Traders and investors find predicting stock market values an intriguing subject to study in stock exchange markets. Accurate projections lead to high financial revenues and protect investors from market risks. This research proposes a unique filtering-combination approach to increase forecast accuracy. The first step is to filter the original series of stock market prices into two new series, consisting of a nonlinear trend series in the long run and a stochastic component of a series, using the Hodrick-Prescott filter. Next, all possible filtered combination models are considered to get the forecasts of each filtered series with linear and nonlinear time series forecasting models. Then, the forecast results of each filtered series are combined to extract the final forecasts. The proposed filtering-combination technique is applied to Pakistan's daily stock market price index data from January 2, 2013 to February 17, 2023. To assess the proposed forecasting methodology's performance in terms of model consistency, efficiency and accuracy, we analyze models in different data set ratios and calculate four mean errors, correlation coefficients and directional mean accuracy. Last, the authors recommend testing the proposed filtering-combination approach for additional complicated financial time series data in the future to achieve highly accurate, efficient and consistent forecasts.

The rise in global ozone levels over the last few decades has harmed human health. This problem exists in several cities throughout South America due to dangerous levels of particulate matter in the air, particularly during the winter season, making it a public health issue. Lima, Peru, is one of the ten cities in South America with the worst levels of air pollution. Thus, efficient and precise modeling and forecasting are critical for ozone concentrations in Lima. The focus is on developing precise forecasting models to anticipate ozone concentrations, providing timely information for adequate public health protection and environmental management. This work used hourly O ${}_3$ data in metropolitan areas for multi-step-ahead (one-, two-, three-, and seven-day-ahead) O ${}_3$ forecasts. A multiple linear regression model was used to represent the deterministic portion, and four-time series models, autoregressive, nonparametric autoregressive, autoregressive moving average, and nonlinear neural network autoregressive, were used to describe the stochastic component. The various horizon out-of-sample forecast results for the considered data suggest that the proposed component-based forecasting technique gives a highly consistent, accurate, and efficient gain. This may be expanded to other districts of Lima, different regions of Peru, and even the global level to assess the efficacy of the proposed component-based modeling and forecasting approach. Finally, no analysis has been undertaken using a component-based estimation to forecast ozone concentrations in Lima in a multi-step-ahead manner.