The Macroeconomic Determinants of Volatility in Precious Metals Markets

Note that this process assumes the price return is characterized as a submartingale
process (Ross, 1989) and X denotes the vector of macroeconomic explanatory variables
at time t. Since we are interested in volatility linkages, the conditional standard deviation
of returns can be written as:

E_t (σ_t∖I_t-ι) = f ( Et (σtX ))                                              (2)

Macroeconomic factors are observed monthly, therefore, we rely on the methodology
developed by Davidian and Carroll (1987) when estimating the conditional standard
deviations. It is noteworthy that this approach is used in prior work by Sadorsky (2003),
Kearney (2000) and Kautolas and Kryzanowski (1996) among others. Allow σ_t^x to
denote the unconditional standard deviation of the vector of macroeconomic variables
and h_t^x to denote the conditional standard deviations of these variables. The conditional
standard deviations are then estimated as h_t^x = σ_t^x - u₂^x_,t utilizing the equation below,
where

12
σt^x=β1(L)σt^x+∑βs,jDUMj,t+ut^x,t                              (3)

j

and β₁(L) is a 12^th order polynomial in the lag operator, while DUM is a monthly
seasonal dummy variable. The series σ^x =∖ u₁^x_,t ∖ is calculated as the residuals from the
following regression

12

u1^x,t =∆Xt-Et(∆Xt ∖It-1)=∆Xt-λ1(L)∆Xt-∑λs,jDUMj,t             (4)

j=1

This approach is based on the notion that standard deviations based on the absolute value
of the prediction errors are more robust than measures based on the squared residuals
alone (Davidian and Carroll, 1987). Moreover, as argued by Sadorsky (2003), the

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