Limited Dynamic Forecasting of Hidden Markov Models

Abstract

Hidden Markov Models (HMMs) have emerged as an empirical “workhorse” in the marketing literature in capturing and forecasting within-customer non-stationary behaviors. Extant research has demonstrated that HMMs typically outperform nested benchmarks when examining fit statistics aggregated over individuals and time, but have remained largely silent on the set of dynamic out-of-sample forecasting paths offered by an HMM at the individual level. We examine the capabilities of a two-state HMM using theory and reveal a surprising result: an HMM’s forecasting paths are generally limited to monotonic mean-reverting trajectories. Specifically, they lack the notable flexibility associated with the in-sample state-switching imputations, which are generally (but, as we show, erroneously) presumed to exist in the holdout sample as well. Further, we find that common HMM extensions such as adding more hidden states, allowing for heterogeneity, allowing for covariates, and using hidden semi-Markov models do not alleviate the limited forecasting flexibility. Using a simulation design, we show how these limitations can affect forecasting performance empirically. We discuss implications of the limited forecasting properties of HMMs for researchers and managers.