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highly volatile state. Subsequent to 2011 the model reverts to switching between Regime #2 and
Regime #3.
It is clear that choosing the initial number of states to apply to a real returns stream is a
challenging problem. It will depend upon the asset class being utilised, how the trading for that
asset is carried out as well as the time period chosen.
14.4 Next Steps
In a later chapter the Hidden Markov Model will be used by a RiskManager subclass in QSTrader.
It will determine when to veto and close signals generated by a Strategy class in an attempt to
improve profitability over the case of no risk management.
14.5 Bibliographic Note
An overview of Markov Models (as well as their various categorisations), including Hidden Markov
Models (and algorithms to solve them), can be found in the introductory articles on Wikipedia[8],
[5], [7], [9], [6], [14], [18].
A highly detailed textbook mathematical overview of Hidden Markov Models, with applications
to speech recognition problems and the Google PageRank algorithm, can be found in
Murphy (2012)[71]. Bishop (2007)[22] covers similar ground to Murphy (2012), including the
derivation of the Maximum Likelihood Estimate (MLE) for the HMM as well as the Forward-
Backward and Viterbi Algorithms. The discussion concludes with Linear Dynamical Systems
and Particle Filters.
Regime detection has a long history in the quant blogosphere. Quantivity (2009, 2012)[83,
82, 84] replicates the research of Kritzman et al (2012)[65] using R to determine US equity
"regimes" via macroeconomic indicators. Slaff (2015)[93] applies the depmixS4 HMM library in
R to EUR/USD forex data to detect volatility regimes.
Systematic Investor (2012, 2015)[56, 57] initially uses simulated data and the RHmm package
in R to determine regime states, but then applies these methods to SPY using a rolling window
approach. A later post[58] reintroduces the methods using the depmixS4 package.
Gekkoquant (2014, 2015)[44, 43, 42, 45] provides a four-part series on applying HMM for
regime detection, using the RHmm package. The first two posts concentrate solely on the mathematics
of the model along with the derivation of the Viterbi algorithm. The third post considers
two approaches to using HMM: One HMM with each state representing a regime and another
with multiple HMM, one per regime. The final post applies this to a trend-following strategy,
ultimately leading to a Sharpe Ratio of 0.857.
Wiecki (2013)[100] presents a Guassian HMM in the Quantopian framework, although this is
not directly applied to a trading strategy.
14.6 Full Code
# Import the necessary packages and set
# random seed for replication consistency
install.packages(’depmixS4’)