Journal of Statistical Modeling & Analytics (JOSMA)

A Monte Carlo Experiment on the Asymptotic Efficiency of System Estimators under Multicollinearity

EMMANUEL ODUNTAN — Wed, 25 Oct 2023 00:00:00 +0800

Classical linear regression model assumes that there is no multicollinearity among the explanatory variables in a regression model. Contrary to this assumption, where multicollinearity is perfect, the regression coefficients of the explanatory variables are indeterminable and their standard errors are infinite. On the other hand, where multicollinearity is less than perfect, the regression coefficients, although determinable, possess large standard errors. This implies that the coefficients cannot be estimated with great precision. Hence multicollinearity problem is a major problem in econometric analysis. Using Monte Carlo Simulation, we evaluated the asymptotic efficiency of six estimators (OLS, ILS,2SLS, 3SLS, LIML and FIML), under different magnitudes of the unintended linear relationship between the exogenous variables. Using the SSR criteria, we found that OLS followed by ILS turned out the best estimates amongst the six estimators under multicollinearity. We also found that with increasing sample size, there is no remarkable asymptotic effect in the performance of the estimators at the levels of multicollinearity.

Bayesian Restricted Stein-rule Least Squares with non-spherical Disturbances

Isiaka Oloyede — Wed, 25 Oct 2023 00:00:00 +0800

Bayesian restricted stein-rule least squares is a novelty estimator introduced to obtain parameters of the family of restricted least squares with intertwined heteroscedastic and autocorrelated disturbance errors. Errors in regression modelling set to measure the quality of the data and or model of which intertwining of most prominent errors disturbances play a significant role in determining the quality of the aforementioned. Efforts were geared towards the comparison of the performances and relative efficiency of the small sample property of Bayesian and classical family of restricted stein-rule least squares. The sample size was set at 25 to capture the intertwined disturbance errors, and the iteration of the Monte Carlo simulation was set at 10000 for both classical and Bayesian paradigms. and for both Autoregressive of order one (AR(1)) and Moving average of order one (MA(1)) processes respectively were set asymmetrically as -0.8,-0.5,-0.3, 0,0.3,0.5 and 0.8 while as a scale of heteroscedasticity was set at 0-homoscedasticity, -0.3-mild,-0.5-moderate and (0.7,0.9)-severe. The outcome of the study pointed out that Bayesian estimation (both posterior mean and Bayes estimates) for both restricted and restricted stein-rule estimators outperformed classical restricted and restricted stein-rule estimators in both performances and relative efficiency. It is therefore recommended to make use of the Bayesian framework when encountering similar disturbances in a small sample size.

The Use of Standardized Exponentiated Gumbel Error Innovation Distribution to Forecast Volatility: A Comparative Study

Michael Sunday Olayemi — Wed, 25 Oct 2023 00:00:00 +0800

This study is designed to model several selected volatility models using a newly developed error innovation distribution called Standardized Exponentiated Gumbel Error Innovation Distribution (SEGEID) to determine the efficiency and effectiveness of the model in terms of its adaptability and forecast evaluation. SEGEID improves some existing error distributions and uses the standard&Poor-500 index data returned from 2004 to 2022.The use of this error innovation distribution, GJR-GARCH (1,1), has been shown to be more effective than other volatility models considered in this study. The results of the study show that GJR-GARCH (1,1) is better than GARCH (1,1), EGARCH (1,1) and TGARCH (1, 1) because it has the lowest AIC and RMSE.

Predicting Indonesia’s Gross Domestic Product (GDP): A Comparative Analysis of Regression and Machine Learning Models

Christopher Kevin Widjaja, Huei Ching Soo, Bernadette Marini Lawardi — Wed, 25 Oct 2023 00:00:00 +0800

This research paper presents an analysis of Indonesia's quarterly Gross Domestic Product (GDP) growth spanning a significant 13-year period, from the first quarter of 2010 to the fourth quarter of 2022. The study focuses on utilizing four key economic indicators to gain insights into the country's economic performance during this timeframe. To develop accurate predictive models, we utilize Multiple Linear Regression (MLR), K-Nearest Neighbours (K-NN), and Artificial Neural Network (ANN) approaches. The models are compared based on performance metrics, including the Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE). Our findings indicate that the MLR model outperforms the machine learning models, K-NN and ANN, in forecasting Indonesia's GDP. This suggests that a simpler and more explainable model, such as MLR, suffices to provide meaningful and interpretable results. The paper's insights are valuable to economists, policymakers, and researchers, offering a practical and understandable means to predict Indonesia's economic trajectory.

Keywords: Artificial Neural Network (ANN), Gross Domestic Product (GDP), K-Nearest Neighbours (K-NN), Multiple Linear Regression (MLR), Predictive Models.

Parameter Estimation for Circular Simultaneous Functional Relationship Model (CSFRM) for Unequal Variances

FATIN NAJIHAH BADARISAM, Mohd Syazwan Mohamad Anuar — Wed, 25 Oct 2023 00:00:00 +0800

In this study, we propose an extended model of the Circular Simultaneous Functional Relationship Model from the Circular Functional Relationship Model. In this case, the circular model and the circular variable will be applied where assuming the error variances are not equal. All estimations of the parameter followed von Mises distribution. The angular and slope parameters are obtained using the ms function, while concentration parameter estimation is obtained from the polyroot function provided in the SPLUS statistical package. The simulation study has been conducted to assess the efficiency of the proposed model. The simulation results showed that as sample size and concentration parameters increase, all parameters’ estimates are close to the true value and have a smaller bias. The illustration of real wind and wave direction data from two different bases of data is given to show its practical applicability. We note that the proposed method for parameter estimation works well with the proposed model.

Keywords: circular simultaneous functional relationship model, ms function, parameter estimates, polyroot function, unequal variances

Nonlinear Autoregressive Neural Network for Forecasting COVID-19 Confirmed Cases in Malaysia

NUR HAIZUM ABD RAHMAN — Wed, 25 Oct 2023 00:00:00 +0800

A nonlinear autoregressive neural network (NARNN) model is a feedforward neural network for handling complex nonlinear time series problem. In this study, the tangent sigmoid (tansig) activation function with different number of past values and different number of hidden neurons for NARNN model is determined. The COVID-19 daily confirmed cases in Malaysia are collected with different amount of sample used which are 100, 500 and 900. Therefore, data of 100, 500 and 900 days prior to 21 September 2022 are extracted for the NARNN model training, validation and testing procedure. The lowest average mean squared error (MSE) are considered as the best combination. Result shown that the past value 1:10 and number of neurons of 10 when the sample size is 100. At sample size 500, past values of 1:10 and number of neurons of 8 enables the model to perform at its best. Whereas for sample size 900, network setting of 1:5 past value and 5 hidden neurons gives the least MSE. Multi-step ahead time series forecasting is conducted to forecast the number of COVID-19 confirmed cases in 7 days which is from 22 to 28 September 2022. The result shown for 7-days-ahead confirmed cases forecasting Malaysia datasets, the best forecasting outcome occurs when 900 samples are inputted.