What explains long memory in futures price volatility?

Abstract

Long memory in futures price volatility is a well-documented stylized fact with implications for market efficiency, risk management, forecasting and option pricing bias. The implications of long-memory differ, however, based on whether it is of a ‘fractional’ or of a ‘stochastic’ type. The aims of this article are to determine, in the case of agricultural commodity futures data, which type better describes price volatility and also to evaluate several competing explanations for findings of long memory. The evidence presented here finds little support for three out of four potential explanations, namely, excessive noise in the volatility measure, bias in the long-memory estimator and understated SEs of the long-memory parameter. For the data considered, price volatility appears to be most likely generated by a nonfractional long-memory process such as a stochastic break or stochastic unit root.

Notes

¹ We thank a journal reviewer for particularly helpful comments on this issue.

² In this article, long memory is described by the fractional difference parameter d and not the Hurst coefficient H (Hurst, 1951), but the findings about d may be related to the value of H without difficulty. More details are available upon request.

³ Granger and Hyung (2004) find that in typical financial time series (daily absolute log returns of prices), estimates of the fractional difference parameter d are close to 0.5 in large samples but vary between 0.3 and 0.7 for shorter sub-samples.

⁴ Calendar effects are expected to have only a negligible effect. These anomalies have essentially disappeared since 1987 (Fortune, 1998) and they are generally not significant once unintentional data snooping is accounted for (Sullivan et al., 2001).

⁵ To be precise, log returns should be computed as deviations from the long-run mean, but the empirical literature has found that assuming a long-run mean of zero provides a substantial efficiency gain at the expense of only a very small bias.

⁶ Test details are omitted but available from the authors.

⁷ The optimal estimator naturally depends on the assumptions and objectives of the article. For example, the FIGARCH (Baillie et al., 1996) and long-memory stochastic volatility (Breidt et al., 1998) models are ideally suited to capture volatility dynamics in the presence of long memory, but less so to accurately estimate d (Alizadeh et al., 2002).

⁸ The ML estimator is exact because wavelets provide a sparse representation of the covariance matrix (Jensen, 2000).