Hidden Markov Model & Stock Prediction

Hidden Markov Model & Stock Prediction

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  HMM & Stock Prediction DavidChiu @ ML/DM Monday http://ywchiu-tw.appspot.com/
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  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
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  STOCK PRICE PREDICTION
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  Every time historyrepeats 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
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  BENEFIT OF USINGHMM • Handle new data robustly • Computationally efficient to develop and evaluate • Able to predict similar patterns efficiently
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  HMM ON STOCKPREDICTION • 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.
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  CHARACTERIZE HMM • Numberof 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}
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  MODELING HMM
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  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?
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  BAUM-WELCH ALGORITHM • Findthe 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.
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  FIREARM
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  TOOL KIT • RPackage – HMM – RHMM • JAVA – JHMM • Python – Scikit Learn
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  DEMO
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  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$TWII.Volume)
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  BUILD HMM MODEL #Include RHMM Library •library(RHmm) # Baum-Welch Algorithm •hm_model <- HMMFit(obs =TWII_Train , nStates = 5) # Viterbi Algorithm •VitPath <- viterbi(hm_model, TWII_Train)
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  SCATTER PLOT • TWII_Predict<- cbind(TWII_Subset$TWII.Close, VitPath$states) • chartSeries(TWII_Predict[,1]) • addTA(TWII_Predict[TWII_Predict[,2]==1,1],on=1,type="p",col=5,pch=25) • addTA(TWII_Predict[TWII_Predict[,2]==2,1],on=1,type="p",col=6,pch=24) • addTA(TWII_Predict[TWII_Predict[,2]==3,1],on=1,type="p",col=7,pch=23) • addTA(TWII_Predict[TWII_Predict[,2]==4,1],on=1,type="p",col=8,pch=22) • addTA(TWII_Predict[TWII_Predict[,2]==5,1],on=1,type="p",col=10,pch=21)
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  DATA VISUALIZATION
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  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)
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  MODELING SAMPLE
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  MODELING SAMPLE
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  PREDICTION #State Prediction –using Scikit-learn •data_vec = [diff[last_day], volume[last_day]] •State = model.predict([data_vec])
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  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.