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historical financial data.
14.3.3 Financial Data
In the above section it was straightforward for the Hidden Markov Model to determine regimes
because they had been simulated from a pre-specified set of Gaussians. The problem of regime
detection is actually an unsupervised learning challenge since the number of states is not known
a priori, nor is there any "ground truth" on which to train the HMM.
In this section two separate modelling tasks will be carried out. The first will involve fitting
the HMM with two regime states to S&P500 returns, while the second will utilise three states.
The results between the two models will be compared.
The process for applying the Hidden Markov Model provided by depmixS4 is similar to that
carried out for the simulated data. Instead of generating the returns stream from two Gaussian
distributions it will simply be downloaded using the quantmod library:
> # Obtain S&P500 data from 2004 onwards and
> # create the returns stream from this
> getSymbols( "^GSPC", from="2004-01-01" )
> gspcRets = diff( log( Cl( GSPC ) ) )
> returns = as.numeric(gspcRets)
The gspcRets time series object can be plotted, showing the volatile periods around 2008
and 2011. See Figure 14.5.
> plot(gspcRets)
Figure 14.5: Returns of the S&P500 over the period from 2004 onwards
As before a two-state Hidden Markov Model is fitted using the EM algorithm. The returns
and posterior probabilities of each regime are plotted. See Figure 14.6.