General Interface for ARIMA Regression Models

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

Usage

arima_reg(
  mode = "regression",
  seasonal_period = NULL,
  non_seasonal_ar = NULL,
  non_seasonal_differences = NULL,
  non_seasonal_ma = NULL,
  seasonal_ar = NULL,
  seasonal_differences = NULL,
  seasonal_ma = 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.
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.

Details

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

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

"auto_arima" (default) - Connects to forecast::auto.arima()
"arima" - Connects to forecast::Arima()

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.

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.

Engine Details

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

modeltime	forecast::auto.arima	forecast::Arima
seasonal_period	ts(frequency)	ts(frequency)
non_seasonal_ar, non_seasonal_differences, non_seasonal_ma	max.p(5), max.d(2), max.q(5)	order = c(p(0), d(0), q(0))
seasonal_ar, seasonal_differences, seasonal_ma	max.P(2), max.D(1), max.Q(2)	seasonal = c(P(0), D(0), Q(0))

Other options can be set using set_engine().

auto_arima (default engine)

The engine uses forecast::auto.arima().

Function Parameters:

#> function (y, d = NA, D = NA, max.p = 5, max.q = 5, max.P = 2, max.Q = 2, 
#>     max.order = 5, max.d = 2, max.D = 1, start.p = 2, start.q = 2, start.P = 1, 
#>     start.Q = 1, stationary = FALSE, seasonal = TRUE, ic = c("aicc", "aic", 
#>         "bic"), stepwise = TRUE, nmodels = 94, trace = FALSE, approximation = (length(x) > 
#>         150 | frequency(x) > 12), method = NULL, truncate = NULL, xreg = NULL, 
#>     test = c("kpss", "adf", "pp"), test.args = list(), seasonal.test = c("seas", 
#>         "ocsb", "hegy", "ch"), seasonal.test.args = list(), allowdrift = TRUE, 
#>     allowmean = TRUE, lambda = NULL, biasadj = FALSE, parallel = FALSE, 
#>     num.cores = 2, x = y, ...)

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 forecast::auto.arima() 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).

arima

The engine uses forecast::Arima().

Function Parameters:

#> function (y, order = c(0, 0, 0), seasonal = c(0, 0, 0), xreg = NULL, include.mean = TRUE, 
#>     include.drift = FALSE, include.constant, lambda = model$lambda, biasadj = FALSE, 
#>     method = c("CSS-ML", "ML", "CSS"), model = NULL, x = y, ...)

The nonseasonal ARIMA terms (order) and seasonal ARIMA terms (seasonal) are provided to forecast::Arima() via arima_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).
method - The default is set to "ML" (Maximum Likelihood). This method is more robust at the expense of speed and possible selections may fail unit root inversion testing. Alternatively, you can add method = "CSS-ML" to evaluate Conditional Sum of Squares for starting values, then Maximium Likelihood.

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 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)

# 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 ARIMA ----

# Model Spec
model_spec <- arima_reg() %>%
    set_engine("auto_arima")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
#> frequency = 12 observations per 1 year
model_fit
#> parsnip model object
#> 
#> Series: outcome 
#> ARIMA(0,1,1)(1,1,1)[12] 
#> 
#> Coefficients:
#>           ma1    sar1     sma1
#>       -0.3591  0.2034  -0.7114
#> s.e.   0.0702  0.1166   0.0970
#> 
#> sigma^2 = 0.0003485:  log likelihood = 592.09
#> AIC=-1176.17   AICc=-1176   BIC=-1162.4


# ---- STANDARD ARIMA ----

# Model Spec
model_spec <- arima_reg(
        seasonal_period          = 12,
        non_seasonal_ar          = 3,
        non_seasonal_differences = 1,
        non_seasonal_ma          = 3,
        seasonal_ar              = 1,
        seasonal_differences     = 0,
        seasonal_ma              = 1
    ) %>%
    set_engine("arima")

# Fit Spec
model_fit <- model_spec %>%
    fit(log(value) ~ date, data = training(splits))
model_fit
#> parsnip model object
#> 
#> Series: outcome 
#> ARIMA(3,1,3)(1,0,1)[12] 
#> 
#> Coefficients:
#>          ar1     ar2      ar3      ma1      ma2     ma3    sar1     sma1
#>       0.2258  0.2542  -0.2801  -0.5205  -0.2663  0.2491  0.9846  -0.5381
#> s.e.  0.6883  0.4581   0.2378   0.6995   0.4192  0.3959  0.0077   0.0751
#> 
#> sigma^2 = 0.0003465:  log likelihood = 613.46
#> AIC=-1208.91   AICc=-1208.14   BIC=-1177.48