R/parsnip-arima_reg.R

In modeltime: The Tidymodels Extension for Time Series Modeling

#' 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`.
#'
#' @param mode A single character string for the type of model.
#'  The only possible value for this model is "regression".
#' @param 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.
#' @param non_seasonal_ar The order of the non-seasonal auto-regressive (AR) terms. Often denoted "p" in pdq-notation.
#' @param non_seasonal_differences The order of integration for non-seasonal differencing. Often denoted "d" in pdq-notation.
#' @param non_seasonal_ma The order of the non-seasonal moving average (MA) terms. Often denoted "q" in pdq-notation.
#' @param seasonal_ar The order of the seasonal auto-regressive (SAR) terms. Often denoted "P" in PDQ-notation.
#' @param seasonal_differences The order of integration for seasonal differencing. Often denoted "D" in PDQ-notation.
#' @param 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.
#'
#'
#' @section Engine Details:
#'
#' The standardized parameter names in `modeltime` can be mapped to their original
#' names in each engine:
#'
#' ```{r echo = FALSE}
#' # parsnip::convert_args("arima_reg")
#' tibble::tribble(
#'     ~ "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))"
#' ) %>% knitr::kable()
#' ```
#'
#' Other options can be set using `set_engine()`.
#'
#' __auto_arima (default engine)__
#'
#' The engine uses [forecast::auto.arima()].
#'
#' Function Parameters:
#' ```{r echo = FALSE}
#' str(forecast::auto.arima)
#' ```
#' 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:
#' ```{r echo = FALSE}
#' str(forecast::Arima)
#' ```
#'
#' 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.
#'
#'
#' @section 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.
#'  - XY Interface: `fit_xy(x = data[,"date"], y = data$y)` will ignore xreg's.
#'
#' __Multivariate (xregs, Exogenous Regressors)__
#'
#'  The `xreg` parameter is populated using the `fit()` or `fit_xy()` function:
#'
#'  - Only `factor`, `ordered factor`, and `numeric` data will be used as xregs.
#'  - Date and Date-time variables are not used as xregs
#'  - `character` data should be converted to factor.
#'
#'  _Xreg Example:_ Suppose you have 3 features:
#'
#'  1. `y` (target)
#'  2. `date` (time stamp),
#'  3. `month.lbl` (labeled month as a ordered factor).
#'
#'  The `month.lbl` is an exogenous regressor that can be passed to the `arima_reg()` using
#'  `fit()`:
#'
#'  - `fit(y ~ date + month.lbl)` will pass `month.lbl` on as an exogenous regressor.
#'  - `fit_xy(data[,c("date", "month.lbl")], y = data$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`.
#'
#'
#'
#' @seealso `fit.model_spec()`, `set_engine()`
#'
#' @examples
#' library(dplyr)
#' library(parsnip)
#' library(rsample)
#' library(timetk)
#'
#' # Data
#' m750 <- m4_monthly %>% filter(id == "M750")
#' m750
#'
#' # 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))
#' model_fit
#'
#'
#' # ---- 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
#'
#' @export
arima_reg <- function(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) {

    args <- list(
        seasonal_period           = rlang::enquo(seasonal_period),
        non_seasonal_ar           = rlang::enquo(non_seasonal_ar),
        non_seasonal_differences  = rlang::enquo(non_seasonal_differences),
        non_seasonal_ma           = rlang::enquo(non_seasonal_ma),
        seasonal_ar               = rlang::enquo(seasonal_ar),
        seasonal_differences      = rlang::enquo(seasonal_differences),
        seasonal_ma               = rlang::enquo(seasonal_ma)
    )

    parsnip::new_model_spec(
        "arima_reg",
        args     = args,
        eng_args = NULL,
        mode     = mode,
        method   = NULL,
        engine   = NULL
    )

}

#' @export
print.arima_reg <- function(x, ...) {
    cat("ARIMA Regression Model Specification (", x$mode, ")\n\n", sep = "")
    parsnip::model_printer(x, ...)

    if(!is.null(x$method$fit$args)) {
        cat("Model fit template:\n")
        print(parsnip::show_call(x))
    }

    invisible(x)
}

#' @export
#' @importFrom stats update
update.arima_reg <- function(object, parameters = NULL,
                             seasonal_period = NULL, non_seasonal_ar = NULL, non_seasonal_differences = NULL, non_seasonal_ma = NULL,
                             seasonal_ar = NULL, seasonal_differences = NULL, seasonal_ma = NULL,
                             fresh = FALSE, ...) {

    eng_args <- parsnip::update_engine_parameters(object$eng_args, fresh, ...)

