FxPaul

Math in finance or vice versa

Posts Tagged ‘Markov

Markov Chain for historical volatility

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In previous post we used Markov Chain to discover a behavior of historical volatility and find out the 3/2 rule for ups and downs of random variable.

Now let’s construct more complicated model with the following volatility changes as states in chain:

  1. Less than -25%: denote it as -100.
  2. From -25% to -15% : -20.
  3. From -15% to -5% : -10.
  4. From -5% to 5% : 0.
  5. From 5% to 15% : 10.
  6. From 15% to 25% : 20.
  7. More than 25% : 100.

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Written by fxpaul

November 22, 2011 at 22:32

Posted in trading math

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Hidden Markov Model for application store ratings

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Hidden Markov model (HMM) is a statistical model in which the system is assumed to be a Markov process with hidden states. Those states can be recovered by outputs, observed sequences. In other words, it is possible to infer some probabilistic properties of the system by outputs.

As an off-topic, application stores usually give ranking to apps by user comments and rankings. The simplest way to derive an app rating is to calculate average or median, i.e. some statistical property based on rating samples. For average rating not being a robust statistics, its value is affected by outliers, for instance, by deviant rankings submitted by users. Thus a robust procedure might be used to improve ranking.

In fact we can apply HMM mechanics to infer real application rating by the most likely explanation of observed user rankings. Let’s see how to do that.

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Written by fxpaul

November 2, 2011 at 17:10

Posted in thoughts

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