adam_reg() is a way to generate a specification of an ADAM model before fitting and allows the model to be created using different packages. Currently the only package is smooth.

## Usage

adam_reg(
mode = "regression",
ets_model = NULL,
non_seasonal_ar = NULL,
non_seasonal_differences = NULL,
non_seasonal_ma = NULL,
seasonal_ar = NULL,
seasonal_differences = NULL,
seasonal_ma = NULL,
use_constant = NULL,
regressors_treatment = NULL,
outliers_treatment = NULL,
outliers_ci = NULL,
probability_model = NULL,
distribution = NULL,
loss = NULL,
information_criteria = NULL,
seasonal_period = NULL,
select_order = NULL
)

## Arguments

mode

A single character string for the type of model. The only possible value for this model is "regression".

ets_model

The type of ETS model. The first letter stands for the type of the error term ("A" or "M"), the second (and sometimes the third as well) is for the trend ("N", "A", "Ad", "M" or "Md"), and the last one is for the type of seasonality ("N", "A" or "M").

non_seasonal_ar

The order of the non-seasonal auto-regressive (AR) terms. Often denoted "p" in pdq-notation.

non_seasonal_differences

The order of integration for non-seasonal differencing. Often denoted "d" in pdq-notation.

non_seasonal_ma

The order of the non-seasonal moving average (MA) terms. Often denoted "q" in pdq-notation.

seasonal_ar

The order of the seasonal auto-regressive (SAR) terms. Often denoted "P" in PDQ-notation.

seasonal_differences

The order of integration for seasonal differencing. Often denoted "D" in PDQ-notation.

seasonal_ma

The order of the seasonal moving average (SMA) terms. Often denoted "Q" in PDQ-notation.

use_constant

Logical, determining, whether the constant is needed in the model or not. This is mainly needed for ARIMA part of the model, but can be used for ETS as well.

regressors_treatment

The variable defines what to do with the provided explanatory variables: "use" means that all of the data should be used, while "select" means that a selection using ic should be done, "adapt" will trigger the mechanism of time varying parameters for the explanatory variables.

outliers_treatment

Defines what to do with outliers: "ignore", so just returning the model, "detect" outliers based on specified level and include dummies for them in the model, or detect and "select" those of them that reduce ic value.

outliers_ci

What confidence level to use for detection of outliers. Default is 99%.

probability_model

The type of model used in probability estimation. Can be "none" - none, "fixed" - constant probability, "general" - the general Beta model with two parameters, "odds-ratio" - the Odds-ratio model with b=1 in Beta distribution, "inverse-odds-ratio" - the model with a=1 in Beta distribution, "direct" - the TSB-like (Teunter et al., 2011) probability update mechanism a+b=1, "auto" - the automatically selected type of occurrence model.

distribution

what density function to assume for the error term. The full name of the distribution should be provided, starting with the letter "d" - "density".

loss

The type of Loss Function used in optimization.

information_criteria

The information criterion to use in the model selection / combination procedure.

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.

select_order

If TRUE, then the function will select the most appropriate order. The values list(ar=...,i=...,ma=...) specify the maximum orders to check in this case.

## Details

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

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

• "auto_adam" (default) - Connects to smooth::auto.adam()

• "adam" - Connects to smooth::adam()

Main Arguments

The main arguments (tuning parameters) for the model are:

• seasonal_period: The periodic nature of the seasonality. Uses "auto" by default.

• non_seasonal_ar: The order of the non-seasonal auto-regressive (AR) terms.

• non_seasonal_differences: The order of integration for non-seasonal differencing.

• non_seasonal_ma: The order of the non-seasonal moving average (MA) terms.

• seasonal_ar: The order of the seasonal auto-regressive (SAR) terms.

• seasonal_differences: The order of integration for seasonal differencing.

• seasonal_ma: The order of the seasonal moving average (SMA) terms.

• ets_model: The type of ETS model.

