Skip to main content

Advertisement

Log in

Causal inference for time series analysis: problems, methods and evaluation

  • Survey Paper
  • Published:
Knowledge and Information Systems Aims and scope Submit manuscript

Abstract

Time series data are a collection of chronological observations which are generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting and clustering have been proposed to analyze this type of data. Time series data have been also used to study the effect of interventions overtime. Moreover, in many fields of science, learning the causal structure of dynamic systems and time series data is considered an interesting task which plays an important role in scientific discoveries. Estimating the effect of an intervention and identifying the causal relations from the data can be performed via causal inference. Existing surveys on time series discuss traditional tasks such as classification and forecasting or explain the details of the approaches proposed to solve a specific task. In this paper, we focus on two causal inference tasks, i.e., treatment effect estimation and causal discovery for time series data and provide a comprehensive review of the approaches in each task. Furthermore, we curate a list of commonly used evaluation metrics and datasets for each task and provide an in-depth insight. These metrics and datasets can serve as benchmark for research in the field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Abadie A, Diamond A, Hainmueller J (2010) Synthetic control methods for comparative case studies: estimating the effect of Californias tobacco control program. J Am Stat Assoc 105(490):493–505

    Article  MathSciNet  Google Scholar 

  2. Abadie A, Gardeazabal J (2003) The economic costs of conflict: a case study of the Basque Country. Am Econ Rev 93(1):113–132

    Article  Google Scholar 

  3. Abanda A, Mori U, Lozano JA (2019) A review on distance based time series classification. Data Min Knowl Dis 33(2):378–412

    Article  MathSciNet  MATH  Google Scholar 

  4. Abrevaya J, Hsu YC, Lieli RP (2015) Estimating conditional average treatment effects. J Bus Econ Stat 33(4):485–505

    Article  MathSciNet  Google Scholar 

  5. Amjad M, Shah D, Shen D (2018) Robust synthetic control. J Mach Learn Res 19(1):802–852

    MathSciNet  MATH  Google Scholar 

  6. Amornbunchornvej C, Zheleva E, Berger-Wolf TY (2019) Variable-lag Granger Causality for Time Series Analysis. In: 2019 IEEE international conference on data science and advanced analytics (DSAA). IEEE, pp 21–30

  7. Andrieu C, Doucet A, Holenstein R (2010) Particle Markov chain Monte Carlo methods

  8. Angrist JD, Pischke JS (2008) Mostly harmless econometrics: an empiricists companion. Princeton University Press, Princeton

    Book  MATH  Google Scholar 

  9. Angrist JD, Pischke JS (2014) Masteringmetrics: the path from cause to effect. Princeton University Press, Princeton

    MATH  Google Scholar 

  10. Anwar AR et al (2014) Multi-modal causality analysis of eyes-open and eyes-closed data from simultaneously recorded EEG and MEG. In: 2014 36th annual international conference of the IEEE engineering in medicine and biology society. IEEE, pp 2825–2828

  11. Arnold A, Liu Y, Abe N (2007) Temporal causal modeling with graphical granger methods. In: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining. pp 66–75

  12. Atanasov VA, Black BS (2016) Shock-based causal inference in corporate finance and accounting research. Crit Financ Rev 5:207–304

    Article  Google Scholar 

  13. Athey S, Imbens GW (2006) Identification and inference in nonlinear difference-in-differences models. Econometrica 74(2):431–497

    Article  MathSciNet  MATH  Google Scholar 

  14. Athey S, Imbens GW (2017) The state of applied econometrics: causality and policy evaluation. J Econ Perspec 31(2):3–32

    Article  Google Scholar 

  15. Auffhammer M, Kellogg R (2011) Clearing the air? The effects of gasoline content regulation on air quality. Am Econ Rev 101(6):2687–2722

    Article  Google Scholar 

  16. Aytuğ H et al (2017) Twenty years of the EU-Turkey customs union: a synthetic control method analysis. JCMS J Common Market Stud 55(3):419–431

    Article  Google Scholar 

  17. Bagnall A, Lines J, Hills J, Bostrom A (2015) Time-series classification with COTE: the collective of transformation-based ensembles. IEEE Trans Knowl Data Eng 27(09):1. https://doi.org/10.1109/TKDE.2015.2416723

