Forecasting with Global Models • modeltime

Why is global modeling important for time series? For starters, the ability to forecast many time series with a single model that is trained on many time series groups was a winning strategy in recent Kaggle M5 Forecasting Competition. In fact, it’s the solution we recommend in our Time Series Course when forecasting many time series as part of a high-performance forecasting system. Why? Because it speeds up forecasting, allowing the data scientist to more rapidly experiment and find good solutions.

Global Forecasting

In general, there are two methods for forecasting at scale (a slow and accurate method and a fast and good method):

Iterative Forecasting (Slow and Accurate): Best for accuracy but takes much longer than global model (due to for-loop iteration), results in many models (more memory required), and is often needed to be run in parallel to scale to thousands of time series (otherwise it can take days to complete). But, iterative forecasting can yield great results. See Nested Forecasting for our Iterative Forecasting implementation.
Global Modeling (Fast and Good): Best for scalability to thousands of time series. Uses a Panel Data structure. Can scale to 10,000+ time series easily because only a single model is made that generates predictions (forecasts) for all of the time series. Requires feature engineering and parameter tuning to get best performance, which can be challenging for beginners.

Important Concepts

Students can struggle with global modeling. To help, I have a few terms to cover that will help you understand how global modeling works (and how it differs from iterative modeling).

Panel Data

The panel data structure is the format used for global modeling. In it’s simplest form, Panel Data is a time series dataset that has more than one series. Each time series is stacked row-wise (on-top) of each other.

Panel Data Structure

Traditional Modeling (Iteration)

Traditional modeling techniques like ARIMA can only be used on one time series at a time. The widely accepted forecasting approach is to iterate through each time series producing a unique model and forecast for each time series identifier. The downside with this approach is that it’s expensive when you have many time series. Think of the number of products in a database. As the number of time series approaches the range of 1000-10,000, the iterative approach becomes unscalable.

Problem: 1000 ARIMA Models Needed for 1000 Time Series

Global Modeling

Global Models are alternatives to the iterative approach. A Global Model is a single model that forecasts all time series at once. Global Models are highly scalable, which solves the problem of 1-10,000 time series. An example is an XGBoost Model, which can determine relationships for all 1000 time series panels with a single model.

Solution: A Single XGBOOST Model can Model 1000 Time Series

Importance of Feature Engineering

The downside is that an global approach can be less accurate. To improve accuracy, feature engineering and localized model selection by time series identifier become critical to large-scale forecasting success. We recommend learning feature engineering techniques that are proven to get results in our Time Series Forecasting Course.

Modeling Panel Data

Getting Started

We’ll cover a short tutorial on global forecasting. The first thing to do is to load the following libraries:

library(tidymodels)
library(modeltime)
library(timetk)

library(tidyverse)

Dataset

Next, let’s use the walmart_sales_weekly dataset that comes with timetk.

data_tbl <- walmart_sales_weekly %>%
    select(id, date = Date, value = Weekly_Sales)

data_tbl
#> # A tibble: 1,001 × 3
#>    id    date        value
#>    <fct> <date>      <dbl>
#>  1 1_1   2010-02-05 24924.
#>  2 1_1   2010-02-12 46039.
#>  3 1_1   2010-02-19 41596.
#>  4 1_1   2010-02-26 19404.
#>  5 1_1   2010-03-05 21828.
#>  6 1_1   2010-03-12 21043.
#>  7 1_1   2010-03-19 22137.
#>  8 1_1   2010-03-26 26229.
#>  9 1_1   2010-04-02 57258.
#> 10 1_1   2010-04-09 42961.
#> # ℹ 991 more rows

The dataset is that is already set up for panel data modeling. The important columns are:

“id”: This separates the time series groups (in this case these represent sales from departments in a walmart store)
“date”: This is the weekly sales period
“value”: This is the value for sales during the week and store/department

We can visualize this by time series group to expose the differences in sales by department.

data_tbl %>%
  group_by(id) %>%
  plot_time_series(
    date, value, .interactive = F, .facet_ncol = 2
  )

We can clearly see that there are 7 time series groups with different weekly sales patterns.

