On modeling and forecasting the stock risk using a new statistical distribution and time series models

The value of probability distributions in reflecting practical events, especially in financial risk, is significant. The flexible Weibull extension distribution, recognized as a significant modification of the Weibull distribution, serves as a foundational distribution in our study. Thus, we present a new distribution known as the sine cosine flexible Weibull extension (SCFWE) distribution. We conduct a detailed study of the mathematical properties associated with the SCFWE distribution. We also detail the methodology for parameter estimation and present simulation studies that explore various combinations of parameter values. Furthermore, we analyze a practical data set that highlights the volatility of the financial market, thereby demonstrating the relevance of the SCFWE distribution within the financial sector. Furthermore, we use the traditional time series models such as the autoregressive (AR), autoregressive integrated moving average (ARIMA), and random walk for forecasting the stock volatility. Our findings show that ARIMA is the most accurate model having the lowest root mean squared error and mean absolute error, the AR performed poorly with the highest errors, while, the random walk showed moderate performance, but ARIMA emerged as the most reliable model for precise predictions.