advanced-algorithmic-trading

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> # Fit a Hidden Markov Model with two states
> # to the S&P500 returns stream
> hmm <- depmix(returns ~ 1, family = gaussian(), nstates = 2,
data=data.frame(returns=returns))
> hmmfit <- fit(hmm, verbose = FALSE)
> post_probs <- posterior(hmmfit)
>
> # Plot the returns stream and the posterior
> # probabilities of the separate regimes
> layout(1:2)
> plot(returns, type=’l’, main=’Regime Detection’, xlab=’’, ylab=’Returns’)
> matplot(post_probs[,-1], type=’l’,
main=’Regime Posterior Probabilities’,
ylab=’Probability’)
> legend(x=’bottomleft’, c(’Regime #1’,’Regime #2’), fill=1:2, bty=’n’)
Figure 14.6: Two-state Hidden Markov Model applied to S&P500 returns data
Notice that within 2004 and 2007 the markets were calmer and hence the Hidden Markov
Model has given high posterior probability to Regime #2 for this period. However between 2007-
2009 the markets were incredibly volatile due to the financial crisis. This has the initial effect of
rapidly changing the posterior probabilities between the two states but being fairly consistently
in Regime #1 during 2008 itself.
The markets became calmer in 2010 but additional volatility occurred in 2011, leading once
again for the HMM to give high posterior probability to Regime #1. Subsequent to 2011 the
markets became calmer once again and the HMM is consistently giving high probability to
Regime #2. In 2015 the markets once again became choppier and this is reflected in the increased
switching between regimes for the HMM.