Panel Data Tutorial Overview

This is an advanced tutorial. Working with Panel Data requires working with multiple time series groups at the same time, and you need to be comfortable setting up the datasets required to generate training sets and forecast sets. I cover working with Panel Data and Time Series Groups in my High-Performance Time Series Course.

Libraries

Load the following R packages.

library(tidymodels)
library(modeltime)
library(modeltime.resample)
library(timetk)
library(tidyverse)
library(tidyquant)

Data

We’ll use the walmart_sales_weekly dataset from timetk. This contains 7 time series groups, which correspond to the revenue over time for seven departments in one Walmart Store.

walmart_sales_weekly %>%
  group_by(id) %>%
  plot_time_series(Date, Weekly_Sales, .facet_ncol = 3, .interactive = FALSE)

Data Preparation

We’ll create 2 datasets that incorporate a grouping variable:

• Training Data Set, data_prepared_tbl: Dataset that contains information on the training region for each time series group

• Forecast Data Set, future_tbl: Dataset that contains information on the forecast region for each time series group. We’ll extend each time series group by "3 months" based on the business forecast needs.

# Full = Training + Forecast Datasets
full_data_tbl <- walmart_sales_weekly %>%
  select(id, Date, Weekly_Sales) %>%
  
  # Apply Group-wise Time Series Manipulations
  group_by(id) %>%
  future_frame(
    .date_var   = Date,
    .length_out = "3 months",
    .bind_data  = TRUE
  ) %>%
  ungroup() %>%
  
  # Consolidate IDs
  mutate(id = droplevels(id))

# Training Data
data_prepared_tbl <- full_data_tbl %>%
  filter(!is.na(Weekly_Sales))

# Forecast Data
future_tbl <- full_data_tbl %>%
  filter(is.na(Weekly_Sales))

Resampling Panel Data

The first step is to make a resample strategy. Our business objective is to forecast 3 months so we’ll use time_series_cv() with the following strategy:

• assess: 3 months. Corresponds to our business objective.
• skip: 3 months. Use 3 months to avoid overlapping assessment sets.
• cumulative: TRUE. Maximizes the Training Set (alternatively we could do initial = “18 months” to have sliding training sets)
• slice_limit: 6. Keep the 6 largest train/test resamples to prevent too few observations. If we go below one full year, we will not be able to take advantage of the week of the year feature.

This generates 6 resample sets.

walmart_tscv <- data_prepared_tbl %>%
  time_series_cv(
    date_var    = Date, 
    assess      = "3 months",
    skip        = "3 months",
    cumulative  = TRUE,
    slice_limit = 6
  )

walmart_tscv

## # Time Series Cross Validation Plan 
## # A tibble: 6 × 2
##   splits           id    
##   <list>           <chr> 
## 1 <split [917/84]> Slice1
## 2 <split [833/84]> Slice2
## 3 <split [749/84]> Slice3
## 4 <split [665/84]> Slice4
## 5 <split [581/84]> Slice5
## 6 <split [497/84]> Slice6

We can visualize the resample sets with plot_time_series_cv_plan(). They look a little crazy because there are multiple time series groups. The important thing is to make sure the red and blue parts line up as expected in relation to our sampling strategy.

walmart_tscv %>%
  tk_time_series_cv_plan() %>%
  plot_time_series_cv_plan(Date, Weekly_Sales, 
                           .facet_ncol = 2, .interactive = F)

Modeling

We’ll create:

• 1 Recipe: This applies engineered features from calendar variables

• 3 Fitted Models: Prophet, XGBoost, and Prophet Boost fitted on the data_prepared_tbl dataset

recipe_spec <- recipe(Weekly_Sales ~ ., 
                      data = training(walmart_tscv$splits[[1]])) %>%
  step_timeseries_signature(Date) %>%
  step_rm(matches("(.iso$)|(.xts$)|(day)|(hour)|(minute)|(second)|(am.pm)")) %>%
  step_mutate(Date_week = factor(Date_week, ordered = TRUE)) %>%
  step_dummy(all_nominal(), one_hot = TRUE)

