Abstract
In this chapter we measure the effect a scheduled event, like the opening or closing of a regional foreign exchange market, or a unscheduled act, such as a market crash, a political upheaval, or a surprise news announcement, has on the foreign exchange rate’s level of volatility and its well documented long-memory behavior. Volatility in the foreign exchange rate is modeled as a non-stationary, long-memory, stochastic volatility process whose fractional differencing parameter is allowed to vary over time. This non-stationary model of volatility reveals that long-memory is not a spurious property associated with infrequent structural changes, but is a integral part of the volatility process. Over most of the sample period, volatility exhibits the strong persistence of a long-memory process. It is only after a market surprise or unanticipated economic news announcement that volatility briefly sheds its strong persistence.
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- 1.
Departure from the assumption of stationarity can be found in Stăriciă and Granger (2005).
- 2.
Our notation is such that u will always represent a time point in the rescaled time domain [0, 1]; i.e., \(u = t/T\).
- 3.
All proofs are rendered to Appendix 1.
- 4.
See Percival and Walden (2000) for an introduction to the MODWT.
- 5.
See Mallat (1989) for the seminal article on wavelets as presented from a multiresolution analysis point of view.
- 6.
The third equation in Assumption A.4 guarantees the orthogonality of the filters to double shifts and the first two conditions ensure that the wavelet has at least one vanishing moment and normalizes to one, respectively.
- 7.
Since the ‘central portion’ is dependent on the particular family and order of the wavelet filter, there is no closed-form expression for g(L j ). However, Whitcher and Jensen (2000) do tabulate the time width of Λ j for the Daubechies family of wavelets.
- 8.
A possible alternative to our semi-parametric OLS estimator of d(u) is the MCMC methodology of Jensen (2004), but this would first require developing a Bayesian sampling method for locally stationary processes. This is a topic for future research.
- 9.
Table 1 provides the actual conversion between the scaling parameter, j, of the MODWT and the time scale of the DM-$ time series.
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Acknowledgements
Mark Jensen would like to personally thank James Ramsey for his guidance and advice and for his openness to wavelet analysis and the inference it makes possible in economics, finance and econometrics. Both authors thank the seminar and conference participants at the University of Kansas, Brigham Young University, the Federal Reserve Bank of Atlanta, the Midwest Economic Meetings, the Symposium on Statistical Applications held at the University of Missouri–Columbia, the Conference on Financial Econometrics held at the Federal Reserve Bank of Atlanta, and the James Ramsey Invited Session of the 2014 Symposium on Nonlinear Dynamics and Econometrics held in New York, The views expressed here are ours and are not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.
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Jensen, M.J., Whitcher, B. (2014). Measuring the Impact Intradaily Events Have on the Persistent Nature of Volatility. In: Gallegati, M., Semmler, W. (eds) Wavelet Applications in Economics and Finance. Dynamic Modeling and Econometrics in Economics and Finance, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-07061-2_5
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