Markov Process Modeling on Derived State Spaces of the Price Dynamics of Stock Market Indices

We explore and contrast two distinct ways of extracting discrete predictive models for the evolution of stock market time-series data. In particular, the two methods for constructing models are one, applying the commonly used “hollow candlestick” framework to the time series data on the daily level and feeding the result into a Markov chain inference module in R; two, applying the popular technical indicator “Fibonacci extension levels” to a filtered time-series data, then transcribing the price movements into a sequence to be fed into the same Markov chain inference module. Whereas continuous-time stochastic models are well studied and widely deployed in the computational trading industry and among econometrics scholars, models that are discrete in nature remain extremely popular among professional and amateur traders. In this paper, we set out to apply formal statistical methods to two discrete trading models to gain a better understanding of their predictive power and utility.