    Article  Google Scholar 

  18. Bagnall A et al (n.d) The great time series classification bake off: An experimental evaluation of recently proposed algorithms. Extended version. arXiv 2016. In: arXiv preprint arXiv:1602.01711

  19. Balzer LB, Petersen ML, van der Laan MJ, Search Collaboration (2016) Targeted estimation and inference for the sample average treatment effect in trials with and without pair-matching. Stat Med 35(21):3717–3732

  20. Barnett L, Barrett AB, Seth AK (2009) Granger causality and transfer entropy are equivalent for Gaussian variables. Phys Rev Lett 103(23):238701

    Article  Google Scholar 

  21. Baum LE et al (1970) A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains. Ann Math Stat 41(1):164–171. https://doi.org/10.1214/aoms/1177697196

    Article  MathSciNet  MATH  Google Scholar 

  22. Baydogan MG, Runger G (2015) Learning a symbolic representation for multivariate time series classification. Data Min Knowl Dis 29(2):400–422

    Article  MathSciNet  MATH  Google Scholar 

  23. Bernal JL, Cummins S, Gasparrini A (2017) Interrupted time series regression for the evaluation of public health interventions: a tutorial. Int J Epidemiol 46(1):348–355

    Google Scholar 

  24. Berndt DJ, Clifford J (1994) Using dynamic time warping to find patterns in time series. In: Proceedings of the 3rd international conference on knowledge discovery and data mining. AAAIWS’94. AAAI Press, Seattle, WA pp 359–370

  25. Bertrand M, Duflo E, Mullainathan S (2004) How much should we trust differences-in-differences estimates? Q J Econ 119(1):249–275

    Article  MATH  Google Scholar 

  26. Bica I, Alaa AM, van der Schaar M (2019) Time series deconfounder: estimating treatment effects over time in the presence of hidden confounders. In: arXiv preprint arXiv:1902.00450

  27. Boruvka A, Almirall D, Witkiewitz K, Murphy SA (2018) Assessing time-varying causal effect moderation in mobile health. J Am Stat Assoc 113(523):1112–1121

    Article  MathSciNet  Google Scholar 

  28. Box GEP, Jenkins GM (1968) Some recent advances in forecasting and control. J R Stat Soc Series C 17(2):91–109. https://doi.org/10.2307/2985674

    Article  MathSciNet  Google Scholar 

  29. Braei M, Wagner S (2020) Anomaly Detection in Univariate Time-series: A Survey on the State-of-the-Art

  30. Brodersen KH, Gallusser F, Koehler J, Remy N, Scott SL (2015) Inferring causal impact using Bayesian structural time-series models. Ann Appl Stat 9(1):247–274

    Article  MathSciNet  MATH  Google Scholar 

  31. Brouillard P et al (2020) Differentiable causal discovery from interventional data. In: arXiv preprint arXiv:2007.01754

  32. Brown RG (1956) Exponential smoothing for predicting demand. Little https://books.google.com/books?id=Eo_rMgEACAAJ

  33. Bruhn CAW et al (2017) Estimating the population-level impact of vaccines using synthetic controls. Proc Natl Acad Sci 114(7):1524–1529

    Article  Google Scholar 

  34. Cai R et al (2018) Causal discovery from discrete data using hidden compact representation In: Advances in neural information processing systems, p 2666

  35. Cavallo E et al (2013) Catastrophic natural disasters and economic growth. Rev Econ Stat 95(5):1549–1561

    Article  Google Scholar 

  36. Chan MK, Kwok S et al (2016) Policy evaluation with interactive fixed effects. In: Preprint. Available at https://ideas.repec.org/p/syd/wpaper/2016-11.html

  37. Chen, L, Ng R (2004) On the marriage of lp-norms and edit distance. In: Proceedings of the thirtieth international conference on very large data bases, 30:792–803

