Forecasting

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.

Software

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

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).)

asap

asap:

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.org

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. http://arxiv.org/abs/1802.09064.

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. https://doi.org/10.2478/demo-2013-0004.

Alquier, Pierre, and Olivier Wintenberger. 2012. “Model Selection for Weakly Dependent Time Series Forecasting.” Bernoulli. http://arxiv.org/abs/0902.2924.

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. https://doi.org/10.1109/TNNLS.2015.2411629.

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. https://doi.org/10.1016/j.csda.2017.11.003.

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. https://doi.org/10.1214/14-AOAS788.

Broersen, Petrus MT. 2006. Automatic Autocorrelation and Spectral Analysis. Secaucus, NJ, USA: Springer. http://dsp-book.narod.ru/AASA.pdf.

Chevillon, Guillaume. 2007. “Direct Multi-Step Estimation and Forecasting.” Journal of Economic Surveys 21 (4): 746–85. https://doi.org/10.1111/j.1467-6419.2007.00518.x.

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.

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Dahl, Astrid, and Edwin V. Bonilla. 2019. “Sparse Grouped Gaussian Processes for Solar Power Forecasting,” March. http://arxiv.org/abs/1903.03986.

Ding, J., V. Tarokh, and Y. Yang. 2018. “Model Selection Techniques: An Overview.” IEEE Signal Processing Magazine 35 (6): 16–34. https://doi.org/10.1109/MSP.2018.2867638.

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———. 2015. “Learning Theory and Algorithms for Forecasting Non-Stationary Time Series.” In Advances in Neural Information Processing Systems, 541–49. Curran Associates, Inc. http://papers.nips.cc/paper/5836-learning-theory-and-algorithms-for-forecasting-non-stationary-time-series.

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