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I have constructed a simple HMM (Hidden Markov Model) with 2 states on the Vol (stdev) of a time series of currency returns.

The state vector I produce looks reasonable, in the sense that it appears to have identified periods of high or low vol.

However, I appear to be able to generate a very similar state vector just by applying a simple rule like:

if (Vol) > x then 1 else 0.

Is there any advantage/difference to using a HMM?

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Maybe that in the HMM case you let the data decide the best set of regimes for you? –  Lisa Ann Aug 12 '13 at 13:55
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But maybe HMM just splits states in middle of range? if vol goes from 5% to 15% perhaps it just says if Vol > 10% then 1 else 0. If this is case why bother why more complicated HMM? –  user2675052 Aug 12 '13 at 14:19
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According to my experience with RHmm package, it usually does only when the two states have got the same st. dev. As instance, try that with the VIX index: you will get the "panic" state quite above 24 but with a huge variance (which explains the over 40 spikes). If you splitted in the middle range, you'd get different values. –  Lisa Ann Aug 12 '13 at 14:24
    
OK I see. So, the informational value of this simple HMM is not very different to my simple rule. BUT the fact I have not picked(optimised it) is useful right? –  user2675052 Aug 12 '13 at 14:42
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Cross-posted to NP. –  Joshua Ulrich Aug 12 '13 at 17:57

2 Answers 2

Have a look at the following paper:
Regime Shifts: Implications for Dynamic Strategies by Kritzman, Page and Turkington

From the paper (p. 25):

But why go through all the trouble? When dealing with regime shifts, we expect Markov-switching models to perform better than simple data partitions based on thresholds. For example, in Figure 1, if we had simply classified the observations that were in the highest quartile as being associated with Regime 2 (the high-mean regime), we would have misidentified the actual regime 40 times out of 200 observations. In contrast, a well calibrated Markov-switching model would have misidentified the actual regime only three times. Arbitrary thresholds give false signals because they fail to capture the persistence in regimes as well as changing volatilities

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Thanks you - that's a very interesting paper –  user2675052 Aug 12 '13 at 16:11
    
@user2675052: Thank you, I would appreciate if you could upvote and accept my answer then :-) –  vonjd Aug 13 '13 at 16:29

HMM allows to get transition matrix that provides additional information itself about probabilities of switching.

As HMM looks on complete state path it allows to identify, for example, short periods of low volatility in high volatility regime that were not a result of regime switching. If we apply some simple rule we have a larger number of switches and thus have biased transition matrix. If the results of this analysis are used in some forecasting or simulations, error in transition matrix would be crucial.

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