Modelling the GDP of KSA using linear and non-linear NNAR and hybrid stochastic time series models.

BACKGROUND: Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. METHODOLOGY: Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. RESULTS: The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. CONCLUSION: The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics.

On estimation procedures of stress-strength reliability for Weibull distribution with application.

For the first time, ten frequentist estimation methods are considered on stress-strength reliability R = P(Y < X) when X and Y are two independent Weibull distributions with the same shape parameter. The start point to estimate the parameter R is the maximum likelihood method. Other than the maximum likelihood method, a nine frequentist estimation methods are used to estimate R, namely: least square, weighted least square, percentile, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, method of Cramér-von Mises, Anderson-Darling and Right-tail Anderson-Darling. We also consider two parametric bootstrap confidence intervals of R. We compare the efficiency of the different proposed estimators by conducting an extensive Mont Carlo simulation study. The performance and the finite sample properties of the different estimators are compared in terms of relative biases and relative mean squared errors. The Mont Carlo simulation study revels that the percentile and maximum product of spacing methods are highly competitive with the other methods for small and large sample sizes. To show the applicability and the importance of the proposed estimators, we analyze one real data set.