Bayesian Structural Time Series and ARIMA; why not both?
I recently completed a small online course videocation on ARIMA and found it to be quite fascinating. I had previously seen many posts written about ARIMA, and many of them were often related to computer programming. Notwithstanding, I must confess that programming languages are really not one of my best strengths, though I am nonetheless quite captivated by the mathematics involved in computer science, as I consider it to be one of my many interests.
Trendy forecasting
In any context, be it political, business, entrepreneurial or even medical, we all rely on accurate forecasting as it is critical for making informed decisions and for keeping ahead. Therefore I consider the importance of having an understanding and statistical comphrension of such tools such as Bayesian Structural Time Series (BSTS) and ARIMA to be both future-proof and solid.
Bayesian Structural Time Series is a tool that analyses time-series data and predicts future trends by combining Bayesian statistics with time-series analysis. It provides a flexible and user-friendly framework for studying a broad range of time-series data, including financial data, economic data, and social data, and also medical research such as viral infection data.
As of such, I recently came across a highly informative and intuitive video on this topic by Aric LaBarre, an Associate Professor of Analytics at North Carolina State University. In his video, he demonstrated the classical time forecasting with autoregressive modelling and the moving averages, taking into consideration both the long term- and short term data for integrating it into a more precise estimation, hence the abbreviation ARIMA.
But being an ardent Bayesianist myself, I had to ask: What if we treated these data as a prior data, the likelihood of these time points data, in order to estimate a posterior distribution of what the future data will look like?
In his video aptly named the “Bayesians are coming to Time Series”, Professor LaCarre addresses this combination of BSTS and autoregressive modelling, as he made a quite useful and amusing analogy of the intrinsic differences between Freuquentists and Bayesianists methods: How would a Freuquentists and Bayesianists choose different fishing strategies when fishing in a pond?
As a frequentist, do you believe that the fish is stationary, and you cast several different nets or lures, hoping that they land in front of the fish? Or do you, in contrast, as a Bayesian, already know the probability of where the fish is moving and its movement patterns, allowing you to strategically cast one net or lure based on the probability that the fish will be in that area?
I also did enjoy the way he explained about MCMC, where his explanations made it so much easier to see the similarities in the statistical approaches of both MCMC (Markov Chain Monte Carlo) and BSTS.
Historic data repeats itself
The most exciting development in the field of time-series analysis is the combination of BSTS with ARIMA (AutoRegressive Integrated Moving Average) models. ARIMA models are another popular method for studying time-series data, and by combining them with BSTS, even more precise and accurate predictions can be made. As his brilliant video showed, the Mean Absolute Percentage Error (MAPE) showed to lowest by combining both autoregressive (AR) and Bayesian autoregressive methods, as demonstrated by the forecast of income vs. consumption.
By combing both frequentist and bayesian methods, you do not need to choose between either BSTS or ARIMA: as Professor LaCarre shows, the best is to combine both.
https://www.linkedin.com/in/martin-withaven-hansen/?locale=en_US
https://www.linkedin.com/in/martin-withaven-hansen/?locale=de_DE
https://towardsdatascience.com/bayesian-structural-time-series-interruption-method-5018761db92b
https://readmedium.com/forecasting-think-bayesian-9defa5f34502