  38. Chu T, Glymour C, Ridgeway G (2008) Search for additive nonlinear time series causal models. J Mach Learn Res 9(5)

  39. Cole MA, Elliott RJR, Liu B (2020) The impact of the Wuhan Covid-19 lockdown on air pollution and health: a machine learning and augmented synthetic control approach. Environ Res Econ 1–28

  40. Cooley J, Navarro S, Takahashi Y (2010) Identification and estimation of time-varying treatment effects: How the timing of grade retention affects outcomes. In: manuscrit, University of Wisconsin-Madison

  41. Cooper GF, Yoo C (2013) Causal discovery from a mixture of experimental and observational data. In: arXiv preprint arXiv:1301.6686

  42. Cunningham J, Ghahramani Z, Rasmussen C (2012) Gaussian processes for time-marked time-series data In: Artificial intelligence and statistics, pp 255–263

  43. Damianou A, Lawrence N (2013) Deep gaussian processes. In: Artificial intelligence and statistics, pp 207–215

  44. Dang XH, Shah SY, Zerfos P (2018) seq2graph: discovering dynamic dependencies from multivariate time series with multi-level attention. In: arXiv preprint arXiv:1812.04448

  45. Ding M, Chen Y, Bressler SL (2006) 17 Granger causality: basic theory and application to neuroscience. In: Handbook of time series analysis: recent theoretical developments and applications 437

  46. Eichler M, Didelez V (2012) Causal reasoning in graphical time series models. In: arXiv preprint arXiv:1206.5246

  47. Ellis B, Wong WH (2008) Learning causal Bayesian network structures from experimental data. J Am Stat Assoc 103(482):778–789

    Article  MathSciNet  MATH  Google Scholar 

  48. Entner D, Hoyer PO (2010) On causal discovery from time series data using FCI. In: Probabilistic graphical models, pp 121–128

  49. Fawaz HI et al (2019) Deep learning for time series classification: a review. Data Min Knowl Dis 33(4):917–963

    Article  MathSciNet  MATH  Google Scholar 

  50. Fu T (2011) A review on time series data mining. Eng Appl Artif Intel 24(1):164–181. https://doi.org/10.1016/j.engappai.2010.09.007

    Article  Google Scholar 

  51. Gamboa JCB (2017) Deep learning for time-series analysis. In: arXiv preprint arXiv:1701.01887

  52. Ghahramani Z (1998) Learning Dynamic Bayesian Networks. In: In Adaptive processing of sequences and data structures, Lecture Notes in Artificial Intelligence, pp 168–197

  53. Ghahramani Z, Hinton GE (1996) Switching State-Space Models. Tech. rep. Kings College Road, Toronto M5S 3H5

  54. Ghahramani Z, Jordan MI (1996) Factorial Hidden Markov Models. In: Machine Learning, MIT Press

  55. Gobillon L, Magnac T (2016) Regional policy evaluation: interactive fixed effects and synthetic controls. Rev Econ Stat 98(3):535–551

    Article  Google Scholar 

  56. Gong M et al (2017) Causal discovery from temporally aggregated time series. In: Uncertainty in artificial intelligence: proceedings of the... conference. In: conference on uncertainty in artificial intelligence Vol. 2017. NIH Public Access

  57. González R, Hosoda EB (2016) Environmental impact of aircraft emissions and aviation fuel tax in Japan. J Air Transp Manag 57:234–240

    Article  Google Scholar 

  58. Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econom J Econom Soc 37:424–438

    MATH  Google Scholar 

  59. Graves A (2013) Generating sequences with recurrent neural networks. In: CoRR arXiv:1308.0850

  60. Gregorova M, Kalousis A, Marchand-Maillet S (2015) Learning Leading Indicators for Time Series Predictions. In: arXiv preprint arXiv:1507.01978

  61. Guo R et al (2018) A survey of learning causality with data: problems and methods. In: arXiv preprint arXiv:1809.09337

  62. HajiGhassemi N, Deisenroth M (2014) Analytic long-term forecasting with periodic Gaussian processes. In: Artificial Intelligence and Statistics, pp 303–311

  63. Haufe S et al (2010) Sparse causal discovery in multivariate time series. In: causality: objectives and assessment, pp 97–106

