QUANTITATIVE FORECASTING AND RISK ANALYSIS IN BUSINESS MANAGEMENT USING APPLIED MATHEMATICS

Abstract

Quantitative forecasting refers to the mathematical practice of forecasting the future based on organized numerical patterns, statistical relations and model-based understandings. This paper applies mathematical methods to create risk-assessment and forecasting models on the basis of a high-dimensional multivariate lagged financial dataset. The analysis uses logistic regression and random forest classifier with 150 standardized lagged predictors obtained using five major financial instruments. The computations were all done in Python to guarantee accuracy, efficiency and transparency of methods. The empirical findings show that both models perform moderately in predicting results with accuracy values slightly above 0.50 which is inherently volatile and has a low signal to noise ratio of short-term financial movements. Random Forest is better in recall and F1-score than Logistic Regression, as it is more efficient to detect the upward directional trends. The results of feature importance indicate further that immediate (t-0) as well as more profound lag structures are also important determinants of prediction performance, which proves the existence of longer-term dependence in market behaviour. Complementary risk analysis indicates that volatility is high and Value-at-Risk is large, which supports the fact that forecasting is important when quantifying risk. On the whole, the results indicate the utility and the weakness of mathematical modelling in financial decision-making and suggest superior nonlinear approaches to enhancement in the future.