Haruspicy 2.0

Time series prediction niceties, where what needs to be predicted is the future. Filed under forecasting because in machine learning terminology, prediction is a general term that does not imply extrapolation into the future necessarily.

🏗 handball to Rob Hyndman.

Model selection

Rob Hyndman explains how to cross-validate time series models that use only the lagged observations. Cosma Shalizi mentions the sample splitting problem for time series for post-selection inference and has supervised students to do some work with it, notably (Lunde 2019).

For a different emphasis upon the same problem consider statistical learning theory.


Not comprehensive, just noting some useful here as I encounter them.

Hyndman lab tidyverse time series analysis and forecasting packages

A good first stop.

You can find a presentation on these tools by Rob Hyndman.

  • tsibble: Tidy Temporal Data Frames and Tools [CRAN]
  • tsibbledata: Example datasets for tsibble [CRAN]
  • feasts: Feature Extraction And Statistics for Time Series [CRAN]
  • fable: Forecasting Models for Tidy Time Series [CRAN]
  • sugrrants: Supporting Graphs for Analysing Time Series. Tools for plotting temporal data using the tidyverse and grammar of graphics framework. [CRAN]
  • gravitas: Explore Probability Distributions for Bivariate Temporal Granularities. [CRAN]


prophet (R/Python/Stan):

is a procedure for forecasting time series data. It is based on an additive model where non-linear trends are fit with yearly and weekly seasonality, plus holidays. It works best with daily periodicity data with at least one year of historical data. Prophet is robust to missing data, shifts in the trend, and large outliers.

Causal impact

🏗 find out how Causal impact works. (Based on Brodersen et al. (2015).)



Automatic Smoothing for Attention Prioritization in Time Series

ASAP automatically smooths time series plots to remove short-term noise while retaining large-scale deviations.

micropredictions is a quixotic project my colleagues have forwarded to me. Included here as a spur. Their FAQ says:

What’s microprediction you say?

The act of making thousands of predictions of the same type over and over again. Microprediction can

  • Clean and enrich live data
  • Alert you to outliers and anomalies
  • Provide you short term forecasts
  • Identify patterns in model residuals

Moreover it can be combined with patterns from Control Theory and Reinforcement Learning to

  • Engineer low cost but tailored intelligent applications

Often enough AI is microprediction, albeit bundled with other mathematical or application logic.

  1. You publish a live data value.
  2. The sequence of these values gets predicted by a swarm of algorithms.
  3. Anyone can write a crawler that tries to predict many different streams.

Microprediction APIs make it easy to:

  • Separate the act of microprediction from other application logic.
  • Invite contribution from other people and machines
  • Benefit from other data you may never have considered.

… Seamless data and algorithm reuse is accomplished here.

  1. Algorithms crawl from one stream to another.
  2. Algorithms discover causal links between streams.

Let’s say your store is predicting sales and I'm optimizing an HVAC system across the street. Your feature space and mine probably have a lot in common.

I am unclear how this incorporates domain knowledge and private side information, which seems the hallmark of natural intelligence and, e.g. science. Perhaps they feel domain knowledge is a bug standing in the way of truly general artificial intelligence? If I had free time I might try to get a better grip on what they are doing, whoever they are.

Agarwal, Anish, Muhammad Jehangir Amjad, Devavrat Shah, and Dennis Shen. 2018. “Time Series Analysis via Matrix Estimation,” February.

Alquier, Pierre, Xiaoyin Li, and Olivier Wintenberger. 2013. “Prediction of Time Series by Statistical Learning: General Losses and Fast Rates.” Dependence Modeling 1: 65–93.

Alquier, Pierre, and Olivier Wintenberger. 2012. “Model Selection for Weakly Dependent Time Series Forecasting.” Bernoulli.

Ben Taieb, Souhaib, and Amir F. Atiya. 2016. “A Bias and Variance Analysis for Multistep-Ahead Time Series Forecasting.” IEEE Transactions on Neural Networks and Learning Systems 27 (1): 62–76.

Bergmeir, Christoph, Rob J. Hyndman, and Bonsoo Koo. 2018. “A Note on the Validity of Cross-Validation for Evaluating Autoregressive Time Series Prediction.” Computational Statistics & Data Analysis 120 (April): 70–83.

Box, George E. P., Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung. 2016. Time Series Analysis: Forecasting and Control. Fifth edition. Wiley Series in Probability and Statistics. Hoboken, New Jersey: John Wiley & Sons, Inc.

Brodersen, Kay H., Fabian Gallusser, Jim Koehler, Nicolas Remy, and Steven L. Scott. 2015. “Inferring Causal Impact Using Bayesian Structural Time-Series Models.” The Annals of Applied Statistics 9 (1): 247–74.

Broersen, Petrus MT. 2006. Automatic Autocorrelation and Spectral Analysis. Secaucus, NJ, USA: Springer.

Chevillon, Guillaume. 2007. “Direct Multi-Step Estimation and Forecasting.” Journal of Economic Surveys 21 (4): 746–85.

Commandeur, Jacques J. F., and Siem Jan Koopman. 2007. An Introduction to State Space Time Series Analysis. 1 edition. Oxford ; New York: Oxford University Press.

