This study aims to forecast asset variances and covariances through the application of multi-scale risk models. Using daily data for 61 firms listed on the Amman Stock Exchange (ASE) over the period from January 1, 2001, to December 31, 2015, the analysis investigates the dynamic behaviour of asset returns across different time horizons. To enhance the robustness and reliability of the findings, several econometric and statistical techniques are employed, including the CUSUM test to assess structural stability, the Granger causality test to examine predictive relationships, wavelet transformation to capture time-frequency dynamics, and unit root tests to verify stationarity properties. The multi-scale risk model serves as the principal analytical framework, allowing for a comprehensive examination of the evolving interdependencies among asset returns. The empirical results indicate that market risk premium coefficients significantly explain variations in portfolio returns, highlighting the importance of systematic risk factors in asset pricing. Furthermore, portfolios composed of lower-value stocks outperform those containing higher-value stocks, while smaller-sized portfolios consistently generate higher returns than larger-sized portfolios during the sample period. Overall, the findings demonstrate the effectiveness of multi-scale risk models in forecasting asset variances and covariances. The model exhibits strong explanatory power in capturing daily portfolio return dynamics on the ASE, thereby contributing to improved portfolio optimization strategies and more accurate risk prediction. These results underscore the practical and theoretical value of multi-scale modelling in financial risk management.
Hallaq et al. (Sat,) studied this question.