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8 L. Bauwens et al. should increase with the number of information events in that period. This chain of reasoning is the essence of the so-called “mixture of distribution hypothesis” (MDH) associated with Clark (1973) and others. Several versions of the MDH have been put forward, including one that suggests the size of the steps depends negatively on the number of traders, see for example Tauchen and Pitts (1983). In other words, an increase in the number of traders, a measure of liquidity, should decrease the size of the steps and thus volatility. Exchange rate volatility may of course depend on other factors too, including country-specific institutional factors, market conditions and economic fundamentals. Bringing such factors together in a general framework and trying to disentangle their distinct effects on exchange rate volatility leads to economic or explanatory volatility modelling as opposed to “pure” forecast modelling, which may remain silent about the economic reasons for variation in volatility. When Karpoff (1987) surveyed the relationship between financial volatility and trading volume (a measure of information intensity) during the mid-eighties, only one out of the 19 studies he cited was on exchange rates. The increased availability of data brought by the nineties has changed this, and currently we are aware of ten studies that directly or indirectly investigate the relationship between exchange rate volatility and information intensity. The ten studies are summarised in Table 1 and our study of Norwegian weekly exchange rate volatility from 1993 to 2003 adds to this literature in several ways. First, our study spans more than a decade covering three different exchange rate regimes. Second, not only do we find that the impact of changes in the number of information events on exchange rate volatility is positive and statistically significant, recursive parameter analysis suggests the impact is relatively stable across the different exchange rate regimes. Finally, our results do not support the hypothesis that an increase in the number of traders reduces exchange rate volatility. Another contribution of our study concerns the economic modelling of exchange rate volatility as such. We report a case in which undesirable residual properties are easily removed by applying the logarithmic transformation on volatilities. In particular, we show that OLS-regressions of the logarithm of volatility on its own lags and on several economic variables can produce uncorrelated and homoscedastic residuals. Moreover, in the log of realised volatility case the residuals are also normal. When Geweke (1986), Pantula (1986) and Nelson (1991) proposed that volatilities should be analysed in logs it was first and foremost in order to ensure non-negativity. In our case the motivation stems from unsatisfactory residual properties and fragile inference results. Without the log-transformation we do not generally produce uncorrelated residuals, and when we do the results are very sensitive to small changes in specification. The rest of this paper contains three sections. In Section 2, we review the link between exchange rate volatility and the MDH hypothesis, and discuss measurement issues. We also present our data and other economic variables that we believe may impact on the volatility of the Norwegian exchange rate. In Section 3, we present the models we use and the empirical results. We conclude in the last section, whereas an Appendix provides the details of the data sources and transformations.
Exchange rate volatility and the mixture of distribution hypothesis 9 Table 1 Summary of empirical studies that investigate the impact of information intensity on exchange rate volatility Publication Data Period Supportive of MDH? Grammatikos and Daily currency futures contracts (DEM, CHF, 1978–1983 Yes Saunders (1986) GBP, CAD and JPY) denominated in USD Goodhart (1991) Intradaily quotes (USD against GBP, DEM, 14/9–15/9 No CHF, JPY, FRF, NLG, ITL, ECU) and Reuters’ news-headline page 1987 Goodhart (2000) Intradaily quotes (USD against GBP, DEM, JPY, 9/4-19/6 No FRF, AUD) and Reuters’ news-headline pages 1989 Bollerslev and Intradaily USD/DEM quotes and quoting 9/4–30/6 No Domowitz (1993) frequency 1989 Demos and Intradaily DEM/USD and JPY/USD quotes 5 weeks in Yes Goodhart (1996) and quoting frequency 1989 Jorion (1996) Daily DEM/USD futures and options Jan. 1985– Feb. 1992 Yes Melvin and Xixi Intradaily DEM/USD and JPY/USD quotes, 1/12 1993– Yes (2000) quoting frequency and Reuters’ headline-news screen 26/4 1995 Galati (2003) Daily quotes (USD against JPY and seven 1/1 1998– Yes emerging market currencies) and trading volume 30/6 1999 Bauwens et al. Intradaily EUR/USD quotes, quoting frequency 15/5 2001– Yes (2005) and Reuters’ news-alert screens 14/11 2001 Bjønnes et al. (2005) Daily SEK/EUR quotes and transaction volume 1995–2002 Yes 2 Exchange rate volatility and economic determinants The purpose of this section is to motivate and describe our exchange rate volatility measures, and the economic determinants that we use in our empirical study. In Subsection 2.1, we define our volatility measures and present the Norwegian exchange rate data. We make a distinction between period volatility on the one hand and within or intra-period volatility on the other, arguing that analysis of both is desirable since level-expectations may have an impact. In Subsection 2.2, we review the link between volatility and the MDH, and after presenting our quote frequency data we explain how we use them to construct the explanatory variables we include in our volatility equations. In Subsection 2.3, we motivate and describe the other economic determinants of volatility which we include as explanatory variables in the empirical part. 2.1 Period vs. intra-period volatility measures Conceptually we may distinguish between period volatility on the one hand and within or intra-period volatility on the other. If {S0,S 1,...,S n,..., S N−1,S N} denotes a sequence of exchange rates between two currencies at times {0,1,...,N}, then the squared (period) return [log(S N/S 0)] 2 is an example of a period measure of observ-
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Page 3 and 4: Prof. Luc Bauwens CORE Voie du Roma
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Page 56 and 57: 50 1 Introduction A. Escribano and
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58 with AtðLÞ ¼ 0 B @ 1 ð ÞAab
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60 A. Escribano and R. Pascual cros
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62 Hasbrouck (1991). The system is
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64 unitary seller-initiated shock (
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66 6.1 Estimation of the baseline m
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Table 2 The base-line VEC model for
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70 Table 3 Simulation of the base-l
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72 revert towards narrow levels. As