  64. Hausman C, Rapson DS (2018) Regression discontinuity in time: considerations for empirical applications. Annu Rev Res Econ 10:533–552

    Article  Google Scholar 

  65. Marton H, Hernéndez-Lobato JM, Murillo-Fuentes JJ (2018) Inference in deep gaussian processes using stochastic gradient hamiltonian monte carlo. In: Advances in neural information processing systems, pp 7506–7516

  66. Heckerman D (2013) A Bayesian approach to learning causal networks. In: arXiv preprint arXiv:1302.4958

  67. Hedeker D, Gibbons RD (2006) Longitudinal data analysis, vol 451. Wiley, Hoboken

    MATH  Google Scholar 

  68. Hernán MA, Robins JM (2010) Causal inference

  69. Hernán MA, Brumback B, Robins JM (2000) Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. In: Epidemiology, pp 561–570

  70. Hiemstra C, Jones JD (1994) Testing for linear and nonlinear Granger causality in the stock price-volume relation. J Financ 49(5):1639–1664

    Google Scholar 

  71. Hinton GE (2002) Training products of experts by minimizing contrastive divergence. Neural Comput 14(8):1771–1800

    Article  MATH  Google Scholar 

  72. Hoyer P et al (2008) Nonlinear causal discovery with additive noise models. Adv Neural Inf Process Syst 21:689–696

    Google Scholar 

  73. Huang B et al (2019) Causal discovery and forecasting in nonstationary environments with state-space models. Proc Mach Learn Res 97:2901

    Google Scholar 

  74. Huang Y, Kleinberg S (2015) Fast and accurate causal inference from time series data. In: The twenty-eighth international flairs conference

  75. Hyndman RJ, Koehler AB (2006) Another look at measures of forecast accuracy. Int J Forecast 22(4):679–688

    Article  Google Scholar 

  76. Rob H et al (2002) A state space framework for automatic forecasting using exponential smoothing methods. Int J Forecast 18:439–454. https://doi.org/10.1016/S0169-2070(01)00110-8

    Article  Google Scholar 

  77. Hyttinen A, Plis S, Järvisalo M, Eberhardt F, Danks D (2016) Causal discovery from subsampled time series data by constraint optimization. In: Conference on probabilistic graphical models. PMLR, pp 216–227

  78. Hyvärinen A, Shimizu S, Hoyer PO (2008) Causal modelling combining instantaneous and lagged effects: an identifiable model based on non-Gaussianity. In: Proceedings of the 25th international conference on Machine learning, pp 424–431

  79. Iglesias F, Kastner W (2013) Analysis of similarity measures in times series clustering for the discovery of building energy patterns. Energies 6(2):579–597

    Article  Google Scholar 

  80. Jaber A et al (2020) Causal discovery from soft interventions with unknown targets: characterization and learning. In: Advances in neural information processing systems 33

  81. Jackson MO, Lin Z, Yu NN (2020) Adjusting for peer-influence in propensity scoring when estimating treatment effects. In: Available at SSRN 3522256

  82. Jangyodsuk P, Seo DJ, Gao J (2014) Causal graph discovery for hydrological time series knowledge discovery

  83. Johnson AEW et al (2016) MIMIC-III, a freely accessible critical care database. Sci Data 3(1):1–9

    Article  Google Scholar 

  84. Julier SJ, Uhlmann JK (1997) A new extension of the kalman filter to nonlinear systems. In: pp 182–193

  85. Kalman RE et al (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82(1):35–45

    Article  MathSciNet  Google Scholar 

  86. Karl M et al (2017) Deep variational bayes filters: unsupervised learning of state space models from raw data. arXiv:1605.06432 [stat.ML]

  87. Kerman J, Wang P, Vaver J (2017) Estimating ad effectiveness using geo experiments in a time-based regression framework

  88. Khanna S, Tan VYF (2019) Economy statistical recurrent units for inferring nonlinear granger causality. In: arXiv preprint arXiv:1911.09879

  89. Kleinberg S (2013) Causal inference with rare events in large-scale time-series data. In: twenty-third international joint conference on artificial intelligence

  90. Kontopantelis E et al (2015) Regression based quasi-experimental approach when randomisation is not an option: interrupted time series analysis. BMJ 350:h2750

