Further Evidence on Modeling Wind Speed and Time-Varying Turbulence

Abstract

In a recent study of the simultaneous modeling of mean wind speed and its volatility, [Ewing, Kruse, and Thompson (2008), Analysis of time-varying turbulence in geographically-dispersed wind energy markets, Energy Sources, Part B: Economics, Planning, and Policy, 3:340–347] employ an ARMA-GARCH-M model to find that (1) current wind speed is dependent on immediate past wind speed; (2) regardless of location wind speed exhibits time-varying turbulence; and (3) the degree to which turbulence and wind speed are statistically correlated varies by location. This study extends the ARMA-GARCH-M model by examining the ARMA-Component GARCH-M model to differentiate between the permanent and transitory components of the conditional volatility (turbulence) associated with wind speed. The results indicate that shocks to wind speed (i.e., wind gusts) have varying effects on the transitory and permanent components of wind turbulence. At measurement heights of 20 and 40 meters, the shocks primarily affect the permanent component whereas the transitory component is larger than the permanent component at measurement heights of 70, 77, and 78 meters.

Keywords:

• GARCH models
• time-varying turbulence
• wind speed

Acknowledgments

The author would like to thank Brian Carroll for providing research assistance in the compilation of the wind speed data. He also appreciates the financial support of Dave Loomis, Executive Director of the Institute for Regulatory Policy Studies at Illinois State University.

Notes

¹ Conditional variance reflects the time-varying wind turbulence. Within wind engineering the standard deviation of record is normalized by the mean wind speed of record to yield turbulence intensity. Though turbulence intensity is relatively stable from record to record irrespective of mean wind speed, changes in the direction of wind may impact the upstream terrain conditions and affect the turbulence generation process (Ewing et al., 2007, footnote 4).

² For an overview see the edited volume by Ewing and Kruse (2006) entitled Economics and Wind for research related to the economic impact of wind related natural disasters.

³ Graphs of the wind speeds measured at different heights are available upon request.

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⁴ Engle et al. (1987) introduce the conditional variance (standard deviation) into the mean equation.

⁵ α + β = 1 denote an integrated (IGARCH) model in which shocks will have a permanent impact on wind turbulence.

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Quasi-maximum likelihood covariances and standard errors were calculated (Bollerslev and Wooldridge, 1992).

⁷ The eight cities include Atlanta, Las Vegas, Los Angeles, Philadelphia, Phoenix, Sacramento, San Francisco, and Seattle.

⁸ If ρ > α + β, the permanent variance component, q _t , exhibits the longest memory. If ρ = 1, the long-run volatility (turbulence) is an integrated process. Indeed, the CGARCH(1,1)-M model reduces to the GARCH(1,1) model if ρ = 0 or α + β = 0 (Engle and Lee, 1993).

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