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 highperformance 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 forloop 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 rowwise (ontop) of each other.
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 100010,000, the iterative approach becomes unscalable.
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 110,000 time series. An example is an XGBoost Model, which can determine relationships for all 1000 time series panels with a single model.
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 largescale forecasting success. We recommend learning feature engineering techniques that are proven to get results in our Time Series Forecasting Course.
Getting Started
We’ll cover a short tutorial on global forecasting. The first thing to do is to load the following libraries:
Dataset
Next, let’s use the walmart_sales_weekly
dataset that comes with timetk
.
data_tbl < walmart_sales_weekly %>%
select(id, Date, Weekly_Sales) %>%
set_names(c("id", "date", "value"))
data_tbl
#> # A tibble: 1,001 × 3
#> id date value
#> <fct> <date> <dbl>
#> 1 1_1 20100205 24924.
#> 2 1_1 20100212 46039.
#> 3 1_1 20100219 41596.
#> 4 1_1 20100226 19404.
#> 5 1_1 20100305 21828.
#> 6 1_1 20100312 21043.
#> 7 1_1 20100319 22137.
#> 8 1_1 20100326 26229.
#> 9 1_1 20100402 57258.
#> 10 1_1 20100409 42961.
#> # … with 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 3months of the year to test a global model on a 3month forecast. The message on overlapping dates is to let us know that multiple time series are being processed using the last 3month 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 columnstep_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 onehot 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 HighPerformance 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> <chr> <chr> <chr>
#> 1 value numeric outcome original
#> 2 date_index.num numeric predictor derived
#> 3 date_year numeric predictor derived
#> 4 date_year.iso numeric predictor derived
#> 5 date_half numeric predictor derived
#> 6 date_quarter numeric predictor derived
#> 7 date_month numeric predictor derived
#> 8 date_month.xts numeric predictor derived
#> 9 date_day numeric predictor derived
#> 10 date_mday numeric predictor derived
#> # … with 28 more rows
Machine Learning
We’ll create an xgboost
workflow by fitting the default xgboost model to our derived features from our insample 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: 46.5 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
#> 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.
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 outofsample 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)
Accuracy Table  
.model_id  .model_desc  .type  mae  mape  mase  smape  rmse  rsq 

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)
Accuracy Table  
.model_id  .model_desc  .type  id  mae  mape  mase  smape  rmse  rsq 

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 52weeks 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 20121102
#> 2 1_1 20121109
#> 3 1_1 20121116
#> 4 1_1 20121123
#> 5 1_1 20121130
#> 6 1_1 20121207
#> 7 1_1 20121214
#> 8 1_1 20121221
#> 9 1_1 20121228
#> 10 1_1 20130104
#> # … with 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 highperformance forecasting course.
Take the HighPerformance Forecasting Course
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HighPerformance 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 HighPerformance Time Series Forecasting System (HPTSF)  Accurate, Robust, and Scalable Forecasting.
HighPerformance Forecasting Systems will save companies by improving accuracy and scalability. Imagine what will happen to your career if you can provide your organization a “HighPerformance Time Series Forecasting System” (HPTSF System).
How to Learn HighPerformance Time Series Forecasting
I teach how to build a HPTFS System in my HighPerformance Time Series Forecasting Course. You will learn:

Time Series Machine Learning (cuttingedge) 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 crossvalidation
 Ensembling Multiple Machine Learning & Univariate Modeling Techniques (Competition Winner)
 Scalable Forecasting  Forecast 1000+ time series in parallel
 and more.
Become the Time Series Expert for your organization.