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Table 5 Impulse-response functions
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76 We also show that NYSE buyer-ini
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78 As 0 < a m < 1; L ð Þ ¼ 1 a m
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80 NYSE 2000 Stocks AOL America Onl
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82 A. Escribano and R. Pascual Madh
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84 1 Introduction S. Frey, J. Gramm
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86 develops the empirical methodolo
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Table 1 Sample descriptives Company
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90 comparability across stocks, we
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92 subtracting the deviations from
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94 market order distribution that c
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96 Table 2 First stage GMM results
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Table 4 First stage GMM results bas
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100 S. Frey, J. Grammig quotes on e
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102 S. Frey, J. Grammig approximate
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104 To obtain the estimates in the
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106 Hence, using the liquidity stat
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108 In the main text we discuss the
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Pierre Giot . Joachim Grammig How l
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How large is liquidity risk in an a
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134 A. D. Hall, N. Hautsch In this
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136 includes order book variables,
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138 An important determinant of liq
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140 The innovation term ei is compu
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Table 1 Order book characteristics
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144 data covering the normal tradin
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146 Table 3 Descriptive statistics
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Table 4 Fully specified ACI models
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Table 4 (continued) BHP NAB NCP TLS
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Table 5 ACI models without dynamics
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Table 6 ACI models without covariat
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160 specification which includes or
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162 5.2.5 The impact of the bid-ask
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164 contrast to those of Pascual an
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Roman Liesenfeld . Ingmar Nolte . W
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Modelling financial transaction pri
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200 W. B. Omrane, H. V. Oppens anal
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202 W. B. Omrane, H. V. Oppens of s
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204 The extrema detection method ba
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206 price 0.8565 0.8575 0.8585 0.85
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208 We distinguish three possible c
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210 originates. The most active tra
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212 Table 2 Predictability of the c
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214 6 Conclusion Using 5-min euro/d
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216 where σk is the standard devia
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218 If we meet a particular case su
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220 C.5. Triple bottom (TB) TB is c
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222 References W. B. Omrane, H. V.
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Juan M. Rodríguez-Poo · David Ver
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Semiparametric estimation for finan
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254 between price changes and durat
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256 simply aggregated. Even after a
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258 is to make use of the fact that
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260 together with the restrictions
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Table 3 Estimated probabilities of
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264 A. S. Tay, C. Ting More interes
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Table 4 Estimated probabilities of
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268 Acknowledgements Tay gratefully
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270 This paper explores the effect
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272 contrast, price responses to po
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274 Fig. 1 Continuous line is the T
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276 the β’s can form a convex sh
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278 fixing some intervals around th
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280 . That is for a given absolute
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282 30 25 20 15 10 5 CC UNEMW ISM U
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Appendix Table A1 Consumer confiden
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Table A3 Non-farm payrolls • ✓
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Table A5 Weekly unemployment claims
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290 Table A8 Retail sales • ✓ 1
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292 Table A12 GDP, BI, TB and PI Re
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294 V. Voev with the problem of how
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296 V. Voev 2.1 A sample covariance
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298 V. Voev Using the equicorrelate
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300 V. Voev where �kl(t) is the (
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302 V. Voev where hkl,k ′ l ′ i
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304 V. Voev is 1.9%. From the daily
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306 V. Voev ACF ACF ACF 0.5 0.5 0.5
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308 V. Voev autocorrelated. Indeed,
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310 V. Voev 5 Conclusion Table 2 Ro
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312 V. Voev Engle R (1982) Autoregr
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