wflw_fit_prophet <- workflow() %>%
  add_model(
    prophet_reg() %>% set_engine("prophet") 
  ) %>%
  add_recipe(recipe_spec) %>%
  fit(training(walmart_tscv$splits[[1]]))

wflw_fit_xgboost <- workflow() %>%
  add_model(
    boost_tree("regression") %>% set_engine("xgboost") 
  ) %>%
  add_recipe(recipe_spec %>% step_rm(Date)) %>%
  fit(training(walmart_tscv$splits[[1]]))

wflw_fit_prophet_boost <- workflow() %>%
  add_model(
    prophet_boost(
      seasonality_daily  = FALSE, 
      seasonality_weekly = FALSE,
      seasonality_yearly = FALSE
    ) %>% 
      set_engine("prophet_xgboost") 
  ) %>%
  add_recipe(recipe_spec) %>%
  fit(training(walmart_tscv$splits[[1]]))

model_tbl <- modeltime_table(
  wflw_fit_prophet,
  wflw_fit_xgboost,
  wflw_fit_prophet_boost
)

model_tbl

## # Modeltime Table
## # A tibble: 3 × 3
##   .model_id .model     .model_desc              
##       <int> <list>     <chr>                    
## 1         1 <workflow> PROPHET W/ REGRESSORS    
## 2         2 <workflow> XGBOOST                  
## 3         3 <workflow> PROPHET W/ XGBOOST ERRORS

Assess a Single Resample Split

We can make a Panel Data forecast, which forecasts all of the time series groups at once. This method is much more efficient than iteratively performing predictions. However, not all time series models respond well to this approach.

# Calibrate using the Test Sample
calibration_tbl <- model_tbl %>%
  modeltime_calibrate(testing(walmart_tscv$splits[[1]]))

# Forecast the Test Sample
forecast_panel_tbl <- calibration_tbl %>%
  modeltime_forecast(
    new_data      = testing(walmart_tscv$splits[[1]]),
    actual_data   = data_prepared_tbl,
    # Keep data allows us keep the ID feature for the time series groups
    keep_data = TRUE
  ) 

We can visualize the Panel Data forecasts on a single split. It’s a bit difficult to tell how each model is performing.

forecast_panel_tbl %>%
  group_by(id) %>%
  plot_modeltime_forecast(
    .facet_ncol  = 3,
    .y_intercept = 0, 
    .interactive = FALSE,
    .title       = "Panel Forecasting | 7 Time Series Groups"
  )

Panel Forecasting | 7 Time Series Groups

Quantifying Prediction Error Over Time

We’ve made predictions, but this doesn’t tell us how the models will do over time. We need to quantify prediction error. To do so, we’ll evaluate our models using time series resamples. This technique involves making resamples across time series windows and refitting our models to the resample data sets, producing predictions, and quantifying the error from the predictions.

resample_results <- model_tbl %>%
  modeltime_fit_resamples(
    resamples = walmart_tscv,
    control   = control_resamples(verbose = FALSE)
  )

resample_results

## # Modeltime Table
## # A tibble: 3 × 4
##   .model_id .model     .model_desc               .resample_results
##       <int> <list>     <chr>                     <list>           
## 1         1 <workflow> PROPHET W/ REGRESSORS     <rsmp[+]>        
## 2         2 <workflow> XGBOOST                   <rsmp[+]>        
## 3         3 <workflow> PROPHET W/ XGBOOST ERRORS <rsmp[+]>

resample_results %>%
  plot_modeltime_resamples(
    .summary_fn  = mean, 
    .point_size  = 3,
    .interactive = FALSE
  )

resample_results %>%
  modeltime_resample_accuracy(summary_fns = list(mean = mean, sd = sd)) %>%
  table_modeltime_accuracy(.interactive = FALSE)

Wrapup

Working with Panel Data can be challenging due to managing multiple models, overlapping time series groups, and multiple resample sets.

Modeltime Resample makes working with Panel Data much easier. We saw how we can evaluate multiple models on varying time series windows. This increased our confidence that selecting either the XGBoost or Prophet Boost models were best for this data.

This is a quick overview of working with Panel Data. To learn how to evaluate Panel Data in-depth, take my High-Performance Time Series Course.