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Nikolay Gudkov (ETH Zurich)
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This paper proposes an efficient approach for modeling high-frequency commodity prices. Our methodology is purely data-driven as it combines wavelet analysis and kernel-based nonparametric statistics. By applying maximal overlap discrete wavelet transform, we estimate the smooth component of the wavelet decomposition, which is associated with low-frequency variations in the time series. The detail component of the wavelet decomposition is represented with a nonlinear autoregressive conditional heteroskedastic time series model of the form $X_{t+1} -X_t=\mu(X_t)dt+\sigma(X_t)\epsilon_{t+1}$. Using a local kernel regression, we estimate the drift and diffusion functions, $\mu(X_t)$ and $\sigma(X_t)$, thereby avoiding making parametric assumptions about the functional form of the coefficients. Particular attention is provided to selecting the bandwidth parameter, which is akin to model selection in parametric settings. From the analysis of high-frequency data for crude oil prices, we show that besides offering a convenient way of estimating the models for commodity prices, the procedure performs well, leading to consistent estimates that fall within the bootstrap confidence intervals and providing accurate price forecasting. We test our nonparametric estimates against various known diffusion specifications and document that the diffusion coefficient can be fitted efficiently using the parametric function of the form $(a+bX+cX^d)$. These results contrast with existing literature on the equity markets and underpin a particular nature of the commodity prices. This is joint work with Prof Katja Ignatieva from the School of Risk and Actuarial Studies, UNSW Sydney, Australia.

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