Time Series Lab

Advanced Time Series Forecasting Software

Time Series Lab Articles

The Time Series Lab - Article Series are a collection of articles dedicated to research performed with Time Series Lab software. The scope of the series includes the analysis and forecasting of a wide range of time series in fields including economics, finance, sports, climatology, biology, and health science.

Please contact us if you find a contribution is missing.


For the Main Edition:

How to cite Time Series Lab:
We recommend citing the software as follows, depending on your preferred format:

APA 
Lit, R., Koopman, S. J., & Harvey, A. C. (2025). Time Series Lab (Version 3.0.0) [Computer software]. https://timeserieslab.com
BibTeX 
@misc{lit2025tsl,
  author       = {Rutger Lit and S. J. Koopman and A. C. Harvey},
  title        = {Time Series Lab},
  year         = {2025},
  version      = {3.0.0},
  howpublished = {\url{https://timeserieslab.com}},
  note         = {Computer software}
}

Download BibTeX file

MLA 
Lit, Rutger, et al. Time Series Lab. Version 3.0.0, 2025, https://timeserieslab.com.
Chicago 
Lit, Rutger, S. J. Koopman, and A. C. Harvey. Time Series Lab. Version 3.0.0. 2025. https://timeserieslab.com.

Dynamic Score Edition:

How to cite Time Series Lab:
We recommend citing the software as follows, depending on your preferred format:

APA 
Lit, R., Koopman, S. J., & Harvey, A. C. (2021). Time Series Lab - Score Edition (Version 1.5.0) [Computer software]. https://timeserieslab.com
BibTeX 
@misc{lit2021tsl,
  author       = {Rutger Lit and S. J. Koopman and A. C. Harvey},
  title        = {Time Series Lab - Score Edition},
  year         = {2021},
  version      = {1.5.0},
  howpublished = {\url{https://timeserieslab.com}},
  note         = {Computer software}
}

Download BibTeX file

MLA 
Lit, Rutger, et al. Time Series Lab - Score Edition. Version 1.5.0, 2021, https://timeserieslab.com.
Chicago 
Lit, Rutger, S. J. Koopman, and A. C. Harvey. Time Series Lab - Score Edition. Version 1.5.0. 2021. https://timeserieslab.com.

Sports Statistics Edition:
Lit, R. (2020), Time Series Lab - Sports Statistics Edition: https://timeserieslab.com.

Articles

Articles

July 2, 2025

Climate-Assisted Data-Driven Decadal Snowfall Predictions in the Swiss Foothills

By Nazzareno Diodato, Fredrik Charpentier Ljungqvist, and Gianni Bellocchi

Published on: ResearchGate

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Decadal-scale climate predictability is crucial for societal planning, especially in regions sensitive to winter extremes. This study predicts the number of heavy snowfall days in the Swiss Pre-Alpine Region (SPAR) through 2060, using a time-varying autoregressive model based on data from 1884 to 2023. The model integrates a pattern index combining large-scale (Arctic Oscillation and Dipole Model Index) and regional-scale (spring–winter temperature differential) climate forcings. Results indicate a slight upward trend—about one to two additional heavy snowfall days by the 2050s—though not statistically significant, and consistent with regionally downscaled climate models. After 2045, variability is expected to rise, with periods of snowfall deficits and a cluster of exceedance years emerging toward the end of the projection period. While extreme snowfall events may become less frequent in the Northern Hemisphere, their intensity is unlikely to diminish. These findings improve understanding of snowfall dynamics in SPAR and contribute to broader cryospheric change insights.

March 18, 2025

Climate-driven generative time-varying model for improved decadal storm power predictions in the Mediterranean

By Nazzareno Diodato, Cristina Di Salvo, and Gianni Bellocchi

Published in: Nature - Communications Earth & Environment

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Decadal climate predictions are crucial for communities engaged in scenario planning under Sustainable Development Goals. However, uncertainties in future precipitation extremes hinder climate mitigation and adaptation efforts. Here we present a hybrid statistical climate-driven time-varying model to predict the Areal Mean Storm Erosivity Index, a key indicator of hydrological events, for the Mediterranean region. By integrating historical data (1884–2022) with large-scale (El Niño–Southern Oscillation) and small-scale (precipitation variability) climate forcings, our model captures past storm behavior and projects future dynamics. The Hurst exponent (0.63) suggests a long-term positive memory in the Areal Mean Storm Erosivity Index, enhancing prediction accuracy. Projections show an Index increase until 2040, then a decline until 2050, and a resurgence. While consistent with other regional models at the interdecadal scale, finer variations are less pronounced at the interannual scale. This approach offers valuable insights into hydroclimate variability, aiding climate resilience planning in the Mediterranean and beyond.

