Hidden Markov Model & Stock Prediction

HMM & Stock
Prediction
David Chiu @ ML/DM Monday
http://ywchiu-tw.appspot.com/

HIDDEN MARKOV MODEL
• Finite state machine which has some fixed number of
states
• Provides a probabilistic framework for modeling a time
series of multivariate observations

Every time history repeats itself
• Stock behavior of past is similar to behavior of current day
• The Next day’s stock price should follow about the same past data
pattern

BENEFIT OF USING HMM
• Handle new data robustly
• Computationally efficient to develop and evaluate
• Able to predict similar patterns efficiently

HMM ON STOCK PREDICTION
• Using the trained HMM, likelihood value P for current
day’s dataset is calculated
• From the past dataset using the HMM we locate those
instances that would produce the nearest P likelihood
value.

CHARACTERIZE HMM
• Number of states in the model: N
• Number of observation symbols: M
• Transition matrix A = {aij} , where aij represents the transition
probability from state i to state j
• Observation emission matrix B = {bj(Ot)} , where bj(Ot) represent the
probability of observing Ot at state j
• Initial state distribution π = {πi}

Hidden Markov Model & Stock Prediction

PROBLEM OF HMM
1. The Evaluation Problem - Forward
– What is the probability that the given observations O = o1 ,o2
,...,oT are generated by the model p{O|λ} with a given HMM λ ?
1. The Decoding Problem - Viterbi
– What is the most likely state sequence in the given model λ that
produced the given observations O = o1 ,o2 ,...,oT ?
1. The Learning Problem - Baum-Welch
– How should we adjust the model parameters {A,B,π } in order to
maximize p{O|λ} , whereat a model λ and a sequence of
observations O = o1 ,o2 ,...,oT are given?

BAUM-WELCH ALGORITHM
• Find the unknown parameters of a hidden Markov model(HMM).
• Generalized expectation-maximization (GEM) algorithm
• Compute maximum likelihood estimates and posterior
mode estimates for the parameters (transition and emission
probabilities) of an HMM, when given only emissions as training
data.

TOOL KIT
• R Package
– HMM
– RHMM
• JAVA
– JHMM
• Python
– Scikit Learn

GET DATASET
• library(quantmod)
• getSymbols("^TWII")
• chartSeries(TWII)
• TWII_Subset<- window(TWII, start = as.Date("2012-01-01"))
• TWII_Train <- cbind(TWIISubset$TWII.Close - TWII_Subset$TWII.Open,
TWII_Subset$TWII.Volume)

BUILD HMM MODEL
# Include RHMM Library
•library(RHmm)
# Baum-Welch Algorithm
•hm_model <- HMMFit(obs =TWII_Train , nStates = 5)
# Viterbi Algorithm
•VitPath <- viterbi(hm_model, TWII_Train)

SCATTER PLOT
• TWII_Predict <- cbind(TWII_Subset$TWII.Close, VitPath$states)
• chartSeries(TWII_Predict[,1])
• addTA(TWII_Predict[TWII_Predict[,2]==1,1],on=1,type="p",col=5,pch=25)

SCIKIT LEARN
#Baum-Welch Algorithm
•n_components = 5
•model = GaussianHMM(n_components, "diag")
•model.fit([X], n_iter=1000)
# predict the optimal sequence of internal hidden state
•hidden_states = model.predict(X)

PREDICTION
#State Prediction – using Scikit-learn
•data_vec = [diff[last_day], volume[last_day]]
•State = model.predict([data_vec])

REFERENCE
• Hassan, M. (2009). A combination of hidden Markov model and
fuzzy model for stock market forecasting. Neurocomputing, 72(16),
3439-3446.
• Gupta, A., & Dhingra, B. (2012, March). Stock Market Prediction
Using Hidden Markov Models. In Engineering and Systems (SCES),
2012 Students Conference on (pp. 1-4). IEEE.

Hidden Markov Model & Stock Prediction

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