Python implementations of time series forecasting and anomaly detection

Date

7 October 2022

Topics

Python

forecasting

anomalies

hts

Regular readers will know that I develop statistical models and algorithms, and I write R implementations of them. I’m often asked if there are also Python implementations available. There are.

Nixtla

The best Python implementations for my time series methods are available from Nixtla. Here are some of their packages related to my work, all compatible with scikit-learn.

statsforecast: Automatic ARIMA and ETS forecasting (Hyndman et al., 2002; Hyndman & Khandakar, 2008).
hierarchicalforecast: Hierarchical forecasting (Hyndman et al., 2011; Wickramasuriya et al., 2019).
tsfeatures: Time series features (Kang et al., 2017; Montero-Manso et al., 2020; T. S. Talagala et al., 2023).

They have also produced a lot of other great time series tools that are fast (optimized using numba) and perform well compared to various alternatives.

GluonTS

GluonTS from Amazon is excellent and provides lots of probabilistic time series forecasting models, with wrappers to some of my R code, and statsforecast from Nixtla. The other models in GluonTS are also well worth exploring.

Merlion

Merlion from Salesforce is another interesting python library which includes both my automatic ARIMA and automatic ETS algorithms, along with other forecasting methods. It also has some anomaly detection methods for time series.

pmdarima

The first attempt to port my auto.arima() function to Python was pmdarima.

sktime

sktime has the most complete set of time series methods for Python including

AutoARIMA: (Hyndman & Khandakar, 2008);
ETS: (Hyndman et al., 2002);
BATS/TBATS: (De Livera et al., 2011);
Theta: (Assimakopoulos & Nikolopoulos, 2000; Hyndman & Billah, 2003);
STLForecaster: (Bandara et al., 2025);
Croston: (Shenstone & Hyndman, 2005);
Bagged-ETS: (Bergmeir et al., 2016);

and more. These are also compatible with scikit-learn.

Recently, Kate Buchhorn has ported some of my anomaly detection algorithms to Python and made them available in sktime including:

STRAY: High-dimensional anomaly detection (P. D. Talagala et al., 2021).
DOBIN: Dimension reduction for anomaly detection (Kandanaarachchi & Hyndman, 2021).

statsmodels

The statsmodels collection includes a few functions based on my work:

ETS: (Hyndman et al., 2002);
Theta: (Assimakopoulos & Nikolopoulos, 2000; Hyndman & Billah, 2003);
MSTL: (Bandara et al., 2025);
functional boxplot: (Hyndman & Shang, 2010);
functional HDR boxplot: (Hyndman & Shang, 2010);
rainbowplot: (Hyndman & Shang, 2010).

pyhts

Bohan Zhang has produced pyhts, a re-implementation of the hts package in Python, based on Hyndman et al. (2011), Hyndman et al. (2016) and Wickramasuriya et al. (2019).

Darts

Darts is a Python library for wrangling and forecasting time series. It includes wrappers for ETS, ARIMA and other models from statsforecast and pmdarima, and some reconciliation functionality.

References

Assimakopoulos, V., & Nikolopoulos, K. (2000). The theta model: A decomposition approach to forecasting. International Journal of Forecasting, 16(4), 521–530. https://doi.org/10.1016/S0169-2070(00)00066-2

Bandara, K., Hyndman, R. J., & Bergmeir, C. (2025). MSTL: A seasonal-trend decomposition algorithm for time series with multiple seasonal patterns. International J Operational Research, 52(1). https://doi.org/10.1504/IJOR.2022.10048281

Bergmeir, C., Hyndman, R. J., & Benítez, J. M. (2016). Bagging exponential smoothing methods using STL decomposition and Box-Cox transformation. International J Forecasting, 32(2), 303–312. https://doi.org/10.1016/j.ijforecast.2015.07.002

De Livera, A. M., Hyndman, R. J., & Snyder, R. D. (2011). Forecasting time series with complex seasonal patterns using exponential smoothing. J American Statistical Association, 106(496), 1513–1527. https://doi.org/10.1198/jasa.2011.tm09771

Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., & Shang, H. L. (2011). Optimal combination forecasts for hierarchical time series. Computational Statistics & Data Analysis, 55(9), 2579–2589. https://doi.org/10.1016/j.csda.2011.03.006

Hyndman, R. J., & Billah, M. B. (2003). Unmasking the theta method. International J Forecasting, 19(2), 287–290. https://doi.org/10.1016/S0169-2070%2801%2900143-1

Hyndman, R. J., & Khandakar, Y. (2008). Automatic time series forecasting: The forecast package for R. J Statistical Software, 27(3), 1–22.

Hyndman, R. J., Koehler, A. B., Snyder, R. D., & Grose, S. (2002). A state space framework for automatic forecasting using exponential smoothing methods. International J Forecasting, 18(3), 439–454. https://doi.org/10.1016/S0169-2070%2801%2900110-8

Hyndman, R. J., Lee, A., & Wang, E. (2016). Fast computation of reconciled forecasts for hierarchical and grouped time series. Computational Statistics & Data Analysis, 97, 16–32. https://doi.org/10.1016/j.csda.2015.11.007

Hyndman, R. J., & Shang, H. L. (2010). Rainbow plots, bagplots and boxplots for functional data. J Computational & Graphical Statistics, 19(1), 29–45. https://doi.org/10.1198/jcgs.2009.08158

Kandanaarachchi, S., & Hyndman, R. J. (2021). Dimension reduction for outlier detection using DOBIN. J Computational & Graphical Statistics, 30(1), 204–219. https://doi.org/10.1080/10618600.2020.1807353

Kang, Y., Hyndman, R. J., & Smith-Miles, K. (2017). Visualising forecasting algorithm performance using time series instance spaces. International J Forecasting, 33(2), 345–358. https://doi.org/10.1016/j.ijforecast.2016.09.004

Montero-Manso, P., Athanasopoulos, G., Hyndman, R. J., & Talagala, T. S. (2020). FFORMA: Feature-based forecast model averaging. International J Forecasting, 36(1), 86–92. https://doi.org/10.1016/j.ijforecast.2019.02.011

Shenstone, L., & Hyndman, R. J. (2005). Stochastic models underlying croston’s method for intermittent demand forecasting. J Forecasting, 24(6), 389–402. https://doi.org/10.1002/for.963

Talagala, P. D., Hyndman, R. J., & Smith-Miles, K. (2021). Anomaly detection in high-dimensional data. J Computational & Graphical Statistics, 30(2), 360–374. https://doi.org/10.1080/10618600.2020.1807997

Talagala, T. S., Hyndman, R. J., & Athanasopoulos, G. (2023). Meta-learning how to forecast time series. J Forecasting, 42(6), 1476–1501. https://doi.org/10.1002/for.2963

Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2019). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. J American Statistical Association, 114(526), 804–819. https://doi.org/10.1080/01621459.2018.1448825