exp_smoothing: General Interface for Exponential Smoothing State Space...

In modeltime: The Tidymodels Extension for Time Series Modeling

General Interface for Exponential Smoothing State Space Models

Description

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", persistence = NULL, phi = NULL, initial = c("optimal", 
#>     "backcasting"), initialSeason = NULL, ic = c("AICc", "AIC", "BIC", 
#>     "BICc"), loss = c("likelihood", "MSE", "MAE", "HAM", "MSEh", "TMSE", 
#>     "GTMSE", "MSCE"), h = 10, holdout = FALSE, cumulative = FALSE, interval = c("none", 
#>     "parametric", "likelihood", "semiparametric", "nonparametric"), level = 0.95, 
#>     bounds = c("usual", "admissible", "none"), silent = c("all", "graph", 
#>         "legend", "output", "none"), xreg = NULL, xregDo = 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:

1. seasonal_period = "auto": A period is selected based on the periodicity of the data (e.g. 12 if monthly)

2. seasonal_period = 12: A numeric frequency. For example, 12 is common for monthly data

3. 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:

1. y (target)

2. date (time stamp),

3. 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.

See Also

fit.model_spec(), set_engine()

Examples

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

# Data
m750 <- m4_monthly %>% filter(id == "M750")
m750

# 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))
model_fit


# ---- 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


# ---- CROSTON ----

# 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




# ---- THETA ----

#' # Model Spec
model_spec <- exp_smoothing() %>%
    set_engine("theta")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
model_fit





#' # ---- SMOOTH ----

#' # 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

modeltime documentation built on Sept. 2, 2023, 5:06 p.m.