Train/Test Splitting

We can split the data into training and testing sets using time_series_split(). We’ll investigate the last 3-months of the year to test a global model on a 3-month forecast. The message on overlapping dates is to let us know that multiple time series are being processed using the last 3-month window for testing.

splits <- data_tbl %>% 
  time_series_split(
    assess     = "3 months", 
    cumulative = TRUE
  )
#> Using date_var: date
#> Data is not ordered by the 'date_var'. Resamples will be arranged by `date`.
#> Overlapping Timestamps Detected. Processing overlapping time series together using sliding windows.

splits
#> <Analysis/Assess/Total>
#> <917/84/1001>

Recipe

Next, we need to preprocess the data. This is where we add good features to imporve our global model performance. We will use the recipes workflow for generating time series features.

step_mutate_at(): Applies a function to one or more columns. Used to remove extra unused levels in our categorical ID column.
step_timeseries_signature(): Used to add calendar features based on our date column
step_rm(): Used to remove the date column. Machine Learning algorithms like XGBoost don’t handle date columns very well.
step_zv(): Used to remove any zero variance features. Features with no variance don’t add useful information to our model.
step_dummy(): Used to convert categorical features to binary one-hot encoded features that algorithms like XGBoost can model more effectively.

This results in 37 derived features for modeling. We can certainly include more features such as lags and rolling features that are known to improve results. These concepts and more are covered in the High-Performance Time Series Course.

rec_obj <- recipe(value ~ ., training(splits)) %>%
    step_mutate_at(id, fn = droplevels) %>%
    step_timeseries_signature(date) %>%
    step_rm(date) %>%
    step_zv(all_predictors()) %>%
    step_dummy(all_nominal_predictors(), one_hot = TRUE)

summary(prep(rec_obj))
#> # A tibble: 38 × 4
#>    variable       type      role      source  
#>    <chr>          <list>    <chr>     <chr>   
#>  1 value          <chr [2]> outcome   original
#>  2 date_index.num <chr [2]> predictor derived 
#>  3 date_year      <chr [2]> predictor derived 
#>  4 date_year.iso  <chr [2]> predictor derived 
#>  5 date_half      <chr [2]> predictor derived 
#>  6 date_quarter   <chr [2]> predictor derived 
#>  7 date_month     <chr [2]> predictor derived 
#>  8 date_month.xts <chr [2]> predictor derived 
#>  9 date_day       <chr [2]> predictor derived 
#> 10 date_mday      <chr [2]> predictor derived 
#> # ℹ 28 more rows

Machine Learning

We’ll create an xgboost workflow by fitting the default xgboost model to our derived features from our in-sample training data set.

Training the global xgboost model takes approximately 50 milliseconds.
Conversely, an ARIMA model might take several minutes to iterate through possible parameter combinations for each of the 7 time series.

# Workflow
wflw_xgb <- workflow() %>%
    add_model(
        boost_tree("regression") %>% set_engine("xgboost")
    ) %>%
    add_recipe(rec_obj) %>%
    fit(training(splits))