    Article  Google Scholar 

  91. Kreif N et al (2016) Examination of the synthetic control method for evaluating health policies with multiple treated units. Health Econ 25(12):1514–1528

    Article  MathSciNet  Google Scholar 

  92. Lechner M et al (2011) The estimation of causal effects by difference-in-difference methods. Now

  93. Lee SI, Yoo SJ (2019) Multimodal deep learning for finance: integrating and forecasting international stock markets. J Supercomput 1–19

  94. Li L, Prakash BA (2011) Time series clustering: complex is simpler!. In: ICML

  95. Li S (2018) Estimating causal effects from time series. PhD thesis. ETH Zurich

  96. Li S, Bühlmann P (2018) Estimating heterogeneous treatment effects in nonstationary time series with state-space models. In: arXiv preprint arXiv:1812.04063

  97. Li SCX, Marlin B (2016) A scalable end-to-end gaussian process adapter for irregularly sampled time series classification. In: Advances in neural information processing systems, pp 1804–1812

  98. Liao W et al (2010) Evaluating the effective connectivity of resting state networks using conditional Granger causality. Biol Cybern 102(1):57–69

    Article  Google Scholar 

  99. Lim B (2018) Forecasting treatment responses over time using recurrent marginal structural networks. In: advances in neural information processing systems, pp 7483–7493

  100. Lim B, Zohren S (2021) Time-series forecasting with deep learning: a survey. Philos Trans R Soc A 379(2194):20200209

    Article  MathSciNet  Google Scholar 

  101. Linden A, Adams JL (2011) Applying a propensity score-based weighting model to interrupted time series data: improving causal inference in programme evaluation. J Eval Clin Prac 17(6):1231–1238

    Article  Google Scholar 

  102. Lines J, Bagnall A (2014) Ensembles of elastic distance measures for time series classification. In: Proceedings of the 2014 SIAM international conference on data mining. SIAM, pp 524–532

  103. Lines J, Taylor S, Bagnall A (2016) Hive-cote: the hierarchical vote collective of transformation-based ensembles for time series classification. In: 2016 IEEE 16th international conference on data mining (ICDM). IEEE, pp 1041–1046

  104. Liu H et al (2020) When Gaussian process meets big data: a review of scalable GPs. IEEE Trans Neural Netw Learn Syst 31(11):4405–4423

    Article  MathSciNet  Google Scholar 

  105. Liu R, Yin C, Zhang P (2020) Estimating individual treatment effects with time-varying confounders. In: arXiv preprint arXiv:2008.13620

  106. Lok JJ et al (2008) Statistical modeling of causal effects in continuous time. Ann Stat 36(3):1464–1507

    Article  MathSciNet  MATH  Google Scholar 

  107. Louizos C et al (2017) Causal effect inference with deep latent-variable models. In: arXiv preprint arXiv:1705.08821

  108. Löwe S et al (2020) Amortized causal discovery: learning to infer causal graphs from time-series data. In: arXiv preprint arXiv:2006.10833

  109. Qianli M et al (2019) Learning representations for time series clustering. In: Wallach H et al (eds) Advances in neural information processing systems, vol 32. Curran Associates Inc, New York, pp 3781–3791

    Google Scholar 

  110. Maddix DC, Wang Y, Smola A (2018) Deep factors with gaussian processes for forecasting. In: arXiv preprint arXiv:1812.00098

  111. Meganck S, Leray P, Manderick B (2006) Learning causal bayesian networks from observations and experiments: a decision theoretic approach. In: international conference on modeling decisions for artificial intelligence. Springer, pp 58–69

  112. Meng Y (2019) Estimating granger causality with unobserved confounders via deep latent-variable recurrent neural network. In: arXiv preprint arXiv:1909.03704

  113. Mittelman R (2015) Time-series modeling with undecimated fully convolutional neural networks. arXiv preprint arXiv:1508.00317

  114. Mitze T, Kosfeld R, Rode J, Wälde K (2020) Face masks considerably reduce COVID-19 cases in Germany. Proc Nat Acad Sci 117(51):32293–32301