    if (!is.null(parameters)) {
        parameters <- parsnip::check_final_param(parameters)
    }

    args <- list(
        seasonal_period            = rlang::enquo(seasonal_period),
        non_seasonal_ar            = rlang::enquo(non_seasonal_ar),
        non_seasonal_differences   = rlang::enquo(non_seasonal_differences),
        non_seasonal_ma            = rlang::enquo(non_seasonal_ma),
        seasonal_ar                = rlang::enquo(seasonal_ar),
        seasonal_differences       = rlang::enquo(seasonal_differences),
        seasonal_ma                = rlang::enquo(seasonal_ma)
    )

    args <- parsnip::update_main_parameters(args, parameters)

    if (fresh) {
        object$args <- args
        object$eng_args <- eng_args
    } else {
        null_args <- purrr::map_lgl(args, parsnip::null_value)
        if (any(null_args))
            args <- args[!null_args]
        if (length(args) > 0)
            object$args[names(args)] <- args
        if (length(eng_args) > 0)
            object$eng_args[names(eng_args)] <- eng_args
    }

    parsnip::new_model_spec(
        "arima_reg",
        args     = object$args,
        eng_args = object$eng_args,
        mode     = object$mode,
        method   = NULL,
        engine   = object$engine
    )
}


#' @export
#' @importFrom parsnip translate
translate.arima_reg <- function(x, engine = x$engine, ...) {
    if (is.null(engine)) {
        message("Used `engine = 'auto_arima'` for translation.")
        engine <- "auto_arima"
    }
    x <- parsnip::translate.default(x, engine, ...)

    x
}


# FIT - Arima -----

#' Low-Level ARIMA function for translating modeltime to forecast
#'
#' @param x A dataframe of xreg (exogenous regressors)
#' @param y A numeric vector of values to fit
#' @param 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.
#' @param p The order of the non-seasonal auto-regressive (AR) terms. Often denoted "p" in pdq-notation.
#' @param d The order of integration for non-seasonal differencing. Often denoted "d" in pdq-notation.
#' @param q The order of the non-seasonal moving average (MA) terms. Often denoted "q" in pdq-notation.
#' @param P The order of the seasonal auto-regressive (SAR) terms. Often denoted "P" in PDQ-notation.
#' @param D The order of integration for seasonal differencing. Often denoted "D" in PDQ-notation.
#' @param Q The order of the seasonal moving average (SMA) terms. Often denoted "Q" in PDQ-notation.
#' @param ... Additional arguments passed to `forecast::Arima`
#'
#' @keywords internal
#' @export
Arima_fit_impl <- function(x, y, period = "auto",
                           p = 0, d = 0, q = 0, P = 0, D = 0, Q = 0,
                           ...) {

    # X & Y
    # Expect outcomes  = vector
    # Expect predictor = data.frame
    outcome    <- y
    predictor  <- x

    # INDEX & PERIOD
    # Determine Period, Index Col, and Index
    index_tbl <- parse_index_from_data(predictor)
    period    <- parse_period_from_index(index_tbl, period)
    idx_col   <- names(index_tbl)
    idx       <- timetk::tk_index(index_tbl)

    # XREGS
    # Clean names, get xreg recipe, process predictors
    xreg_recipe <- create_xreg_recipe(predictor, prepare = TRUE)
    xreg_matrix <- juice_xreg_recipe(xreg_recipe, format = "matrix")

    # FIT
    outcome <- stats::ts(outcome, frequency = period)

    if (!is.null(xreg_matrix)) {
        fit_arima   <- forecast::Arima(outcome, order = c(p, d, q), seasonal = c(P, D, Q), xreg = xreg_matrix, ...)
    } else {
        fit_arima <- forecast::Arima(outcome, order = c(p, d, q), seasonal = c(P, D, Q), ...)
    }

    # RETURN
    new_modeltime_bridge(
        class = "Arima_fit_impl",

        # Models
        models = list(
            model_1 = fit_arima
        ),

        # Data - Date column (matches original), .actual, .fitted, and .residuals columns
        data = tibble::tibble(
            !! idx_col  := idx,
            .actual      =  as.numeric(fit_arima$x),
            .fitted      =  as.numeric(fit_arima$fitted),
            .residuals   =  as.numeric(fit_arima$residuals)
        ),

        # Preprocessing Recipe (prepped) - Used in predict method
        extras = list(
            xreg_recipe = xreg_recipe
        ),

        # Description - Convert arima model parameters to short description
        desc = get_arima_description(fit_arima)
    )

}

#' @export
print.Arima_fit_impl <- function(x, ...) {
    print(x$models$model_1)
    invisible(x)
}