Commandeur, Jacques J. F., Siem Jan Koopman, and Marius Ooms. 2011. “Statistical Software for State Space Methods.” Journal of Statistical Software 41 (1).

Cox, D. R., Gudmundur Gudmundsson, Georg Lindgren, Lennart Bondesson, Erik Harsaae, Petter Laake, Katarina Juselius, and Steffen L. Lauritzen. 1981. “Statistical Analysis of Time Series: Some Recent Developments [with Discussion and Reply].” Scandinavian Journal of Statistics 8 (2): 93–115.

Dahl, Astrid, and Edwin V. Bonilla. 2019. “Sparse Grouped Gaussian Processes for Solar Power Forecasting,” March.

Ding, J., V. Tarokh, and Y. Yang. 2018. “Model Selection Techniques: An Overview.” IEEE Signal Processing Magazine 35 (6): 16–34.

Gerstenberger, Matthew C., Stefan Wiemer, Lucile M. Jones, and Paul A. Reasenberg. 2005. “Real-Time Forecasts of Tomorrow’s Earthquakes in California.” Nature 435 (7040): 328–31.

Granger, C. W. J., and Roselyne Joyeux. 1980. “An Introduction to Long-Memory Time Series Models and Fractional Differencing.” Journal of Time Series Analysis 1 (1): 15–29.

Hurvich, Clifford M. 2002. “Multistep Forecasting of Long Memory Series Using Fractional Exponential Models.” International Journal of Forecasting, Forecasting Long Memory Processes, 18 (2): 167–79.

Kurniasih, Nuning. n.d. “Knowledge Management of Agricultural Prophecy in the Manuscript of Sundanese Society in Tasikmalaya District of West Java Indonesia.” Accessed February 12, 2019.

Kuznetsov, Vitaly, and Mehryar Mohri. 2014. “Forecasting Non-Stationary Time Series: From Theory to Algorithms.”

———. 2015. “Learning Theory and Algorithms for Forecasting Non-Stationary Time Series.” In Advances in Neural Information Processing Systems, 541–49. Curran Associates, Inc.

Lunde, Robert. 2019. “Sample Splitting and Weak Assumption Inference for Time Series,” February.

Lunde, Robert, and Cosma Rohilla Shalizi. 2017. “Bootstrapping Generalization Error Bounds for Time Series,” November.

Moradkhani, Hamid, Soroosh Sorooshian, Hoshin V. Gupta, and Paul R. Houser. 2005. “Dual State–Parameter Estimation of Hydrological Models Using Ensemble Kalman Filter.” Advances in Water Resources 28 (2): 135–47.

Morvai, Gusztáv, Sidney Yakowitz, and László Györfi. 1996. “Nonparametric Inference for Ergodic, Stationary Time Series.” The Annals of Statistics 24 (1): 370–79.

Phillips, Robert F. 1987. “Composite Forecasting: An Integrated Approach and Optimality Reconsidered.” Journal of Business & Economic Statistics 5 (3): 389–95.

Runge, Jakob, Reik V. Donner, and Jürgen Kurths. 2015. “Optimal Model-Free Prediction from Multivariate Time Series.” Physical Review E 91 (5).

Ryabko, Daniil. 2009. “On Finding Predictors for Arbitrary Families of Processes,” December.

Smith, Leonard A. 2000. “Disentangling Uncertainty and Error: On the Predictability of Nonlinear Systems.” In Nonlinear Dynamics and Statistics.

Sornette, Didier. 2009. “Dragon-Kings, Black Swans and the Prediction of Crises” 2 (1).

Sugihara, George. 1994. “Nonlinear Forecasting for the Classification of Natural Time Series.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 348 (1688): 477.

Taieb, Souhaib Ben, James W. Taylor, and Rob J. Hyndman. 2017. “Coherent Probabilistic Forecasts for Hierarchical Time Series.” In PMLR, 3348–57.

Taleb, Nassim Nicholas. 2018. “Election Predictions as Martingales: An Arbitrage Approach.” Quantitative Finance 18 (1): 1–5.

Taylor, James W. 2008. “Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall.” Journal of Financial Econometrics 6 (3): 382–406.

Taylor, Sean J., and Benjamin Letham. 2017. “Forecasting at Scale.” e3190v2. PeerJ Inc.

Uematsu, Yoshimasa. 2015. “Penalized Likelihood Estimation in High-Dimensional Time Series Models and Its Application,” April.

Wang, Wei, David Rothschild, Sharad Goel, and Andrew Gelman. 2015. “Forecasting Elections with Non-Representative Polls.” International Journal of Forecasting 31 (3): 980–91.

Wen, Ruofeng, Kari Torkkola, and Balakrishnan Narayanaswamy. 2017. “A Multi-Horizon Quantile Recurrent Forecaster,” November.

Werbos, Paul J. 1988. “Generalization of Backpropagation with Application to a Recurrent Gas Market Model.” Neural Networks 1 (4): 339–56.

Werner, Maximilian J, Agnès Helmstetter, David Jackson, Yan Y Kagan, and Stefan Wiemer. 2010. “Adaptively Smoothed Seismicity Earthquake Forecasts for Italy.” Annals of Geophysics, no. 3 (November).