  115. Mogren O (2016) C-RNN-GAN: Continuous recurrent neural networks with adversarial training. In: CoRR arXiv:1611.09904

  116. Moodie EEM, Richardson TS, Stephens DA (2007) Demystifying optimal dynamic treatment regimes. Biometrics 63(2):447–455

    Article  MathSciNet  MATH  Google Scholar 

  117. Mooij JM et al (2016) Distinguishing cause from effect using observational data: methods and benchmarks. J Mach Learn Res 17(1):1103–1204

    MathSciNet  MATH  Google Scholar 

  118. Murphy SA (2003) Optimal dynamic treatment regimes. J R Stat Soc Series B (Stat Methodol) 65(2):331–355

    Article  MathSciNet  MATH  Google Scholar 

  119. van den Oord A et al (2016) WaveNet: a generative model for raw audio. In arXiv:1609.03499

  120. Pan Z et al (2018) Hyperst-net: Hypernetworks for spatio-temporal forecasting. In: arXiv preprint arXiv:1809.10889

  121. Papana A et al (2013) Simulation study of direct causality measures in multivariate time series. Entropy 15(7):2635–2661

    Article  MathSciNet  MATH  Google Scholar 

  122. Penfold RB, Zhang F (2013) Use of interrupted time series analysis in evaluating health care quality improvements. Acad Pediatr 13(6):S38–S44

    Article  Google Scholar 

  123. Peters J, Janzing D, Schölkopf B (2013) Causal inference on time series using restricted structural equation models. In: advances in neural information processing Systems, pp 154–162

  124. Peters J, Janzing D, Schölkopf B (2017) Elements of causal inference. The MIT Press, Cambridge

    MATH  Google Scholar 

  125. Pfister N, Bühlmann P, Peters J (2019) Invariant causal prediction for sequential data. J Am Stat Assoc 114(527):1264–1276

    Article  MathSciNet  MATH  Google Scholar 

  126. Quiñonero-Candela J, Rasmussen CE (2005) A unifying view of sparse approximate Gaussian process regression. J Mach Learn Res 6(Dec):1939–1959

    MathSciNet  MATH  Google Scholar 

  127. Rasmussen CE (2003) Gaussian processes in machine learning. In: summer school on machine learning. Springer, pp 63–71

  128. Roberts PSS (2002) Bayesian time series classification. Adv Neural Inf Process Syst 14:937

    Google Scholar 

  129. Roberts S et al (2013) Gaussian processes for time-series modelling. Philos Trans R Soc A Math Phys Eng Sci 371(1984):20110550

    Article  MathSciNet  MATH  Google Scholar 

  130. Robins J (1992) Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika 79(2):321–334

    Article  MathSciNet  MATH  Google Scholar 

  131. Robins JM (1997) Causal inference from complex longitudinal data. In: Latent variable modeling and applications to causality. Springer, pp 69–117

  132. Robins JM (2004) Optimal structural nested models for optimal sequential decisions. In: Proceedings of the second seattle Symposium in Biostatistics. Springer, pp 189–326

  133. Robins JM, Greenland S, Hu FC (1999) Estimation of the causal effect of a time-varying exposure on the marginal mean of a repeated binary outcome. J Am Stat Assoc 94(447):687–700

    Article  MathSciNet  MATH  Google Scholar 

  134. Robins JM, Hernan MA, Brumback B (2000) Marginal structural models and causal inference in epidemiology

  135. Robins J, Hernan M (2008) Estimation of the causal effects of time-varying exposure. In: pp 553–599 https://doi.org/10.1201/9781420011579.ch23

  136. Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41–55

    Article  MathSciNet  MATH  Google Scholar 

  137. Rothenhäusler D et al (2015) BACKSHIFT: Learning causal cyclic graphs from unknown shift interventions. In: advances in neural information processing systems, pp 1513–1521

  138. Runge J, Sejdinovic D, Flaxman S, (n.d) Detecting causal associations in large nonlinear time series datasets. arXiv 2017. In: arXiv preprint arXiv:1702.07007

