Introducing Modeltime Recursive: Tidy Autoregressive Forecasting with Lags
Written by Matt Dancho and Alberto González Almuiña on April 8, 2021
I’m super excited to introduce modeltime::recursive()
, the new autoregressive forecast solution that allows you to convert any tidymodels
regression algorithm into an autoregressive forecasting algorithm. Think of Recursive as a Lag Management Tool.
The new Autoregressive Machine Learning (ARML) Forecasting Solution handles lags for one or more time series and was just greatly improved in Modeltime 0.5.0 (just released 🎉). This Tidy Forecasting Tutorial introduces modeltime::recursive()
: our new Tidy Autoregressive Forecast Solution.
 We’ll quickly introduce you to the challenges with Autoregressive Modeling.
 Then, we’ll showcase
modeltime::recursive()
in the Tidy Autoregressive Forecast Tutorial.
If you like what you see, I have an Advanced Time Series Course where you will learn the foundations of the growing Modeltime Ecosystem.
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The Problem with Autoregressive Forecasting: Lags make Missing Values
Forecasting with autoregressive features is a challenge. The problem is that Lags make missing values that show up as NA
.
This isn’t a new problem. Algorithms like ARIMA have been managing this internally for one time series at a time for decades. But, they’ve only been doing it for one time series at a time forcing us to loop through every time series for prediction. This iterative approach is not scalable with modern machine learning.
The new challenge is how do we manage this for multiple time series? If you have more than one time series, this quickly becomes a forecasting nightmare that will make your head spin. Then multiply this by the number of different modeling algorithms you want to experiment with, and, well, you get the picture…
Enter modeltime::recursive()
: A new function that is capable of turning any Tidymodels regression algorithm into an autoregressive forecaster.
It’s a Lag Management Tool that handles the lagged predictions on one or more time series.
Solution: modeltime::recursive()
Autoregressive forecasting with lag management.
Modeltime 0.5.0 includes a new and improved modeltime::recursive()
function that turns any tidymodels
regression algorithm into an autoregressive forecaster.
✅ HassleFree
Recursive is a new way to manage lagged regressors used in autoregressive forecasting.
✅ Any Tidymodel can become Autoregressive.
Recursive can be used with any regression model that is part of the tidymodels ecosystem (e.g. XGBoost, Random Forest, GLMNET).
✅ Works with Multiple Time Series.
Recursive works on single time series and multiple time series (panel data).
✅ Works with Ensembles.
Recursive can also be used in Ensembles (Recursive Ensembles) with modeltime.ensemble
0.4.0 (just released, yay! 🎉).
What do you need to do to get Recursive?
Simply upgrade to modeltime
and modeltime.ensemble
. Both were just released to CRAN.
This version of the tutorial uses the “development version” of both packages. We are improving this software a lot as we grow the Modeltime Ecosystem. If you’d like to install the development version with the latest features:
Autoregressive Forecast Tutorial
Combine recursive()
with Modeltime Ensemble
Here’s what we’re making:
 A Recursive Ensemble with
modeltime.ensemble
0.4.0  That uses two submodels: 40% GLMNET and 60% XGBOOST
 With Lags 124 as the main features using
modeltime::recursive()
to manage the process  We will forecast 24 months (2years) using lags < forecast horizon
Get the Cheat Sheet
As you go through this tutorial, you will see many references to the Ultimate R Cheat Sheet. The Ultimate R Cheatsheet covers the Modeltime Forecasting Ecosystem with links to key documentation. You can download the Ultimate R Cheat Sheet for free.
Download the Ultimate R Cheat Sheet (Free)
We’ll be focusing on three key packages: timetk
, modeltime
and modeltime.ensemble
. Links to the documentation are included in the cheat sheet (every package has a hyperlink, and some even have “CS” links to their cheat sheets).
Forecasting Ecosystem Links (Ultimate R Cheat Sheet)
80/20 Recursive Terminology
Things you’ll want to be aware of as we go through this tutorial
Autoregressive Forecast
This is an Autoregressive Forecast. We are using shortterm lags (Lags < Forecast Horizon). These shortterm lags are the key features of the model. They are powerful predictors, but they create missing values (NA
) in the future data. We use modeltime::recursive()
to manage predictions, updating lags.
Panel Data
We are processing MultiTime Series using a single model. The model processes in batches (panels) that are separated by an ID feature. This is a scalable approach to modeling many time series.
Recursive Forecasting

The model will predict (forecast) iteratively in batches (1 time stamp x 4 time series = 4 predictions) per loop.

