Getting Started with Modeltime

Model 1: Auto ARIMA (Modeltime)

First, we create a basic univariate ARIMA model using “Auto Arima” using arima_reg()

# Model 1: auto_arima ----
model_fit_arima_no_boost <- arima_reg() %>%
    set_engine(engine = "auto_arima") %>%
    fit(value ~ date, data = training(splits))

Model 2: Boosted Auto ARIMA (Modeltime)

Next, we create a boosted ARIMA using arima_boost(). Boosting uses XGBoost to model the ARIMA errors. Note that model formula contains both a date feature and derivatives of date - ARIMA uses the date - XGBoost uses the derivatives of date as regressors

Normally I’d use a preprocessing workflow for the month features using a function like step_timeseries_signature() from timetk to help reduce the complexity of the parsnip formula interface.

# Model 2: arima_boost ----
model_fit_arima_boosted <- arima_boost(
    min_n = 2,
    learn_rate = 0.015
) %>%
    set_engine(engine = "auto_arima_xgboost") %>%
    fit(value ~ date + as.numeric(date) + factor(month(date, label = TRUE), ordered = F),
        data = training(splits))

Model 3: Exponential Smoothing (Modeltime)

Next, create an Error-Trend-Season (ETS) model using an Exponential Smoothing State Space model. This is accomplished with exp_smoothing().

# Model 3: ets ----
model_fit_ets <- exp_smoothing() %>%
    set_engine(engine = "ets") %>%
    fit(value ~ date, data = training(splits))

Model 4: Prophet (Modeltime)

We’ll create a prophet model using prophet_reg().

# Model 4: prophet ----
model_fit_prophet <- prophet_reg() %>%
    set_engine(engine = "prophet") %>%
    fit(value ~ date, data = training(splits))

Model 5: Linear Regression (Parsnip)

We can model time series linear regression (TSLM) using the linear_reg() algorithm from parsnip. The following derivatives of date are used:

• Trend: Modeled using as.numeric(date)
• Seasonal: Modeled using month(date)

# Model 5: lm ----
model_fit_lm <- linear_reg() %>%
    set_engine("lm") %>%
    fit(value ~ as.numeric(date) + factor(month(date, label = TRUE), ordered = FALSE),
        data = training(splits))

Model 6: MARS (Workflow)

We can model a Multivariate Adaptive Regression Spline model using mars(). I’ve modified the process to use a workflow to standardize the preprocessing of the features that are provided to the machine learning model (mars).

# Model 6: earth ----
model_spec_mars <- mars(mode = "regression") %>%
    set_engine("earth") 

recipe_spec <- recipe(value ~ date, data = training(splits)) %>%
    step_date(date, features = "month", ordinal = FALSE) %>%
    step_mutate(date_num = as.numeric(date)) %>%
    step_normalize(date_num) %>%
    step_rm(date)
  
wflw_fit_mars <- workflow() %>%
    add_recipe(recipe_spec) %>%
    add_model(model_spec_mars) %>%
    fit(training(splits))

OK, with these 6 models, we’ll show how easy it is to forecast.

5A - Visualizing the Forecast Test

Visualizing the Test Error is easy to do using the interactive plotly visualization (just toggle the visibility of the models using the Legend).

calibration_tbl %>%
    modeltime_forecast(
        new_data    = testing(splits),
        actual_data = m750
    ) %>%
    plot_modeltime_forecast(
      .legend_max_width = 25, # For mobile screens
      .interactive      = interactive
    )

From visualizing the test set forecast:

• Models 1&2: ARIMA & ARIMA Boost are performing well. Both models have “auto” components because we used Auto ARIMA. The XGBoost component has parameters that were specified. We can possibly get better accuracy by tuning, but because the ARIMA component is working well on this data, additional improvement may be low.
• Model 3: ETS(M,A,A) is performing the best. The 80% confidence interval is the most narrow of the bunch, indicating the hold out set is modeled well.
• Model 4: PROPHET is comparable to the ARIMA models, but has a slightly wider test error confidence interval.
• Model 5: LM is over-shooting the local trend. This is because the trend component is a simple linear line, which doesn’t account for the change points.
• Model 6: EARTH is overfitting the local trend. This is because we did not tune the number of change points, so the algorithm is auto-calculating the change points.

5B - Accuracy Metrics

We can use modeltime_accuracy() to collect common accuracy metrics. The default reports the following metrics using yardstick functions:

• MAE - Mean absolute error, mae()
• MAPE - Mean absolute percentage error, mape()
• MASE - Mean absolute scaled error, mase()
• SMAPE - Symmetric mean absolute percentage error, smape()
• RMSE - Root mean squared error, rmse()
• RSQ - R-squared, rsq()

These of course can be customized following the rules for creating new yardstick metrics, but the defaults are very useful.

To make table-creation a bit easier, I’ve included table_modeltime_accuracy() for outputing results in either interactive (reactable) or static (gt) tables.

calibration_tbl %>%
    modeltime_accuracy() %>%
    table_modeltime_accuracy(resizable = TRUE, bordered = TRUE)

From the accuracy metrics:

• Model 3: ETS is clearly the winner here with MAE of 77
• Model 6: MARS is over-fitting the local trend. This comes out in the R-Squared of 0.55.