wflw_xgb
#> ══ Workflow [trained] ══════════════════════════════════════════════════════════
#> Preprocessor: Recipe
#> Model: boost_tree()
#> 
#> ── Preprocessor ────────────────────────────────────────────────────────────────
#> 5 Recipe Steps
#> 
#> • step_mutate_at()
#> • step_timeseries_signature()
#> • step_rm()
#> • step_zv()
#> • step_dummy()
#> 
#> ── Model ───────────────────────────────────────────────────────────────────────
#> ##### xgb.Booster
#> raw: 46.6 Kb 
#> call:
#>   xgboost::xgb.train(params = list(eta = 0.3, max_depth = 6, gamma = 0, 
#>     colsample_bytree = 1, colsample_bynode = 1, min_child_weight = 1, 
#>     subsample = 1), data = x$data, nrounds = 15, watchlist = x$watchlist, 
#>     verbose = 0, nthread = 1, objective = "reg:squarederror")
#> params (as set within xgb.train):
#>   eta = "0.3", max_depth = "6", gamma = "0", colsample_bytree = "1", colsample_bynode = "1", min_child_weight = "1", subsample = "1", nthread = "1", objective = "reg:squarederror", validate_parameters = "TRUE"
#> xgb.attributes:
#>   niter
#> callbacks:
#>   cb.evaluation.log()
#> # of features: 37 
#> niter: 15
#> nfeatures : 37 
#> evaluation_log:
#>   iter training_rmse
#>  <num>         <num>
#>      1     46315.130
#>      2     33003.670
#>    ---           ---
#>     14      3554.521
#>     15      3423.419

Modeltime Workflow

We’ll step through the modeltime workflow, which is used to test many different models on the time series and organize the entire process.

Modeltime Workflow

Step 1: Create a Modeltime Table

The first step is to create a Modeltime Table with modeltime_table().

model_tbl <- modeltime_table(
    wflw_xgb
)

model_tbl
#> # Modeltime Table
#> # A tibble: 1 × 3
#>   .model_id .model     .model_desc
#>       <int> <list>     <chr>      
#> 1         1 <workflow> XGBOOST

Step 2: Calibrate by ID

Next, we need to calibrate, which calculates the forecast error on our test set. Use modeltime_calibrate() to perform calibration. Note that when we add the id, we are able to track the the out-of-sample residual error by the “id” column.

calib_tbl <- model_tbl %>%
    modeltime_calibrate(
      new_data = testing(splits), 
      id       = "id"
    )

calib_tbl
#> # Modeltime Table
#> # A tibble: 1 × 5
#>   .model_id .model     .model_desc .type .calibration_data
#>       <int> <list>     <chr>       <chr> <list>           
#> 1         1 <workflow> XGBOOST     Test  <tibble [84 × 5]>

Step 3: Measure Test Accuracy

Next, we measure the global and local accuracy on the global model.

Global Accuracy

The default is modeltime_accuracy(acc_by_id = FALSE), which returns a global model accuracy.

calib_tbl %>% 
    modeltime_accuracy(acc_by_id = FALSE) %>% 
    table_modeltime_accuracy(.interactive = FALSE)

.model_id	.model_desc	.type	mae	mape	mase	smape	rmse	rsq
Accuracy Table
1	XGBOOST	Test	3698.69	8.3	0.11	8.17	5059.45	0.98

Local Accuracy

By toggling modeltime_accuracy(acc_by_id = TRUE), we can obtain the local model accuracy. This can be useful for identifying specifically which time series the model does well on (and which it does poorly on). We can then apply model selection logic to select specific global models for specific IDs.

calib_tbl %>% 
    modeltime_accuracy(acc_by_id = TRUE) %>% 
    table_modeltime_accuracy(.interactive = FALSE)

.model_id	.model_desc	.type	id	mae	mape	mase	smape	rmse	rsq
Accuracy Table
1	XGBOOST	Test	1_1	2125.99	10.83	1.59	10.30	2596.97	0.50
1	XGBOOST	Test	1_3	3397.33	18.67	0.57	17.60	4048.49	0.91
1	XGBOOST	Test	1_8	2086.84	5.45	0.95	5.62	2283.70	0.67
1	XGBOOST	Test	1_13	1596.47	3.86	0.70	3.96	1913.82	0.53
1	XGBOOST	Test	1_38	8345.09	10.77	1.03	10.99	9685.67	0.01
1	XGBOOST	Test	1_93	4278.75	5.37	0.42	5.57	5440.12	0.75
1	XGBOOST	Test	1_95	4060.36	3.14	0.51	3.18	4875.10	0.65