# FIT - Auto Arima -----

#' Low-Level ARIMA function for translating modeltime to forecast
#'
#' @param x A dataframe of xreg (exogenous regressors)
#' @param y A numeric vector of values to fit
#' @param 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.
#' @param max.p The maximum order of the non-seasonal auto-regressive (AR) terms.
#' @param max.d The maximum order of integration for non-seasonal differencing.
#' @param max.q The maximum order of the non-seasonal moving average (MA) terms.
#' @param max.P The maximum order of the seasonal auto-regressive (SAR) terms.
#' @param max.D The maximum order of integration for seasonal differencing.
#' @param max.Q The maximum order of the seasonal moving average (SMA) terms.
#' @param ... Additional arguments passed to `forecast::auto.arima`
#'
#' @keywords internal
#' @export
auto_arima_fit_impl <- function(x, y, period = "auto",
                                max.p = 5, max.d = 2, max.q = 5,
                                max.P = 2, max.D = 1, max.Q = 2, ...) {

    # X & Y
    # Expect outcomes  = vector
    # Expect predictor = data.frame
    outcome    <- y
    predictor  <- x

    # INDEX & PERIOD
    # Determine Period, Index Col, and Index
    index_tbl <- parse_index_from_data(predictor)
    period    <- parse_period_from_index(index_tbl, period)
    idx_col   <- names(index_tbl)
    idx       <- timetk::tk_index(index_tbl)

    # XREGS
    # Clean names, get xreg recipe, process predictors
    xreg_recipe <- create_xreg_recipe(predictor, prepare = TRUE)
    xreg_matrix <- juice_xreg_recipe(xreg_recipe, format = "matrix")

    # FIT
    outcome <- stats::ts(outcome, frequency = period)

    if (!is.null(xreg_matrix)) {
        xreg_matrix <- as.matrix(xreg_matrix)
        fit_arima   <- forecast::auto.arima(outcome,
                                            max.p = max.p, max.d = max.d, max.q = max.q,
                                            max.P = max.P, max.D = max.D, max.Q = max.Q,
                                            xreg = xreg_matrix, ...)
    } else {
        fit_arima <- forecast::auto.arima(outcome,
                                          max.p = max.p, max.d = max.d, max.q = max.q,
                                          max.P = max.P, max.D = max.D, max.Q = max.Q,
                                          ...)
    }

    # RETURN
    new_modeltime_bridge(
        class = "auto_arima_fit_impl",

        # Models
        models = list(
            model_1 = fit_arima
        ),

        # Data - Date column (matches original), .actual, .fitted, and .residuals columns
        data = tibble::tibble(
            !! idx_col  := idx,
            .actual      =  as.numeric(fit_arima$x),
            .fitted      =  as.numeric(fit_arima$fitted),
            .residuals   =  as.numeric(fit_arima$residuals)
        ),

        # Preprocessing Recipe (prepped) - Used in predict method
        extras = list(
            xreg_recipe = xreg_recipe
        ),

        # Description - Converts arima model arguments to short description
        desc = get_arima_description(fit_arima)
    )

}

#' @export
print.auto_arima_fit_impl <- function(x, ...) {
    print(x$model$model_1)
    invisible(x)
}


# PREDICT ----
# - auto.arima produces an Arima model

#' @export
predict.auto_arima_fit_impl <- function(object, new_data, ...) {
    Arima_predict_impl(object, new_data, ...)
}

#' @export
predict.Arima_fit_impl <- function(object, new_data, ...) {
    Arima_predict_impl(object, new_data, ...)
}

#' Bridge prediction function for ARIMA models
#'
#' @inheritParams parsnip::predict.model_fit
#' @param ... Additional arguments passed to `forecast::Arima()`
#'
#' @keywords internal
#' @export
Arima_predict_impl <- function(object, new_data, ...) {

    # PREPARE INPUTS
    model       <- object$models$model_1
    idx_train   <- object$data %>% timetk::tk_index()
    xreg_recipe <- object$extras$xreg_recipe
    h_horizon   <- nrow(new_data)

    # XREG
    xreg_matrix <- bake_xreg_recipe(xreg_recipe, new_data, format = "matrix")

    # PREDICTIONS
    if (!is.null(xreg_matrix)) {
        preds_forecast <- forecast::forecast(model, h = h_horizon, xreg = xreg_matrix, ...)
    } else {
        preds_forecast <- forecast::forecast(model, h = h_horizon, ...)
    }

    # Return predictions as numeric vector
    preds <- tibble::as_tibble(preds_forecast) %>% purrr::pluck(1)

    return(preds)

}