I would highly recommend this book for anyone interested in performing time series analysis with HMM, and it also contains some great R code templates, which we'll be referencing throughout this post.Ī discrete-time Markov chain is a set of random variables C for which the probability of the next value in the chain is only conditional on the most recent value: The following description is based on the very excellent textbook about Hidden Markov Models by Zucchini and colleagues called Hidden Markov Models for Time Series: An Introduction Using R, Second Edition (CRC Press, 2016). For that reason, alternative approaches were needed to analyze a time series of non-Gaussian data one of which is called the Hidden Markov Model. For time series data, where there are generally many observations on a single individual over time (as opposed to most longitudinal approaches based on a couple of repeated measures per person), either of these methods are impractical due to the size of the covariance matrix needed to be estimated and large number of parameters. Marginal models are used for population average inference, while mixed effects models are used for individual prediction). (This is the reason that analysis on nonlinear panel data requires one or the other of two different methods-marginal models obtained from general estimating equations and mixed effects models-depending on the goal. For a nonlinearly distributed variable, the overall average is not necessarily the same as the average of each group. The reasons for why other nonlinear distributions come up short are somewhat complex, but can generally be summed up as due to the fact that for groups of a Gaussian variable, the average of the pooled sample is the same as the average of each group's average. One of the challenges of prior approaches to time series analysis is that many of these techniques are based on the series being a normal (Gaussian) distributed, continuous variable.
We're not done with them, and will likely return to these approaches in later posts, particularly as we focus on automation of analysis in more detail. We're going to move on from the Box-Jenkins and frequency domain approaches to our data to some more exciting and novel approaches.
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