Point and Figure Portfolio Optimization using Hidden Markov Models and Its Application on the Bumi Resources Tbk Shares

2021 ◽  
Vol 3 (1) ◽  
pp. 44-52
Author(s):  
Kastolan Kastolan ◽  
Berlian Setiawaty ◽  
N. K. Kutha Ardana
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Portfolio Optimization ◽  
Expectation Maximization ◽  
Stock Prices ◽  
Stock Price ◽  
Hidden Markov ◽  
Expectation Maximization Algorithm ◽  
Percentage Error ◽  
Time Sampling

AbstractThe problem of portfolio optimization is to select a trading strategy which maximizes the expected terminal wealth. Since the stocks are traded at discrete random times in a real-world market, we are interested in a time sampling method. The sampling of stock price is obtained from the process of time sampling which is used in a point and figure chart. Point and figure (PF) chart displays the up and down movements of unbalanced stock prices. The basic idea is to describe essential movements of the unbalanced stock prices using a hidden Markov model. The model parameters are transition probability matrices. They are estimated using maximum likelihood method and expectation maximization algorithm. The estimation procedure involves change of measure. The model is then applied to the stock price of Bumi Resources Tbk. collected on a daily basis. The estimated parameters are used to calculate the optimal portfolio using a recursive algorithm. The results show that the discrete hidden Markov model can be applied to describe essential movements of the stock price. The best result gives 93.63% accuracy of the estimate of observation sequence with mean absolute percentage error (MAPE) 3.63%. The numerical calculation shows that the optimal logarithmic PF-portfolio increases the wealth.Keywords: point and figure portfolio; optimization portfolio; discrete hidden Markov model; expectation maximization algorithm; stock price of Bumi Resources Tbk. AbstrakMasalah pengoptimalan portofolio adalah pemilihan strategi perdagangan yang dapat memaksimalkan kekayaan terminal yang diharapkan. Karena di pasar dunia nyata, saham diperdagangkan pada waktu acak yang berbeda, sehingga kami tertarik pada metode pengambilan sampel waktu. Proses pengambilan sampel waktu diperoleh sampling harga saham yang digunakan dalam diagram point and figure (PF-chart). Grafik point and figure hanya menampilkan pergerakan naik atau turun harga saham yang tidak seimbang. Ide dasarnya adalah untuk mendeskripsikan pergerakan esensial dari harga saham yang tidak seimbang menggunakan model hidden Markov. Parameter dari model ini adalah matriks probabilitas transisi. Parameter diestimasi menggunakan metode maximum likelihood dan algoritma expectation maximization. Prosedur estimasi melibatkan perubahan ukuran. Model ini kemudian diaplikasikan pada harga saham Bumi Resources Tbk. dari tanggal 2 Januari 2007 sampai dengan 31 Januari 2011. Hasil estimasi parameter tersebut digunakan untuk menghitung portofolio optimal menggunakan algoritma rekursif. Hasil penelitian ini menunjukkan bahwa model hidden Markov diskrit dapat diterapkan untuk menggambarkan pergerakan esensial dari harga saham. Model terbaik memberikan akurasi 93.63% dari estimasi deretan observasi dengan mean absolute percentage error (MAPE) 3,63% dan 5 faktor penyebab kejadian. Perhitungan numerik menunjukkan bahwa logaritma portofolio-PF yang optimal dapat meningkatkan kekayaan.Kata kunci: portofolio point and figure; optimalisasi portofolio; model hidden Markov diskrit; algoritma expectation maximization; harga saham PT Bumi Resources.

Application of Enhanced Hidden Markov Model in Stock Price Prediction

2020 ◽  
Vol 3 (1) ◽  
pp. 70-78
Author(s):  
Donata D. Acula ◽  
Teofilo De Guzman
Keyword(s):  
Neural Networks ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Stock Price ◽  
Hidden Markov ◽  
Moving Average ◽  
High Price ◽  
Percentage Error ◽  
Autoregressive Integrated Moving Average ◽  
Stock Price Prediction

The main focus of this research is the enhancement of the Hidden Markov Model by using some features of Neural Networks and the forecasted values of predictors by Seasonal Autoregressive Integrated Moving Average. The enhanced method was used to predict the close price of stocks whose predictors are open price, high price, low price, and volume of Apple and Nokia data. The performance of the method was measured using the Mean Absolute Percentage Error of the predicted price. The result was compared against the actual close price by using the paired T-test. The testing of the hypothesis showed that the Enhanced Hidden Markov Model obtained more than 94% accuracy rate. It also shows that in Apple data, the predicted close price of the Enhanced Hidden Markov Model is significantly better than the predicted close price of Neural Networks. Using Nokia data, the test claims that there is no difference between the performance of Enhanced Hidden Markov Model and Neural Network in prediction. 

scholarly journals A Hidden Markov Model inference approach to testing the Random Walk Hypothesis: Empirical evidence from the Nigerian Stock Market

2016 ◽  
Vol 9 (3) ◽  
pp. 696-713
Author(s):  
Edesiri Nkemnole
Keyword(s):  
Random Walk ◽  
Stock Market ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Stock Prices ◽  
Stock Price ◽  
Hidden Markov ◽  
Random Walk Process ◽  
Hidden States ◽  
Stock Price Movements

The movement of stock prices, in capital markets across the world, has been found to be both random and non-random. Basically, for a stock price to follow a random walk, its future price changes randomly based on all currently available information in the stock market, its price history inclusive. Some research findings have shown that the existing traditional unit root tests have low statistical power and hence cannot capture gradual changes over successive observations. Consequently, there is a need to revisit the random walk theory in stock prices using other tests. This study employs a Hidden Markov Model (HMM) with time-varying parameters to assess whether the stock price movements of the Nigerian Stock Exchange (NSE) follow a random walk process, or otherwise. Via hidden states, the HMM allows for periods with different volatility levels characterised by the hidden states. By simply accounting for the non-constant variance of the data with a two-state Hidden Markov Model and taking estimation into account via the Sequential Monte Carlo Expectation Maximisation (SMCEM) technique, this study finds no support of randomness. In conclusion, the stock price movements of the NSE do not follow the random walk process.

Prediction of Facies Distribution in a Clastic Reservoir Using a Hidden Markov Model Combined With an Expectation-Maximization Algorithm

2016 ◽  
Author(s):  
Hwasoo Suk ◽  
Baehyun Min ◽  
Joe M. Kang ◽  
Cheolkyun Jeong
Keyword(s):  
Probability Distribution ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Expectation Maximization ◽  
Hidden Markov ◽  
Transition Probability ◽  
Expectation Maximization Algorithm ◽  
Model Parameters ◽  
Facies Distribution ◽  
Clastic Reservoir

This study determines facies distribution in a clastic reservoir using a hidden Markov model combined with an Expectation-Maximization algorithm. Iterating expectation and maximization steps of the algorithm builds the hidden Markov model by tuning the model parameters including initial state distribution, state transition probability distribution, and observable symbol probability distribution. Optimized model parameters contribute to improving the predictability of facies distribution along the well trajectory using core and logging data.

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