December 30, 2023

Forecasting Potato Production in Major South Asian Countries: A Comparative Study of Machine Learning and Time Series Models

By Pradeep Mishra, Abdullah Mohammad Ghazi Al Khatib, Bayan Mohamad Alshaib, Binita Kuamri, Shiwani Tiwari, Aditya Pratap Singh, Shikha Yadav, Divya Sharma, and Prity Kumari

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This study analyzed and forecasted potato production in eight major South Asian countries from 1961 to 2028 using advanced time series and machine learning approaches. Annual potato production data was modelled with autoregressive integrated moving average (ARIMA), state space, and extreme gradient boosting (XGBoost) models. The models were trained on 1961–2009 data and evaluated on a 2010–2021 validation set. On the training set, XGBoost showed the best performance. However, on the validation set, ARIMA and state space models significantly outperformed XGBoost, indicating issues with overfitting. The ARIMA models produced the lowest forecast errors for Afghanistan, Bangladesh, China, and Myanmar. Meanwhile, state space models were optimal for India, Nepal, Pakistan, and Sri Lanka, demonstrating that no one approach was uniformly best. The top performing models forecast potato production up to 2028. These forecasts reflect the different levels of potato demand, consumption, and trade in each country, as well as the effects of climate change, pests, and diseases on potato yields. The rigorous comparative application of advanced time series and machine learning techniques provides valuable data-driven insights into future South Asian potato supply. The forecasts can assist food security planning and agricultural policymaking in the region.

October 17, 2023

Long-range, time-varying statistical prediction of annual precipitation in a Mediterranean remote site

By Nazzareno Diodato, Maria Lanfredi, and Gianni Bellocchi

Published in: Environmental Research - Climate

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In the Mediterranean basin, climate change signals are often representative of atmospheric transients in precipitation patterns. Remote mountaintop rainfall stations are far from human influence and can more easily unveil climate signals to improve the accuracy of long-term forecasts. In this study, the world's longest annual precipitation time series (1884–2021) from a remote station, the Montevergine site (1284 m a.s.l.) in southern Italy, was investigated to explain its forecast performance in the coming decades, offering a representative case study for the central Mediterranean. For this purpose, a Seasonal AutoRegressive-exogenous Time Varying process with Exponential Generalised Autoregressive Conditional Heteroscedasticity (SARX(TVAR)-EGARCH) model was developed for the training period 1884–1991, validated for the interval 1992–2021, and used to make forecasts for the time horizon 2022–2051, with the support of an exogenous variable (dipole mode index). Throughout this forecast period, the dominant feature is the emergence of an incipient and strong upward drought trend in precipitation until 2035. After this change point, rainfall increases again, more slightly, but with considerable values towards the end of the forecast period. Although uncertainties remain, the results are promising and encourage the use of SARX(TVAR)-EGARCH in climate studies and forecasts in mountain sites.

March 1, 2022

Score-Driven Time Series Models

By Andrew Harvey

Published in: Annual Review of Statistics and Its Application

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The construction of score-driven filters for nonlinear time series models is described, and they are shown to apply over a wide range of disciplines. Their theoretical and practical advantages over other methods are highlighted. Topics covered include robust time series modeling, conditional heteroscedasticity, count data, dynamic correlation and association, censoring, circular data, and switching regimes.

