Incorporating long memory into the modeling of gold prices

Inflation causes many people to move to gold as an option for savings because gold may be used as a hedging tool against currency devaluation and purchasing power erosion. This has contributed to the increased interest in forecasting the prices at the gold market, just like predicting the prices at the stock market, which exhibits uncertain movement, which can be described mathematically with Geometric Brownian Motion (GBM) and Geometric Fractional Brownian Motion (GFBM). This study aims to model Malaysian gold prices using both GBM and GFBM processes and compare the accuracy of these models. Absolute moment and aggregated variance techniques are used to estimate the Hurst exponents to model the prices with GFBM. These models are simulated using the Monte Carlo simulation via the Euler scheme, where the modeled prices will be tested for their accuracy using Mean Average Percentage Error (MAPE). Based on the findings, the MAPE values for both models exhibited significantly low MAPE values, which implies high accuracy in forecasting the gold prices for a long-term period. Nevertheless, the GFBM produces much lower MAPE values than the GBM, thus indicating that the former is more accurate than the latter.

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