Hidden Markov models for multi-scale time series : an application to stock market data

Abstract

Over the last decades, hidden Markov models have emerged as a versatile class of statistical models for time series where the observed variables are driven by latent states. While conventional hidden Markov models are restricted to modeling single-scale data, economic variables are often observed at different temporal resolutions: an economy’s gross domestic product, for instance, is typically observed on a yearly, quarterly, or monthly basis, whereas stock prices are available daily or at even finer temporal resolutions. In this paper, we propose hierarchical hidden Markov models to incorporate such multi-scale data into a joint model, where we illustrate the suggested approach using 16 years of monthly trade volumes and daily log-returns of the Goldman Sachs stock.