Step 4: Forecast the Test Data

Next, we need to forecast the test dataset. This is useful to evaluate the model using a sampling of the time series within the panel dataset. We use modeltime_forecast(conf_by_id = TRUE) to allow the confidence intervals (prediction intervals) to be calculated by time series identifier. Note, that the modeltime_calibrate() must have been performed with an id specified.

calib_tbl %>%
    modeltime_forecast(
        new_data    = testing(splits),
        actual_data = data_tbl,
        conf_by_id  = TRUE
    ) %>%
    group_by(id) %>%
    plot_modeltime_forecast(
        .facet_ncol  = 3,
        .interactive = FALSE
    )

Step 5: Refit and Forecast the Future

We see that our global model performs well on this dataset. Now, we will forecast the future.

Refit the Models

The refitting step is needed to incorporate the most recent information into our models. We use modeltime_refit() to update the model(s) in our modeltime tables.

refit_tbl <- calib_tbl %>%
  modeltime_refit(data = data_tbl)

refit_tbl
#> # Modeltime Table
#> # A tibble: 1 × 5
#>   .model_id .model     .model_desc .type .calibration_data
#>       <int> <list>     <chr>       <chr> <list>           
#> 1         1 <workflow> XGBOOST     Test  <tibble [84 × 5]>

Future Data

Next, make a future dataset using future_frame() from timetk, which creates future time stamps that extend 52-weeks into the future for each ID in the same panel structure needed for our global forecast model.

future_tbl <- data_tbl %>%
  group_by(id) %>%
  future_frame(.length_out = 52, .bind_data = FALSE)

future_tbl
#> # A tibble: 364 × 2
#> # Groups:   id [7]
#>    id    date      
#>    <fct> <date>    
#>  1 1_1   2012-11-02
#>  2 1_1   2012-11-09
#>  3 1_1   2012-11-16
#>  4 1_1   2012-11-23
#>  5 1_1   2012-11-30
#>  6 1_1   2012-12-07
#>  7 1_1   2012-12-14
#>  8 1_1   2012-12-21
#>  9 1_1   2012-12-28
#> 10 1_1   2013-01-04
#> # ℹ 354 more rows

Future Predictions

Finally, we can forecast the future using our future data.

refit_tbl %>%
  modeltime_forecast(
    new_data    = future_tbl,
    actual_data = data_tbl, 
    conf_by_id  = TRUE
  ) %>%
  group_by(id) %>%
  plot_modeltime_forecast(
    .interactive = F,
    .facet_ncol  = 2
  )

Summary

We’ve now successfully completed a Global Forecast. You may find this challenging, especially if you are not familiar with the Modeltime Workflow, terminology, or tidymodeling in R. If this is the case, we have a solution. Take our high-performance forecasting course.

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High-Performance Time Series Course

Time Series is Changing

Time series is changing. Businesses now need 10,000+ time series forecasts every day. This is what I call a High-Performance Time Series Forecasting System (HPTSF) - Accurate, Robust, and Scalable Forecasting.

High-Performance Forecasting Systems will save companies by improving accuracy and scalability. Imagine what will happen to your career if you can provide your organization a “High-Performance Time Series Forecasting System” (HPTSF System).

How to Learn High-Performance Time Series Forecasting

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Time Series Machine Learning (cutting-edge) with Modeltime - 30+ Models (Prophet, ARIMA, XGBoost, Random Forest, & many more)
Deep Learning with GluonTS (Competition Winners)
Time Series Preprocessing, Noise Reduction, & Anomaly Detection
Feature engineering using lagged variables & external regressors
Hyperparameter Tuning
Time series cross-validation
Ensembling Multiple Machine Learning & Univariate Modeling Techniques (Competition Winner)
Scalable Forecasting - Forecast 1000+ time series in parallel
and more.

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