• use_constant: Logical, determining, whether the constant is needed in the model or not.

• regressors_treatment: The variable defines what to do with the provided explanatory variables.

• outliers_treatment: Defines what to do with outliers.

• probability_model: The type of model used in probability estimation.

• distribution: what density function to assume for the error term.

• loss: The type of Loss Function used in optimization.

• information_criteria: The information criterion to use in the model selection / combination procedure.

These arguments are converted to their specific names at the time that the model is fit.

Other options and argument can be set using set_engine() (See Engine Details below).

If parameters need to be modified, update() can be used in lieu of recreating the object from scratch.

The engine uses smooth::auto.adam().

Function Parameters:

#> Registered S3 method overwritten by 'greybox':
#>   method     from
#>   print.pcor lava
#> function (data, model = "ZXZ", lags = c(frequency(data)), orders = list(ar = c(0),
#>     i = c(0), ma = c(0), select = FALSE), formula = NULL, regressors = c("use",
#>     "select", "adapt"), occurrence = c("none", "auto", "fixed", "general",
#>     "odds-ratio", "inverse-odds-ratio", "direct"), distribution = c("dnorm",
#>     "dlaplace", "ds", "dgnorm", "dlnorm", "dinvgauss", "dgamma"), outliers = c("ignore",
#>     "use", "select"), level = 0.99, h = 0, holdout = FALSE, persistence = NULL,
#>     phi = NULL, initial = c("optimal", "backcasting"), arma = NULL, ic = c("AICc",
#>         "AIC", "BIC", "BICc"), bounds = c("usual", "admissible", "none"),
#>     silent = TRUE, parallel = FALSE, ...)

The MAXIMUM nonseasonal ARIMA terms (max.p, max.d, max.q) and seasonal ARIMA terms (max.P, max.D, max.Q) are provided to forecast::auto.arima() via arima_reg() parameters. Other options and argument can be set using set_engine().

Parameter Notes:

• All values of nonseasonal pdq and seasonal PDQ are maximums. The smooth::auto.adam() model will select a value using these as an upper limit.

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

The engine uses smooth::adam().

Function Parameters:

#> function (data, model = "ZXZ", lags = c(frequency(data)), orders = list(ar = c(0),
#>     i = c(0), ma = c(0), select = FALSE), constant = FALSE, formula = NULL,
#>     regressors = c("use", "select", "adapt"), occurrence = c("none", "auto",
#>         "fixed", "general", "odds-ratio", "inverse-odds-ratio", "direct"),
#>     distribution = c("default", "dnorm", "dlaplace", "ds", "dgnorm", "dlnorm",
#>         "dinvgauss", "dgamma"), loss = c("likelihood", "MSE", "MAE", "HAM",
#>         "LASSO", "RIDGE", "MSEh", "TMSE", "GTMSE", "MSCE"), outliers = c("ignore",
#>         "use", "select"), level = 0.99, h = 0, holdout = FALSE, persistence = NULL,
#>     phi = NULL, initial = c("optimal", "backcasting"), arma = NULL, ic = c("AICc",
#>         "AIC", "BIC", "BICc"), bounds = c("usual", "admissible", "none"),
#>     silent = TRUE, ...)

The nonseasonal ARIMA terms (orders) and seasonal ARIMA terms (orders) are provided to smooth::adam() via adam_reg() parameters. 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 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:

1. seasonal_period = "auto": A seasonal 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 (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.

Multivariate (xregs, Exogenous Regressors)

The xreg parameter is populated using the fit() 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.

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

fit.model_spec(), set_engine()

## Examples

if (FALSE) {
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)

# Model Spec

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

# Model Spec
seasonal_period          = 12,
non_seasonal_ar          = 3,
non_seasonal_differences = 1,
non_seasonal_ma          = 3,
seasonal_ar              = 1,
seasonal_differences     = 0,
seasonal_ma              = 1
) %>%