  139. Runge J (2018) Causal network reconstruction from time series: from theoretical assumptions to practical estimation. Chaos Interdiscip J Nonlinear Sci 28(7):075310

    Article  MathSciNet  MATH  Google Scholar 

  140. Runge J (2020) Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets. In: arXiv preprint arXiv:2003.03685

  141. Runge J et al (2019) Inferring causation from time series in Earth system sciences. Nat Commun 10(1):1–13

    Article  Google Scholar 

  142. Saatçi Y (2012) Scalable inference for structured Gaussian process models. PhD thesis. Citeseer

  143. Samartsidis P, Seaman SR, Montagna S, Charlett A, Hickman M, Angelis DD (2020) A bayesian multivariate factor analysis model for evaluating an intervention by using observational time series data on multiple outcomes. J Royal Stat Soc Series A (Statistics in Society) 183(4):1437–1459

    Article  MathSciNet  Google Scholar 

  144. Samartsidis P, Seaman SR, Presanis AM et al (2019) Assessing the causal effect of binary interventions from observational panel data with few treated units. Stat Sci 34(3):486–503

    Article  MathSciNet  MATH  Google Scholar 

  145. Saul LK, Jordan MI (1998) Mixed memory Markov models: decomposing complex stochastic processes as mixtures of simpler ones

  146. Saunders J et al (2015) A synthetic control approach to evaluating place-based crime interventions. J Quant Criminol 31(3):413–434

    Article  Google Scholar 

  147. Schaechtle U, Stathis K, Bromuri S (2013) Multi-dimensional causal discovery. In: twenty-third international joint conference on artificial intelligence

  148. Schreiber T (2000) Measuring information transfer. Phys Rev Lett 85(2):461

    Article  Google Scholar 

  149. Shannon M, Byrne W (2009) A formulation of the autoregressive HMM for speech synthesis

  150. Shimizu S et al (2006) A linear non-Gaussian acyclic model for causal discovery. J Mach Learn Res 7(10):2003–2030

    MathSciNet  MATH  Google Scholar 

  151. Shojaie A, Michailidis G (2010) Discovering graphical Granger causality using the truncating lasso penalty. Bioinformatics 26(18):i517–i523

    Article  Google Scholar 

  152. Siggiridou E, Kugiumtzis D (2015) Granger causality in multivariate time series using a time-ordered restricted vector autoregressive model. IEEE Trans Signal Process 64(7):1759–1773

    Article  MathSciNet  MATH  Google Scholar 

  153. Soleimani H, Subbaswamy A, Saria S (2017) Treatment-response models for counterfactual reasoning with continuous-time, continuous-valued interventions. In: arXiv preprint arXiv:1704.02038

  154. Spirtes P, Glymour C, Scheines R (2000) Causation, prediction, and search, 2nd edn. MIT Press, Cambridge MA

    MATH  Google Scholar 

  155. Spirtes P, Glymour C (1991) An algorithm for fast recovery of sparse causal graphs. Soc Sci Comput Rev 9(1):62–72

    Article  Google Scholar 

  156. Spirtes P, Zhang K (2016) Causal discovery and inference: concepts and recent methodological advances. In: Applied informatics. vol. 3. 1. Springer, p. 3

  157. Steyvers M et al (2003) Inferring causal networks from observations and interventions. Cognit Sci 27(3):453–489

    Article  Google Scholar 

  158. Stips A et al (2016) On the causal structure between CO 2 and global temperature. Sci Rep 6(1):1–9

    Article  Google Scholar 

  159. Sun J, Bollt EM (2014) Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings. Phys D Nonlinear Phenom 267:49–57

    Article  MathSciNet  MATH  Google Scholar 

  160. Sun J, Taylor D, Bollt EM (2015) Causal network inference by optimal causation entropy. SIAM J Appl Dyn Syst 14(1):73–106

    Article  MathSciNet  MATH  Google Scholar 

  161. Sutskever I, Hinton GE (2007) Learning Multilevel Distributed Representations for High-Dimensional Sequences. In: Meila M, Shen X (Eds.), AISTATS Vol 2. JMLR Proceedings. JMLR.org, pp 548–555. http://dblp.uni-trier.de/db/journals/jmlr/jmlrp2.html#SutskeverH07