December 1, 2021

A Score-Driven Model of Short-Term Demand Forecasting for Retail Distribution Centers

By Henrique Hoeltgebaum, Denis Borenstein, Cristiano Fernandes, and Álvaro Veiga

Published in: Journal of Retailing

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Forecasting is one of the fundamental inputs to support planning decisions in retail chains. Frequently, forecasting systems in retail are based on Gaussian models, which may be highly unrealistic when considering daily retail data. In addition, the majority of these systems rely on point forecasts, limiting their practical use in retailing decisions, which often require the full predictive density for decision making. This paper models daily distribution center (DC) level aggregate demand using score-driven models, or Generalized Autoregressive Score (GAS) models. An experimental study was carried out using real data from a large retail chain in Brazil. A log-normal GAS model is compared to usual benchmarks, including neural networks, linear regression, and exponential smoothing. The results show that the GAS model is a competitive alternative for retail demand forecasting at daily frequency, with the advantage of producing a closed-form predictive density by construction.

October 5, 2020

Estimation of final standings in football competitions with premature ending: the case of COVID-19

By Paolo Gorgi, Siem Jan Koopman, and Rutger Lit

Published in: Advances in Statistical Analysis

  |   PDF   |   Citation   |   Data

We study an alternative approach to determine the final league table in football competitions with a premature ending. For several countries, a premature ending of the 2019/2020 football season has occurred due to the COVID-19 pandemic. We propose a model-based method as a possible alternative to the use of the incomplete standings to determine the final table. This method measures the performance of the teams in the matches of the season that have been played and predicts the remaining non-played matches through a paired-comparison model. The main advantage of the method compared to the incomplete standings is that it takes account of the bias in the performance measure due to the schedule of the matches in a season. Therefore, the resulting ranking of the teams based on our proposed method can be regarded as more fair in this respect. A forecasting study based on historical data of seven of the main European competitions is used to validate the method. The empirical results suggest that the model-based approach produces more accurate predictions of the true final standings than those based on the incomplete standings.

August 25, 2020

Time Series Models Based on Growth Curves with Applications to Forecasting Coronavirus

By Andrew Harvey and Paul Kattuman

Published in: Harvard Data Science Review

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Time series models are developed for predicting future values of a variable that when cumulated is subject to an unknown saturation level. Such models are relevant for many disciplines, but here attention is focused on the spread of epidemics and the applications are for coronavirus. The time series models are relatively simple but are such that their specification can be assessed by standard statistical test procedures. In the generalized logistic class of models, the logarithm of the growth rate of the cumulative series depends on a time trend. Allowing this trend to be time-varying introduces further flexibility and enables the effects of changes in policy to be tracked and evaluated.

June 8, 2020: Updated version

Forecasting the VIX in the midst of COVID-19

By Rutger Lit

  |   PDF   |   Citation   |   Supplemental   |  

April 14, 2020

PDF
We study the behavior of the Volatility Index (VIX) time series in the period leading up to the COVID-19 outbreak. Time-varying location/scale models are used to extract a range of time-varying components from the VIX time series. The time-varying components are driven by the score of the predictive density. These so called score-driven models have proven to be powerful in extracting time-varying components like autoregressive processes and seasonal patterns. A range of model specifications is used to forecast the VIX in the COVID-19 period that spans the first quarter of 2020. Explanatory variables are used to improve in-sample model fit and out-of-sample forecast accuracy. All model computations are carried out with the Time Series Lab software package.

May 18, 2020

Coronavirus and the Score-driven Negative Binomial Distribution

By Andrew Harvey and Rutger Lit

  |   PDF   |   Citation   |   Data

A new class of time series models, developed by Harvey and Kattuman (2020), is designed to predict variables which when cumulated are subject to an unknown saturation level. Such models are relevant for many disciplines, but the applications here are for deaths from coronavirus. When numbers are small a score-driven Negative Binomial model can be used. It is shown how such models can be estimated with the Time Series Lab software package and their specification assessed by statistical tests and graphics.

May 11, 2020

Forecasting the 2020 edition of the Boat Race

By Rutger Lit and Siem Jan Koopman

  |   PDF   |   Citation   |   Data

We study the annual outcome of the Boat Race between Oxford and Cambridge and forecast the 2020 edition which was cancelled due to the COVID-19 outbreak. We find a strong presence of cyclical behaviour in the time series dynamics and model it through an autoregressive process with score-driven innovations. The inclusion of explanatory variables improve the fit of the time series further. In particular, the weight difference between the rowers in the boats of the two universities is a statistically significant predictor. All model computations are performed with the Time Series Lab software package and can be easily replicated.