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75
The Distribution of Realized Exchange Rate Volatility
 Journal of the American Statistical Association
, 2001
"... Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately ..."
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Cited by 150 (17 self)
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Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normalityinducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of longmemory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.
LongRange Dependence: revisiting Aggregation with Wavelets.
 Journal of Time Series Analysis
, 1998
"... The aggregation procedure is a natural way to analyse signals which exhibit longrange dependent features and has been used as a basis for estimation of the Hurst parameter, H. In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly ..."
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Cited by 40 (12 self)
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The aggregation procedure is a natural way to analyse signals which exhibit longrange dependent features and has been used as a basis for estimation of the Hurst parameter, H. In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly related to approximations of the signal in the sense of a Haarmultiresolution analysis. A natural wavelet based generalisation to traditional aggregation is then proposed: "aaggregation". It is shown that aaggregation cannot lead to good estimators of H, and so a new kind of aggregation, "daggregation", is defined, which is related to the details rather than the approximations of a multiresolution analysis. An estimator of H based on daggregation has excellent statistical and computational properties, whilst preserving the spirit of aggregation. The estimator is applied to telecommunications network data.
NarrowBand Analysis Of Nonstationary Processes
, 1999
"... The behaviour of averaged periodograms and crossperiodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones, and the crossperiodogram can involve two nonstationa ..."
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Cited by 37 (11 self)
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The behaviour of averaged periodograms and crossperiodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones, and the crossperiodogram can involve two nonstationary processes of possibly di#erent orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or on one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic di#erence, and in particular we indicate how the behaviour of the mean and variance changes across the twodimensional space of integration orders. The results employ only localtozero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be readily applied in case of fractional cointegration with unknown integration orders. 1 1. INTRODUCTION In the analy...
Microeconomic Models for LongMemory in the Volatility of Financial Time Series
"... We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical longmemory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired ..."
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Cited by 27 (2 self)
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We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical longmemory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly, or indirectly by those of the other participants. These "field effects" generate "herding" behaviour which affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I(0), the series of absolute and squared returns display strong dependence, while the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common longmemory properties in the volatility and covolatility of financial time series, revealed by Teyssière (1997, 1998a). These properties are investigated by using various model independent tests and estimators, i.e., semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski, Phillips, Schmidt and Shin (1992), Robinson (1995), Lobato and Robinson (1998), Giraitis, Kokoszka Leipus and Teyssière (2000, 2001). The relative performance of these tests and estimators for longmemory in a nonstandard data generating process is then assessed.
A biasreduced logperiodogram regression estimator for the longmemory parameter. Cowles Foundation Discussion Paper No
, 1999
"... COWLES FOUNDATION DISCUSSION PAPER NO. 1263 ..."
SemiParametric Graphical Estimation Techniques for LongMemory Data.
, 1996
"... This paper reviews several periodogrambased methods for estimating the longmemory parameter H in time series and suggests a way to robustify them. The high frequencies tend to bias the estimates. Using only low frequencies eliminates the bias but increases the variance. We hence suggest plotting t ..."
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Cited by 16 (4 self)
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This paper reviews several periodogrambased methods for estimating the longmemory parameter H in time series and suggests a way to robustify them. The high frequencies tend to bias the estimates. Using only low frequencies eliminates the bias but increases the variance. We hence suggest plotting the estimates of H as a function of a parameter which balances bias versus variance and, if the plot flattens in a central region, to use the flat part for estimating H. We apply this technique to the periodogram regression method, the Whittle approximation to maximum likelihood and to the local Whittle method. We investigate its effectiveness on several simulated fractional ARIMA series and also apply it to estimate the longmemory parameter H in computer network traffic. 1 Introduction Time series with long memory have been considered in many fields including hydrology, biology and computer networks. Unfortunately, estimating the long memory (longrange dependence) parameter H in a given d...
2006) "Residual logperiodogram inference for long run relationships
 Journal of Econometrics
, 2010
"... We assume that some consistent estimatorbβ of an equilibrium relation between nonstationary series integrated of order d ∈ (0.5, 1.5) is used to compute residuals ût = yt −bβxt (or differences thereof). We propose to apply the semiparametric logperiodogram regression to the (differenced) residuals ..."
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Cited by 13 (2 self)
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We assume that some consistent estimatorbβ of an equilibrium relation between nonstationary series integrated of order d ∈ (0.5, 1.5) is used to compute residuals ût = yt −bβxt (or differences thereof). We propose to apply the semiparametric logperiodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence δ of the equilibrium deviation ut. Providedbβ converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of δ. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on δ. This requires that d − δ> 0.5 for superconsistentbβ, so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0 ≤ δ < 0.5, as well as for nonstationary but transitory equilibrium errors, 0.5 < δ < 1. In particular, if xt contains several series we consider the joint estimation of d and δ. Wald statistics to test for parameter restrictions of the system have a limiting χ 2 distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics. JEL Classification: C14, C22.