General Interface for Multiple Seasonality Regression Models (TBATS, STLM)

seasonal_reg() is a way to generate a specification of an Seasonal Decomposition model before fitting and allows the model to be created using different packages. Currently the only package is forecast.

Usage

seasonal_reg(
  mode = "regression",
  seasonal_period_1 = NULL,
  seasonal_period_2 = NULL,
  seasonal_period_3 = NULL
)

Arguments

mode: A single character string for the type of model. The only possible value for this model is "regression".
seasonal_period_1: (required) The primary 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.
seasonal_period_2: (optional) A second seasonal frequency. Is NULL 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.
seasonal_period_3: (optional) A third seasonal frequency. Is NULL 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.

Details

The data given to the function are not saved and are only used to determine the mode of the model. For seasonal_reg(), the mode will always be "regression".

The model can be created using the fit() function using the following engines:

"tbats" - Connects to forecast::tbats()
"stlm_ets" - Connects to forecast::stlm(), method = "ets"
"stlm_arima" - Connects to forecast::stlm(), method = "arima"

Engine Details

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

modeltime	forecast::stlm	forecast::tbats
seasonal_period_1, seasonal_period_2, seasonal_period_3	msts(seasonal.periods)	msts(seasonal.periods)

Other options can be set using set_engine().

The engines use forecast::stlm().

Function Parameters:

#> function (y, s.window = 7 + 4 * seq(6), robust = FALSE, method = c("ets",
#>     "arima"), modelfunction = NULL, model = NULL, etsmodel = "ZZN", lambda = NULL,
#>     biasadj = FALSE, xreg = NULL, allow.multiplicative.trend = FALSE, x = y,
#>     ...)

tbats

Method: Uses method = "tbats", which by default is auto-TBATS.
Xregs: Univariate. Cannot accept Exogenous Regressors (xregs). Xregs are ignored.

stlm_ets

Method: Uses method = "stlm_ets", which by default is auto-ETS.
Xregs: Univariate. Cannot accept Exogenous Regressors (xregs). Xregs are ignored.

stlm_arima

Method: Uses method = "stlm_arima", which by default is auto-ARIMA.
Xregs: Multivariate. Can accept Exogenous Regressors (xregs).

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 yearly seasonal (e.g. For monthly time stamps, seasonal_period = 12, seasonal_period = "12 months", or seasonal_period = "yearly"). There are 3 ways to specify:

seasonal_period = "auto": A seasonal 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 (No xregs, Exogenous Regressors):

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)

The tbats engine cannot accept Xregs.
The stlm_ets engine cannot accept Xregs.
The stlm_arima engine can accept Xregs

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 seasonal_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)

# Data
taylor_30_min
#> # A tibble: 4,032 × 2
#>    date                value
#>    <dttm>              <dbl>
#>  1 2000-06-05 00:00:00 22262
#>  2 2000-06-05 00:30:00 21756
#>  3 2000-06-05 01:00:00 22247
#>  4 2000-06-05 01:30:00 22759
#>  5 2000-06-05 02:00:00 22549
#>  6 2000-06-05 02:30:00 22313
#>  7 2000-06-05 03:00:00 22128
#>  8 2000-06-05 03:30:00 21860
#>  9 2000-06-05 04:00:00 21751
#> 10 2000-06-05 04:30:00 21336
#> # ℹ 4,022 more rows

# Split Data 80/20
splits <- initial_time_split(taylor_30_min, prop = 0.8)

# ---- STLM ETS ----

# Model Spec
model_spec <- seasonal_reg() %>%
    set_engine("stlm_ets")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
#> frequency = 48 observations per 1 day
model_fit
#> parsnip model object
#> 
#> SEASONAL DECOMP: ETS(A,Ad,N)
#> 
#> # A tibble: 1 × 5
#>      aic    bic   aicc loglik       mse
#>    <dbl>  <dbl>  <dbl>  <dbl>     <dbl>
#> 1 -6473. -6437. -6473.  3243. 0.0000415


# ---- STLM ARIMA ----

# Model Spec
model_spec <- seasonal_reg() %>%
    set_engine("stlm_arima")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
#> frequency = 48 observations per 1 day
model_fit
#> parsnip model object
#> 
#> SEASONAL DECOMP: ARIMA(3,1,2)
#> 
#> Series: x 
#> ARIMA(3,1,2) 
#> 
#> Coefficients:
#>          ar1     ar2      ar3      ma1      ma2
#>       1.0031  0.0782  -0.3096  -0.3203  -0.1378
#> s.e.  0.0838  0.1286   0.0575   0.0875   0.0817
#> 
#> sigma^2 = 3.918e-05:  log likelihood = 11786.32
#> AIC=-23560.65   AICc=-23560.62   BIC=-23524.18