Stochastic Forecasting of Stock Prices in Nigeria: Application of Geometric Brownian Motion Model

Purpose: The purpose of the study is to model and simulate the trends and behavioral patterns in The Nigerian Stock Market and hence predict the future stock prices within the Geometric Brownian Motion (GBM) framework. Methodology: The methodology involves a comparison of forecasted daily closing prices to actual prices in order to evaluate the accuracy of the prediction model. Based on the model assumptions of the GBM with drift: continuity, normality and Markov tendency, the study investigated four years (2015 - 2018) of historical closing prices of ten stocks listed on The Nigerian Stock Exchange. The sample for this study is based on the most continuously traded stocks. Findings: The results show that in the simulation there are some actual stock prices located outside trajectory realization that may be from GBM model. Thus, the model did not predict accurately the price behavior of some of the listed stocks. The predictive power of the model is declining towards the longer the evaluated time frame proven by the higher value of the mean absolute percentage error. The value of the MAPE is 50% and below for the one- to two-year holding periods, and above 50% for the three-year holding period. Unique Contribution to theory, Practice and Policy: The MAPE and directional prediction accuracy method provide support that over short periods the GBM model is accurate. Meaning that the GBM is a reasonable predictive model for one or two years, but for three years, therefore, it is an inaccurate predictor. It is recommended that the technical analyst whose primary motive is to make gain at the expense of other participants should identify high volatile portfolio in any holding period for effective prediction Investors with long-range holding position as investment strategy should concentrate more on low capitalized stocks rather than stocks with large market capitalization. This is a unique contribution to theory, practice and policy.

Comparison of Stochastic Forecasting Models

In this work, we compare several stochastic forecasting techniques like Stochastic Differential Equations (SDE), ARIMA, the Bayesian filter, Geometric Brownian motion (GBM), and the Kalman filter. We use historical daily stock prices of Microsoft (MSFT), Target (TGT) and Tesla (TSLA) and apply all algorithms to try to predict 54 days ahead. We find that there are instances in which all algorithms do well, or do poorly. We find that all three stocks have a strong auto-correlation and a high Hurst factor which shows that it is possible to predict future prices based on a short history of past prices. In our geometric Brownian motion model, we have two parameters for drift and diffusion which are not time dependent. In our more general SDE model (TDNGBM), we have time-dependent drift and time-dependent diffusion terms which makes it more effective than GBM. We measure all algorithms on the correlation between the predicted and actual values, the mean absolute error (MAE) and also the confidence bounds generated by the methods. Confidence intervals are more important than point forecasts, and we see that TDNGBM and ARIMA produce good bounds.

Streamflow Prediction Improvement using Deterministic and Stochastic Wavelet-based Methods Coupled with Extreme Learning Machine

Accurate and reliable streamflow forecasting is important in hydrology and water resources planning and management. In the present work, wavelet-based direct (DF) and multi-component (MF) forecast methods performed by the à trous algorithm (AT) are proposed for both deterministic and stochastic monthly streamflow prediction improvement. They are developed in the case of the one-month lead streamflow prediction of the East River basin in China, and then compared with the benchmarks that are implemented without wavelet transform so as to evaluate the effectiveness for forecasting accuracy improvement. An existing blueprint that is flexible and practical to incorporate various sources of forecast uncertainty is extended to generate the stochastic probability prediction of streamflow. Partial mutual information is adopted for predictors selection, and six kinds of Extreme learning machine (i.e. one linear ELM and five common nonlinear kinds) are separately used as the learning algorithms coupled with the wavelet-based forecast methods to conduct a comprehensive performance evaluation. The comparison results indicate that both DF and MF can effectively increase the point prediction accuracy of monthly streamflow under deterministic and stochastic forecasting conditions, while MF performs better than DF. For stochastic prediction, it is much more reasonable to consider both parameter and model error uncertainties than just to consider only parameter uncertainty, and with the reasonable setting MF method can significantly improve the probabilistic interval prediction by greatly improving the forecast sharpness. It can be concluded that the approach using AT wavelet-based DF or MF could provide a feasible way for streamflow prediction improvement.

Mathematical modeling approach to predict COVID-19 infected people in Sri Lanka

<abstract> <p>The novel corona virus (COVID-19) has badly affected many countries (more than 180 countries including China) in the world. More than 90% of the global COVID-19 cases are currently outside China. The large, unanticipated number of COVID-19 cases has interrupted the healthcare system in many countries and created shortages for bed space in hospitals. Consequently, better estimation of COVID-19 infected people in Sri Lanka is vital for government to take suitable action. This paper investigates predictions on both the number of the first and the second waves of COVID-19 cases in Sri Lanka. First, to estimate the number of first wave of future COVID-19 cases, we develop a stochastic forecasting model and present a solution technique for the model. Then, another solution method is proposed to the two existing models (SIR model and Logistic growth model) for the prediction on the second wave of COVID-19 cases. Finally, the proposed model and solution approaches are validated by secondary data obtained from the Epidemiology Unit, Ministry of Health, Sri Lanka. A comparative assessment on actual values of COVID-19 cases shows promising performance of our developed stochastic model and proposed solution techniques. So, our new finding would definitely be benefited to practitioners, academics and decision makers, especially the government of Sri Lanka that deals with such type of decision making.</p> </abstract>

An Ensemble Stochastic Forecasting Framework for Variable Distributed Demand Loads

Accurate forecasting of demand load is momentous for the efficient economic dispatch of generating units with enormous economic and reliability implications. However, with the high integration levels of grid-tie generations, the precariousness in demand load forecasts is unreliable. This paper proposes a data-driven stochastic ensemble model framework for short-term and long-term demand load forecasts. Our proposed framework reduces uncertainties in the load forecast by fusing homogenous models that capture the dynamics in load state characteristics and exploit model diversities for accurate prediction. The ensemble model caters for factors such as meteorological and exogenous variables that affect load prediction accuracy with adaptable, scalable algorithms that consider weather conditions, load features, and state characteristics of the load. We defined a heuristic trained combiner model and an error correction model to estimate the contributions and compensate for forecast errors of each prediction model, respectively. Acquired data from the Korean Electric Power Company (KEPCO), and building data from the Korea Research Institute, together with testbed datasets, were used to evaluate the developed framework. The results obtained prove the efficacy of the proposed model for demand load forecasting.