       value
#>    <fct> <date>     <dbl>
#>  1 M750  1990-01-01  6370
#>  2 M750  1990-02-01  6430
#>  3 M750  1990-03-01  6520
#>  4 M750  1990-04-01  6580
#>  5 M750  1990-05-01  6620
#>  6 M750  1990-06-01  6690
#>  7 M750  1990-07-01  6000
#>  8 M750  1990-08-01  5450
#>  9 M750  1990-09-01  6480
#> 10 M750  1990-10-01  6820
#> # ℹ 296 more rows

# Split Data 80/20
splits <- initial_time_split(m750, prop = 0.8)

# ---- AUTO ETS ----

# Model Spec - The default parameters are all set
# to "auto" if none are provided
model_spec <- exp_smoothing() %>%
    set_engine("ets")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
#> frequency = 12 observations per 1 year
model_fit
#> parsnip model object
#> 
#> ETS(A,A,A) 
#> 
#> Call:
#>  forecast::ets(y = outcome, model = model_ets, damped = damping_ets,  
#> 
#>  Call:
#>      alpha = alpha, beta = beta, gamma = gamma) 
#> 
#>   Smoothing parameters:
#>     alpha = 0.5893 
#>     beta  = 1e-04 
#>     gamma = 0.1771 
#> 
#>   Initial states:
#>     l = 8.7377 
#>     b = 0.002 
#>     s = 0.029 0.0259 0.0144 -0.0272 -0.1369 -0.0764
#>            0.0209 0.0358 0.036 0.035 0.0274 0.016
#> 
#>   sigma:  0.0186
#> 
#>       AIC      AICc       BIC 
#> -584.7384 -582.0304 -525.2865 


# ---- STANDARD ETS ----

# Model Spec
model_spec <- exp_smoothing(
        seasonal_period  = 12,
        error            = "multiplicative",
        trend            = "additive",
        season           = "multiplicative"
    ) %>%
    set_engine("ets")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
model_fit
#> parsnip model object
#> 
#> ETS(M,Ad,M) 
#> 
#> Call:
#>  forecast::ets(y = outcome, model = model_ets, damped = damping_ets,  
#> 
#>  Call:
#>      alpha = alpha, beta = beta, gamma = gamma) 
#> 
#>   Smoothing parameters:
#>     alpha = 0.5889 
#>     beta  = 0.0065 
#>     gamma = 0.203 
#>     phi   = 0.98 
#> 
#>   Initial states:
#>     l = 8.7353 
#>     b = 0.0054 
#>     s = 1.0027 1.0025 1.0012 0.9972 0.9839 0.9921
#>            1.0024 1.0041 1.0045 1.0039 1.0033 1.0022
#> 
#>   sigma:  0.0021
#> 
#>       AIC      AICc       BIC 
#> -576.9488 -573.9088 -513.9998 


# ---- CROSTON ----
# \donttest{
# Model Spec
model_spec <- exp_smoothing(
        smooth_level = 0.2
    ) %>%
    set_engine("croston")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
model_fit
#> parsnip model object
#> 
#> Croston Method
#> ---
# }



# ---- THETA ----
# \donttest{
#' # Model Spec
model_spec <- exp_smoothing() %>%
    set_engine("theta")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
model_fit
#> parsnip model object
#> 
#> Theta Method
#> ---
# }




#' # ---- SMOOTH ----
# \donttest{
#' # Model Spec
model_spec <- exp_smoothing(
               seasonal_period  = 12,
               error            = "multiplicative",
               trend            = "additive_damped",
               season           = "additive"
         ) %>%
    set_engine("smooth_es")

# Fit Spec
model_fit <- model_spec %>%
    fit(value ~ date, data = training(splits))
model_fit
#> parsnip model object
#> 
#> Time elapsed: 0.14 seconds
#> Model estimated using es() function: ETS(MAdA)
#> Distribution assumed in the model: Normal
#> Loss function type: likelihood; Loss function value: 1566.089
#> Persistence vector g:
#>  alpha   beta  gamma 
#> 0.5808 0.0060 0.2281 
#> Damping parameter: 1
#> Sample size: 244
#> Number of estimated parameters: 18
#> Number of degrees of freedom: 226
#> Information criteria:
#>      AIC     AICc      BIC     BICc 
#> 3168.178 3171.218 3231.127 3239.482 
# }

General Interface for Exponential Smoothing State Space Models

Usage

Arguments

Details

Engine Details

Fit Details

See also

Examples