The Role of Jumps in Volatility Spillovers in Foreign Exchange Markets: Meteor Shower and Heat Waves Revisited

ABSTRACT

This article extends the literature on geographic (heat waves) and intertemporal (meteor showers) foreign exchange volatility transmission to characterize the role of jumps and cross-rate propagation. We employ multivariate heterogenous autoregressive (HAR) models to capture the quasi-long memory properties of volatility and both Shapley–Owen R²’s and portfolio optimization exercises to quantify the contributions of information sets. We conclude that meteor showers (MS) are substantially more influential than heat waves (HW), that jumps play a modest but significant role in volatility transmission, that cross-market propagation of volatility is important, and that allowing for differential HW and MS effects and differential parameters across intraday market segments is valuable. Finally, we illustrate what types of news weaken or strengthen heat wave, meteor shower, continuous, and jump patterns with sensitivity analysis. Supplementary materials for this article are available online.

KEY WORDS:

• Exchange rate
• Heat wave
• Meteor shower
• Jumps
• Volatility

SUPPLEMENTARY MATERIALS

Appendix A-1 details periodicity (Appendix A-1.1) and power variation estimators (Appendix A-1.2) used in this article. Appendix A-2 illustrates the construction of the Shapley–Owen R² in a simple example. Appendix A-3 shows unconstrained estimates of linear HAR coefficients and standard errors for all segments, together with standard R² and Ljung-Box statistics (Appendix A-3.1), Shapley-Owen ratios for all models (unconstrained linear, log-variance-fractional logit and logm) for all realized variances (Appendix A-3.2), as well as Wald tests (p-values) for the null hypotheses that the coefficients in various groups of regressors are jointly zero (Appendix A-3.3).

ACKNOWLEDGMENTS

The authors thank Farooq Malik, Michael McCracken, Viviana Fernandez, Carsten Trenkler, Ralf Brüggemann, Carsten Jentsch, and participants in seminars and workshops at the following institutions for helpful discussions and suggestions: the Federal Reserve Bank of St. Louis, the University of Melbourne, the University of Memphis, Midwest Econometrics Group meetings, Midwest Finance Association meetings, Victoria University, West Virginia University, the University of Louvain-la-Neuve, the University of Alabama (SNDE conference), George Washington University (Oxmetrics conference), and Sciences Po Aix-en-Provence. The authors are also grateful to two anonymous referees, the associate editor, and the editor for very useful comments and suggestions. The authors retain responsibility for errors.

Notes

1 Indicative Reuters quotes have the advantages of widespread availability and good informational content (Phylaktis and Chen 2009).

2 Early researchers sometimes cited market inefficiency, in the form of bandwagon effects that might be related to technical trading, as a potential reason for volatility clustering (Ito, Engle, and Lin 1992).

3 We use the Lee and Mykland (2008) / Andersen, Bollerslev, and Dobrev (2007) test, that identifies when intraday jumps occur. On the other hand, Corsi, Pirino, and Reno (2010) proposed an aggregated jump test (i.e., the difference between realized volatility CTBPV) that do not provide jump time information as such. Therefore, our results are not directly comparable to those of Corsi, Pirino, and Reno (2010).

4 We thank a referee for suggesting this approach

5 Additional Tickdata documentation is at https://www.tickdata.com/forex-faq/.

6 Virtually all of our results were robust to including or excluding the year prior to the beginning of our sample, which we exclude from our main results because of its extreme volatility. Our results were also robust to not normalizing by the number of observations.

7 The models included linear models, constrained and unconstrained, linear estimation of logm and Choleski decompositions of the volatility matrix, and direct nonlinear prediction of the volatility matrix through the inverses of these transformations.

8 Unlike Bauer and Vorkink (2011), we do not use factors to reduce the dimensionality of the logm system, as we are interested in evaluating the relative contributions of different types of regressors. To do this with factors require estimating a separate group of factors for each set of regressors, which would lose much of the benefit of reduction in dimensionality and simplicity.

9 Our sample included 1803 daily observations but we lost 20 days in constructing lagged regressors. That left 1783 daily observations or 8915 segments. The last AS observation is at segment 8911.

10 Appendix A-3 shows estimates of linear HAR coefficients for all periods.

11 See Appendix A-2 for the construction of the Shapley–Owen R² in a simple example.

12 See also Chevan and Sutherland (1991) and Grömping (2007).

13 We thank the Associate Editor for this suggestion.

14 Appendix A-3 shows Shapley–Owen ratios for all variances for all models.

15 We compute Wald tests for the null hypotheses that the coefficients in various groups of regressors are jointly zero. Although we omit the full results for brevity, broader groups of regressors, such as HW, MS, cts, and jump, were usually very significant in all or most cases. Breaking these broader groups down into smaller subgroups tended to reduce statistical significance but all groups were significant much more often than one would expect under the null. All series were usually statistically significant in predicting themselves. The Wald tests showed greater statistical significance in the AE, EU, and ES periods than in the AS and US periods. Although we omit these results for brevity, we provide full results in Appendix A-3.

16 Recall that each variance series has 18 “own” regressors, those from its own series and those from its jump series, while each covariance series just has nine “own” regressors from its own history.

17 The high correlations among R²’s and SO ratios and the patterns to intraday predictability (lower panel of Figure 1) are very robust to including the initial year of the financial crisis, but the R²′s are generally 5 to 20 percentage points higher with the volatile financial crisis included.

18 We forego using impulse responses in our study for two reasons. First, previous studies used a single variance series per model at each point in time, creating a natural Wold causal chain in that the observations from earlier segments neatly precede later segments, creating a natural Choleski decomposition for a vector autoregression (VAR). In contrast, we have a full covariance matrix (10 series) plus jumps at each point in time, making it unclear how to identify structural shocks in our system. Second, we believe that impulse responses are not very effective in quantifying the degree to which various types of independent variables predict a given dependent variable.

19 We also considered 1/k portfolio weights as a benchmark, but those weights implied even greater gains in CER for the econometric models—so we omit those results for brevity.

20 These information sets are sometimes but not necessarily mutually exclusive. For example, a given explanatory variable must be either an HW or MS variable but not both. On the other hand, an explanatory variable can be both an HW variable and a jump variable or neither.

21 In the very rare cases—less than 0.1% of observations—in which the forecast covariance matrix was not positive semidefinite, we assigned the rule’s portfolio to hold unconditional weights.

22 The “all predictors” columns from the upper and lower panels differ only because the estimation methods—logm versus log(variance)-fractional logit—differ. Note that the patterns in the sizes of segment returns in the two columns are quite similar, however.

23 Although the results in the upper panel of Table 5 are robust to the inclusion of the financial crisis, its exclusion is important for the “own versus other” results in the lower panel of Table 5. The use of extremely volatile financial crisis data combined with very small models produced excessively volatile and unsuccessful “own” forecasts.

24 We considered other specifications, including quartic time trends, an announcement indicator instead of the absolute value of the shock and day-of-the-week indicators but these alternatives either did not change the inference or did not improve the fit of the relations.

25 Including the very volatile financial crisis period makes many of the monetary shock coefficients statistically significant in the ES segment. The pattern of stronger effects of macro news in ES and stronger effects of monetary shocks in US remains, however. The pattern of signs on the monetary shocks during the US period also remains the same.