The iteration continues until all 24 future time stamps have been predicted.
This process is highly scalable. The loop size is determined by the forecast horizon, and not the number of time series. So if you have 1000 time series, but your forecast horizon is only 24 months, the recursive prediction loop is only 24 iterations.
Transformer Function
During this iterative process, a transformer function is used to create lagged values. We are responsible for defining the transformer function, but we have a lot of tools in timetk
that help us create the Transformer Function:
 You’ll see
tk_augment_lags()
.  There is also
tk_augment_slidify()
and more.
Libraries
First, we need to load the necessary libraries:
Dataset
We’ll use the m4_monthly
dataset, which has four monthly time series:
 This is a single data frame
 That contains 4 time series
 Each time series is identified with an “id”
 The date and value columns specify the timestamp data and the target (feature we are predicting)
We can get a visual using timetk::plot_time_series()
. Refer to the Ultimate R Cheat Sheet for documentation under time series visualization.
We can get a sense of the structure of the data.
 The “id” feature separates the panels.
 The “date” feature contains the timestamp information
 The “value” feature is our target for prediction (forecasting)
Extend with future_frame()
First, we select a forecast horizon of 24 days and extend the data frame with the function future_frame()
that comes from the timetk
package (Refer to the Ultimate R Cheat Sheet).

We do this to create a future dataset, which we can distinguish because its values will be
NA
. 
The data has been extended by 24 x 4 = 96 rows.
Transformer Function
Then we create a Transformer Function that will be in charge of generating the lags for each time series up to each forecasting horizon. Note that this time we use grouped lags to generate lags by group. This is important when we have multiple time series. Make sure to ungroup after the lagging process.
Then, we apply the function and divide the data into training and future set. Note that the tail of the data has NA
values in the lagged regressors, which makes the problem a Recursive Forecasting problem.
Data Split
We split into training data and future data.
 The train data is prepared for training.
 The future data will be used later when we forecast.
Training the Submodels
Next, we are going to create two models that we will then join into an ensemble.

The first model is an Elastic Net (GLMNET) model: An elastic net applies is an improved version of linear regression that applies a penalty to the lagged regressors preventing bad lags from dominating the results. This can show an improvement versus a standard Linear Regression.

The second model is an XGBOOST model: An xgboost model is a treebased algorithm that is very different in how it models vs a linear model. It’s much better for nonlinear data (e.g. seasonality).
Create a Recursive Ensemble
The next step is to create an ensemble with modeltime.ensemble
(Refer to the Ultimate R Cheat Sheet).
We’ll use a Weighted Ensemble ensemble_weighted()
with a 40/60 loading (GLMNETtoXGBOOST).
Right after that we use the recursive()
function to create the recursive model:

transform
: The transform function gets passed torecursive
, which tells the predictions how to generate the lagged features 
train_tail
: We have to use thepanel_tail()
function to create the train_tail by group. 
id
: This indicates how the time series panels are grouped within the incoming dataset.
Modeltime Table
Next, we add the recursive ensemble to the modeltime_table()
, which organizes one or more models prior to forecasting. Refer to the Ultimate R Cheat Sheet for the full Modeltime Documentation with Workflow.
Forecast the Ensemble
Finally, we forecast over our dataset and visualize the forecast by following the Modeltime Workflow.
 Use
modeltime_forecast()
to make the forecast  Use
plot_modeltime_forecast()
to visualize the predictions
It gets better
You’ve just scratched the surface, here’s what’s coming…
The Modeltime Ecosystem functionality is much more featurerich than what we’ve covered here (I couldn’t possibly cover everything in this post). 😀
Here’s what I didn’t cover:

Feature Engineering: We can make this forecast much more accurate by including features from competitionwinning strategies

Hyperparameter Tuning for Time Series: We can vastly improve our models by tuning them, but you need to understand how to tune for time series.

Deep Learning: We can use GluonTS Deep Learning for developing highperformance, scalable forecasts.
So how are you ever going to learn time series analysis and forecasting?
You’re probably thinking:
 There’s so much to learn
 My time is precious
 I’ll never learn time series
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 Time Series Foundations  Visualization, Preprocessing, Noise Reduction, & Anomaly Detection
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Project Roadmap, Future Work, and Contributing to Modeltime
Modeltime is a growing ecosystem of packages that work together for forecasting and time series analysis. Here are several useful links:

Modeltime Ecosystem Roadmap on GitHub  See the past development and future trajectory. Did we miss something? Make a suggestion.

Business Science data science blog  I announce all Modeltime Software happenings
Acknowledgements
I’d like to acknowledge several Business Science University students that are part of the BSU Modeltime Dev Team that have helped develop modeltime::recursive()
. There efforts are truly appreciated.
 Alberto González Almuiña has helped BIG TIME with development of
modeltime::recursive()
contributing the panel forecast software design.
Have questions about Modeltime Recursive?
Make a comment in the chat below. 👇
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for your business, it’s a nobrainer  Join my Time Series Course.