arima_boost() is a way to generate a specification of a time series model
that uses boosting to improve modeling errors (residuals) on Exogenous Regressors.
It works with both "automated" ARIMA (
auto.arima) and standard ARIMA (
The main algorithms are:
Auto ARIMA + XGBoost Errors (engine =
ARIMA + XGBoost Errors (engine =
arima_boost( 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, mtry = NULL, trees = NULL, min_n = NULL, tree_depth = NULL, learn_rate = NULL, loss_reduction = NULL, sample_size = NULL, stop_iter = NULL )
A single character string for the type of model. The only possible value for this model is "regression".
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.
The order of the non-seasonal auto-regressive (AR) terms. Often denoted "p" in pdq-notation.
The order of integration for non-seasonal differencing. Often denoted "d" in pdq-notation.
The order of the non-seasonal moving average (MA) terms. Often denoted "q" in pdq-notation.
The order of the seasonal auto-regressive (SAR) terms. Often denoted "P" in PDQ-notation.
The order of integration for seasonal differencing. Often denoted "D" in PDQ-notation.
The order of the seasonal moving average (SMA) terms. Often denoted "Q" in PDQ-notation.
A number for the number (or proportion) of predictors that will be randomly sampled at each split when creating the tree models (specific engines only)
An integer for the number of trees contained in the ensemble.
An integer for the minimum number of data points in a node that is required for the node to be split further.
An integer for the maximum depth of the tree (i.e. number of splits) (specific engines only).
A number for the rate at which the boosting algorithm adapts from iteration-to-iteration (specific engines only). This is sometimes referred to as the shrinkage parameter.
A number for the reduction in the loss function required to split further (specific engines only).
number for the number (or proportion) of data that is exposed to the fitting routine.
The number of iterations without improvement before
The data given to the function are not saved and are only used
to determine the mode of the model. For
mode will always be "regression".
The model can be created using the
fit() function using the
"auto_arima_xgboost" (default) - Connects to
"arima_xgboost" - Connects to
The main arguments (tuning parameters) for the ARIMA 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.
The main arguments (tuning parameters) for the model XGBoost model are:
mtry: The number of predictors that will be
randomly sampled at each split when creating the tree models.
trees: The number of trees contained in the ensemble.
min_n: The minimum number of data points in a node
that are required for the node to be split further.
tree_depth: The maximum depth of the tree (i.e. number of
learn_rate: The rate at which the boosting algorithm adapts
loss_reduction: The reduction in the loss function required
to split further.
sample_size: The amount of data exposed to the fitting routine.
stop_iter: The number of iterations without improvement before
These arguments are converted to their specific names at the time that the model is fit.
Other options and argument can be
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 standardized parameter names in
modeltime can be mapped to their original
names in each engine:
Model 1: ARIMA:
|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))|
Model 2: XGBoost:
Other options can be set using
auto_arima_xgboost (default engine)
Model 1: Auto ARIMA (
#> 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, ...)
All values of nonseasonal pdq and seasonal PDQ are maximums.
auto.arima will select a value using these as an upper limit.
xreg - This should not be used since XGBoost will be doing the regression
Model 2: XGBoost (
#> function (params = list(), data, nrounds, watchlist = list(), obj = NULL, #> feval = NULL, verbose = 1, print_every_n = 1L, early_stopping_rounds = NULL, #> maximize = NULL, save_period = NULL, save_name = "xgboost.model", xgb_model = NULL, #> callbacks = list(), ...)
XGBoost uses a
params = list() to capture.
Parsnip / Modeltime automatically sends any args provided as
... inside of
params = list(...).
Date and Date-Time Variable
It's a requirement to have a date or date-time variable as a predictor.
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 seasonal (e.g.
seasonal_period = 12 or
seasonal_period = "12 months").
There are 3 ways to specify:
seasonal_period = "auto": A 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.
fit_xy(x = data[,"date"], y = data$y) will ignore xreg's.
Multivariate (xregs, Exogenous Regressors)
xreg parameter is populated using the
ordered factor, and
numeric data will be used as xregs.
Date and Date-time variables are not used as xregs
character data should be converted to factor.
Xreg Example: Suppose you have 3 features:
date (time stamp),
month.lbl (labeled month as a ordered factor).
month.lbl is an exogenous regressor that can be passed to the
fit(y ~ date + month.lbl) will pass
month.lbl on as an exogenous regressor.
fit_xy(data[,c("date", "month.lbl")], y = data$y) will pass x, where x is a data frame containing
date feature. Only
month.lbl will be used as an exogenous regressor.
Note that date or date-time class values are excluded from
library(tidyverse) library(lubridate) library(parsnip) library(rsample) library(timetk) library(modeltime) # Data m750 <- m4_monthly %>% filter(id == "M750") # Split Data 80/20 splits <- initial_time_split(m750, prop = 0.9) # MODEL SPEC ---- # Set engine and boosting parameters model_spec <- arima_boost( # ARIMA args seasonal_period = 12, non_seasonal_ar = 0, non_seasonal_differences = 1, non_seasonal_ma = 1, seasonal_ar = 0, seasonal_differences = 1, seasonal_ma = 1, # XGBoost Args tree_depth = 6, learn_rate = 0.1 ) %>% set_engine(engine = "arima_xgboost") # FIT ---- # Boosting - Happens by adding numeric date and month features model_fit_boosted <- model_spec %>% fit(value ~ date + as.numeric(date) + month(date, label = TRUE), data = training(splits)) model_fit_boosted
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