Open Access Original Research Article

Forecasting of Banking Sector Securities Prices in Kenya Using Machine Learning Technique

Marwa Hassan Chacha, Ayubu Anapapa, John Mutuguta

Asian Journal of Probability and Statistics, Page 19-30
DOI: 10.9734/ajpas/2022/v18i130434

Before investing in any company, an investor should have a basic understanding of how the stock market works. With the introduction of Machine Learning (ML), more resources have been spent to this area of research and it has been proved that stock market prediction is achievable. Although studies have been conducted in this area, there has not been a study to forecast banking sector security prices in Kenya using SVM – ML. Therefore, using the Machine Learning technique, this study aimed to forecast the banking sector security prices in Kenya. The study aimed at fitting ARIMA and SVM models for forecasting banking sector security prices in Kenya. The study targeted all banks listed by the Nairobi Securities Exchange and a sample of three banks was taken – Kenya Commercial bank, Equity bank, and Co-operative bank. To determine the models' performance capability, accuracy error metrics were used to assess them. SVM had an error of 0.01482, 0.1217, 0.1114 and 0.01922 for MSE, RMSE, MAE and MAPE respectively which were lower compared to ARIMA’s error results. SVM was recommended for forecasting banking sector security prices in Kenya as it proved reliable for forecasting.

Open Access Original Research Article

Empirical Investigations of Direction of Causality among Exchange Rates of Naira to Some Foreign Currencies

T. T. Ojewale, M. K. Garba

Asian Journal of Probability and Statistics, Page 31-42
DOI: 10.9734/ajpas/2022/v18i130435

The aim of this paper is to examine the direction of causality among some exchange rate of Nigeria Naira to US Dollar, Pounds Sterling and Euro. It made use of a time series data from the year 2005 to 2014. Toda and Yamamoto [1] procedure was used in analyzing the data. Augmented Dickey-Fuller, KPSS unit root test, the VAR selection method, Error correction model and Granger causality test based on Toda-Yamamoto procedure were used in this study as methods of analysis. The empirical analysis provides enough grounds to conclude that no causality relationship exists between the exchange rates.

Open Access Original Research Article

Stochastic Modeling for the Analysis and Forecasting of Stock Market Trend using Hidden Markov Model

Gulbadin Farooq Dar, Tirupathi Rao Padi, Sarode Rekha, Qaiser Farooq Dar

Asian Journal of Probability and Statistics, Page 43-56
DOI: 10.9734/ajpas/2022/v18i130436

The HMM is generally applied to forecast the hidden system of observation data. In this paper, we deal with the development of HMM for a proper understanding of finance variables in the stock market. Formulation of relationships between and within both the changing share values of Housing Development Finance Corporation Bank Limited (HDFC Bank Ltd) as visible/observed states influenced by the indicators of S&P Bombay Stock Exchange Sensitive Index (Sensex) as invisible/influencing states. Stochastic modeling with hidden Markov models is carried out for exploring various parameters of the model. Mathematical derivations for all the required statistical measures are obtained using the method of moments for the proposed probability distribution. Deducing mathematical formulation of initial probability vector, transition and observed probability matrices were carried out with the empirical data sets. Probability distribution for visible states of various lengths is obtained. It is observed from the empirically analysis that there is the maximum likelihood of rising the share prices of HDFC bank in consecutive two days. Furthermore, an attempt is made to estimate the long-run steady-state behavior of both the SENSEX and HDFC Bank share prices. The share value of HDFC bank will be on rising state from the 19th day onwards and it may be recommended for good investment choice for the long run. The findings of these studies will be valid for effective decision-making in portfolio management.

Open Access Original Research Article

Variational Bayesian Method: Ritz Method in Stochastic System

Hiroshi Isshiki

Asian Journal of Probability and Statistics, Page 57-78
DOI: 10.9734/ajpas/2022/v18i130437

Bayesian inference is to find posterior probabilities, but since it is difficult to find analytical solutions, it is often the case that approximate solutions are found. The variational Bayesian method is a powerful method for finding an approximate solution. It is a variational method in a stochastic system. Variational methods have been developed for the deterministic system since old times, and are one of the most powerful foundations for numerical solutions of a wide range of problems defined by partial differential equations. A detailed comparison and explanation of the classical variational principle and the variational Bayesian method are given, and the basic application examples of the variational Bayesian method are also given. Programming codes written in C are also shown to aid the readers’ understanding.

Open Access Review Article

Inverted Power Ishita Distribution and Its Application to Lifetime Data

A. Omoruyi Frederick, George A. Osuji, Chrisogonus K. Onyekwere

Asian Journal of Probability and Statistics, Page 1-18
DOI: 10.9734/ajpas/2022/v18i130433

In this paper, a new distribution, named ‘the Inverted Power Ishita distribution’, was introduced.  It is an extension of the Ishita distribution and its capable of modelling real life data with upside down bathtub shape and heavy tails was introduced. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions, except for the inverse power rama. As the criterion values, the AIC, BIC, AICc values, for both the proposed distribution and the inverse power rama distribution are approximately the same, stating that both may be interchangeably used.