Modeling and forecasting time series of precious metals: a new approach to multifractal data

We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale. First, the long range and co-movement dependencies of the time series are scrutinized on time-frequency space using multiple wavelet coherence analysis. Then, the multifractal behaviors of the series are verified by multifractal de-trended fluctuation analysis and its local Hurst exponents are calculated. Additionally, root mean squares of residuals at the specified scale are procured from an intermediate step during local Hurst exponent calculations. These internally calculated series have been used to estimate the process with vector autoregressive fractionally integrated moving average (VARFIMA) model and forecasted accordingly. In our study, the daily prices of gold, silver and platinum are used for assessment. The results have shown that all metals do behave in phase movement on long term periods and possess multifractal features. Furthermore, the intermediate time series obtained during local Hurst exponent calculations still appertain the co-movement as well as multifractal characteristics of the raw data and may be successfully re-scaled, modeled and forecasted by using VARFIMA model. Conclusively, VARFIMA model have notably surpassed its univariate counterpart (ARFIMA) in all efficacious trials while re-emphasizing the importance of co-movement procurement in modeling. Our study's novelty lies in using a multifractal de-trended fluctuation analysis, along with multiple wavelet coherence analysis, for forecasting purposes to an extent not seen before. The results will be of particular significance to finance researchers and practitioners.