Modeling Stock Returns

• t-Distribution and GMM cannot perfectly modeling stock returns (ignore time, data not stationary)
• Sequence modeling (HMM) can be used to detect the time sequence clustering data

Graphical Models

Bayes Classifier (貝式分類器)

Markov Model

• States spaces

  [Healthy, Sneezing, Sick]

• Markov assumptions

  $p(w_t|w_{t-1},w_{t-2},w_{t-3},...)=p(w_t|w_{t-1})$

• Transition matrix

  			t
  		Healthy	Sneezing	Sick
  	Healthy	0.99	0.009	0.001
  t-1	Sneezing	0.5	0	0.5
  	Sick	0.2	0	0.8

HMM Graphical Model (Stock Return)

• Transitions probability (Hidden state): z(t) = regime (high volatility or low volatility)
• Emissions probability (Observed state): x(t) = return (or log return)