Bayesian structural time series

<h2 id="general-model-description">General model description</h2>
<p>The model consists of three main components:
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<ol><li><a href="/facts/Kalman_filter/wNK7rnbk">Kalman filter</a>. The technique for time series decomposition. In this step, a researcher can add different state variables: trend, seasonality, regression, and others.</li>
<li><a href="/facts/Spike-and-slab_variable_selection/VhGqpv1c">Spike-and-slab</a> method. In this step, the most important regression predictors are selected.</li>
<li><a href="/facts/Ensemble_learning/GvFsd3Qc">Bayesian model averaging</a>. Combining the results and prediction calculation.</li></ol>
<p>The model could be used to discover the causations with its counterfactual prediction and the observed data.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
</p><p>A possible drawback of the model can be its relatively complicated mathematical underpinning and difficult implementation as a computer program. However, the programming language <a href="/facts/R_(programming_language)/LSrkr8K8">R</a> has ready-to-use packages for calculating the BSTS model,<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> which do not require strong mathematical background from a researcher.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Bayesian_inference_using_Gibbs_sampling/W8vpNEy4">Bayesian inference using Gibbs sampling</a></li>
<li><a href="/facts/Correlation_does_not_imply_causation/IeWeoMB9">Correlation does not imply causation</a></li>
<li><a href="/facts/Spike-and-slab_regression/VhGqpv1c">Spike-and-slab regression</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Scott, S. L., & Varian, H. R. 2014a. <a href="http://people.ischool.berkeley.edu/~hal/Papers/2012/fat.pdf">Bayesian variable selection for nowcasting economic time series</a>. <i>Economic Analysis of the Digital Economy.</i></li>
<li>Scott, S. L., & Varian, H. R. 2014b. <a href="http://people.ischool.berkeley.edu/~hal/Papers/2013/pred-present-with-bsts.pdf">Predicting the present with bayesian structural time series</a>. <i>International Journal of Mathematical Modelling and Numerical Optimisation.</i></li>
<li>Varian, H. R. 2014. <a href="http://people.ischool.berkeley.edu/~hal/Papers/2013/ml.pdf">Big Data: New Tricks for Econometrics</a>. <i>Journal of Economic Perspectives</i></li>
<li>Brodersen, K. H., Gallusser, F., Koehler, J., Remy, N., & Scott, S. L. 2015. <a href="http://research.google.com/pubs/pub41854.html">Inferring causal impact using Bayesian structural time-series models</a>. <i>The Annals of Applied Statistics.</i></li>
<li>R package <a href="https://cran.r-project.org/web/packages/bsts/bsts.pdf">"bsts"</a>.</li>
<li>R package <a href="https://google.github.io/CausalImpact/CausalImpact.html">"CausalImpact"</a>.</li>
<li>O’Hara, R. B., & Sillanpää, M. J. 2009. <a href="https://projecteuclid.org/euclid.ba/1340370391">A review of Bayesian variable selection methods: what, how and which</a>. <i>Bayesian analysis.</i></li>
<li><a href="/facts/Jennifer_A._Hoeting/0GmGrRJU">Hoeting, J. A.</a>, Madigan, D., Raftery, A. E., & Volinsky, C. T. 1999. <a href="https://projecteuclid.org/euclid.ss/1009212519">Bayesian model averaging: a tutorial</a>. <i>Statistical science.</i></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"Inferring causal impact using Bayesian structural time-series models". research.google.com. Retrieved 2016-04-17. <a href="http://research.google.com/pubs/pub41854.html" target="_blank">http://research.google.com/pubs/pub41854.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>"Interrupted Time-Series Design". Interrupted Time-Series Design. Insights Association. Retrieved 21 March 2019.{{cite web}}:  CS1 maint: url-status (link) <a href="https://www.insightsassociation.org/issues-policies/glossary/interrupted-time-series-design" target="_blank">https://www.insightsassociation.org/issues-policies/glossary/interrupted-time-series-design</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"Inferring causal impact using Bayesian structural time-series models". research.google.com. Retrieved 2016-04-17. <a href="http://research.google.com/pubs/pub41854.html" target="_blank">http://research.google.com/pubs/pub41854.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>"Inferring causal impact using Bayesian structural time-series models". research.google.com. Retrieved 2016-04-17. <a href="http://research.google.com/pubs/pub41854.html" target="_blank">http://research.google.com/pubs/pub41854.html</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>"bsts" (PDF). <a href="https://cran.r-project.org/web/packages/bsts/bsts.pdf" target="_blank">https://cran.r-project.org/web/packages/bsts/bsts.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>"CausalImpact". google.github.io. Retrieved 2016-04-17. <a href="https://google.github.io/CausalImpact/CausalImpact.html" target="_blank">https://google.github.io/CausalImpact/CausalImpact.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
</ol>

Bayesian structural time series open-in-new

Bayesian structural time series