  162. Tank A et al (2018) Neural granger causality for nonlinear time series. In: arXiv preprint arXiv:1802.05842

  163. Taylor GW (2009) Composable, distributed-state models for high-dimensional time series. University of Toronto, Toronto

  164. Teräsvirta T, Tjøstheim D, Granger C et al (2010) Modelling nonlinear economic time series. Oxford University Press, Oxford

    Book  MATH  Google Scholar 

  165. Tobar F, Bui TD, Turner RE (2015) Learning stationary time series using Gaussian processes with nonparametric kernels. In: Advances in neural information processing systems, pp 3501–3509

  166. de Vocht F (2016) Inferring the 1985–2014 impact of mobile phone use on selected brain cancer subtypes using Bayesian structural time series and synthetic controls. Environ Int 97:100–107

    Article  Google Scholar 

  167. de Vocht F et al (2017) The intervention effect of local alcohol licensing policies on hospital admission and crime: a natural experiment using a novel Bayesian synthetictime-series method. J Epidemiol Commun Health 71(9):912–918

    Article  Google Scholar 

  168. Wang JM, Fleet DJ, Hertzmann A (2006) Gaussian process dynamical models. In: In NIPS. MIT Press, pp 1441–1448

  169. Wang Y et al (2019) Deep factors for forecasting. In: International conference on machine learning. PMLR, pp 6607–6617

  170. Wilson AG et al (2016) Deep kernel learning. In: Artificial intelligence and statistics, pp 370–378

  171. Wilson AG et al (2016) Stochastic variational deep kernel learning. Adv Neural Inf Process Syst 29:2586–2594

    Google Scholar 

  172. Wilson A, Adams R (2013) Gaussian process kernels for pattern discovery and extrapolation. In: International conference on machine learning, pp 1067–1075

  173. Wilson A, Nickisch H (2015) Kernel interpolation for scalable structured Gaussian processes (KISSGP). In: international conference on machine learning, pp 1775–1784

  174. Wing C, Simon K, Bello-Gomez RA (2018) Designing difference in difference studies: best practices for public health policy research. In: Annual review of public health 39

  175. Wodtke GT (2020) Regression-based adjustment for time-varying confounders. Sociol Methods Res 49(4):906–946

    Article  MathSciNet  Google Scholar 

  176. Wu T, Breuel T, Skuhersky M, Kautz J. Nonlinear causal discovery with minimum predictive information regularization

  177. Xing Z, Pei J, Keogh E (2010) A brief survey on sequence classification. ACM Sigkdd Explor Newsl 12(1):40–48

    Article  Google Scholar 

  178. Xu C, Huang H, Yoo S (2019) Scalable causal graph learning through a deep neural network. In: Proceedings of the 28th ACM international conference on information and knowledge management, pp 1853–1862

  179. Xu Y, Xu Y, Saria S (2016) A Bayesian nonparametric approach for estimating individualized treatment-response curves. In: Machine learning for healthcare conference, pp 282–300

  180. Xu Y (2017) Generalized synthetic control method: causal inference with interactive fixed effects models. Polit Anal 25(1):57–76

    Article  Google Scholar 

  181. Yoon J, Jarrett D, van der Schaar M (2020) Google chrome privacy whitepaper. In: Curran associates, Inc. http://papers.nips.cc/paper/8789-time-series-generative-adversarial-networks.pdf

  182. Zhang K, Chan LW (2006) Extensions of ICA for causality discovery in the hong kong stock market. In: International conference on neural information processing. Springer, pp 400–409

  183. Zheng X et al (2017) State space LSTM models with particle MCMC inference. arXiv:1711.11179 [cs.LG]

  184. Zhu L, Lu W, Song R (2020) Causal effect estimation and optimal dose suggestions in mobile health. In: ICML

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Raha Moraffah.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moraffah, R., Sheth, P., Karami, M. et al. Causal inference for time series analysis: problems, methods and evaluation. Knowl Inf Syst 63, 3041–3085 (2021). https://doi.org/10.1007/s10115-021-01621-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10115-021-01621-0

Keywords

Navigation