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15
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 155 (18 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.
LogPeriodogram Regression Of Time Series With Long Range Dependence
 ANNALS OF STATISTICS
, 1999
"... This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x \Gamma2d f (x), where f (x) is bounded and bounded away from zero. A form of logperiodogram ..."
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Cited by 32 (0 self)
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This paper discusses the use of fractional exponential models (Robinson (1990), Beran (1994)) to model the spectral density f(x) of a covariance stationary process when f(x) may be decomposed as f(x) = x \Gamma2d f (x), where f (x) is bounded and bounded away from zero. A form of logperiodogram regression technique is presented both in the parametric context (i.e. f (x) is a finite order exponential model in the sense of Bloomfield (1973)) and the semiparametric context (f (x) is regarded as a nuisance parameter). Assuming gaussianity and additional conditions on the regularity of f (x) which seem mild, asymptotic normality of the parameter estimates in the parametric and the semiparametric context is established. As a byproduct, some improvements over the results presented by Robinson (1994) have been obtained for the large sample distribution of logperiodogram ordinates for Gaussian processes.
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 15 (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...
Robust covariance matrix estimation: "HAC" estimates with long memory/antipersistence correction. Econometric Theory
, 2005
"... Smoothed nonparametric estimates of the spectral density matrix at zero frequency have been widely used in econometric inference, because they can consistently estimate the covariance matrix of a partial sum of a possibly dependent vector process. When elements of the vector process exhibit long mem ..."
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Cited by 7 (4 self)
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Smoothed nonparametric estimates of the spectral density matrix at zero frequency have been widely used in econometric inference, because they can consistently estimate the covariance matrix of a partial sum of a possibly dependent vector process. When elements of the vector process exhibit long memory or antipersistence such estimates are inconsistent. We propose estimates which are still consistent in such circumstances, adapting automatically to memory parameters that can vary across the vector and be unknown.
Long Memory and Structural Change
, 1999
"... The huge theoretical and empirical econometric literatures on long memory and on structural change have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related. In particular, we show analytically that stochastic regime switching is ea ..."
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Cited by 6 (0 self)
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The huge theoretical and empirical econometric literatures on long memory and on structural change have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related. In particular, we show analytically that stochastic regime switching is easily confused with long memory, so long as only a "small" amount of regime switching occurs (in a sense that we make precise). A Monte Carlo analysis supports the relevance of the asymptotic theory in finite samples and produces additional insights.
Multiple local Whittle estimation in stationary systems
 ANNALS OF STATISTICS
, 2007
"... Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (), at the frequency of principal interest, zero; for short memory series = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional differencing" c ..."
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Cited by 5 (2 self)
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Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (), at the frequency of principal interest, zero; for short memory series = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional differencing" case = ( 2 1) =2; where 1; 2 are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, and relate the consequent properties of crossautocovariances to ones of the (possibly bilateral) moving average representation which, with martingale difference innovations of arbitrary dimension, is used in asymptotic theory for local Whittle parameter estimates depending on a single smoothing number. Incorporating also a regression parameter ( ) which, when nonzero, indicates cointegration, the consistency proof of these implicitlydeā¦ned estimates is nonstandard due to the estimate converging faster than the others. We also establish joint asymptotic normality of the estimates, and indicate how this outcome can apply in statistical inference on several questions of interest. Issues of implemention are discussed, along with implications of knowing and of correct or incorrect specification of; and possible extensions to higherdimensional systems and nonstationary series.
Some New Statistical Approaches to the Analysis of Long Memory Processes
, 1994
"... This thesis describes methods of analysis and synthesis of long memory processes. Long memory processes are those which exhibit correlations between events separated by a long period of time. This phenomenon is characterized in the frequency domain by a sharp peak in the spectral density function as ..."
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Cited by 2 (0 self)
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This thesis describes methods of analysis and synthesis of long memory processes. Long memory processes are those which exhibit correlations between events separated by a long period of time. This phenomenon is characterized in the frequency domain by a sharp peak in the spectral density function as the frequency approaches zero. This characteristic is observed in many physical time series, including those in the fields of geophysics, astronomy and finance. A class of models that captures such long memory behaviour are fractionally differenced processes, the simplest of these processes is obtained by differencing white noise a fractional number of times. We employ two methods of analyzing such processes: Multitaper spectral estimation and Wavelet analysis. Multitaper spectral analysis uses the average of several direct spectral estimators evaluated using orthogonal tapers. We look at two sets of tapers: the discrete prolate spheroidal sequences and sinusoidal tapers. This method of s...
Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends
, 2012
"... We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts and deterministic time trends. The estimators are simple trimmed versions of the popular logperiodogram regression estimator that employ certa ..."
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Cited by 1 (1 self)
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We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts and deterministic time trends. The estimators are simple trimmed versions of the popular logperiodogram regression estimator that employ certain sample sizedependent and, in some cases, datadependent trimmings which discard lowfrequency components. We also show that a previously developed trimmed local Whittle estimator is robust to the same forms of data contamination. Regardless of whether the underlying long/shortmemory process is contaminated by level shifts or deterministic trends, the estimators are consistent and asymptotically normal with the same limiting variance as their standard untrimmed counterparts. Simulations show that the trimmed estimators perform their intended purpose quite well, substantially decreasing both finite sample bias and root meansquared error in the presence of these contaminating components. Furthermore, we assess the tradeoffs involved with their use when such components are not present but the underlying process exhibits strong shortmemory dynamics or is contaminated by noise. To balance the potential finite sample biases involved in estimating the memory parameter, we recommend a particular adaptive version of the trimmed logperiodogram estimator that performs well in a wide variety of circumstances. We apply the estimators to stock market volatility data to find that various time series typically thought to be longmemory processes actually appear to be short or very weak longmemory processes contaminated by level shifts or deterministic trends.
A Note on the Effect of Seasonal Dummies on the Periodogram Regression
"... We discuss how prior regression on seasonal dummies leads to singularities in periodogram regression procedures for the detection of long memory. We suggest a modified procedure. We illustrate the problems using monthly inflation data from Hassler and Wolters (1995). Keywords Long Memory, Seaso ..."
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We discuss how prior regression on seasonal dummies leads to singularities in periodogram regression procedures for the detection of long memory. We suggest a modified procedure. We illustrate the problems using monthly inflation data from Hassler and Wolters (1995). Keywords Long Memory, Seasonal Adjustment 1 A Numerical Problem In this section we propose a numerical problem which came up when we redid a regression analysis of simple fractionally integrated models for inflation, where two packages came up with different answers. In the next sections we propose solutions. Periodogram regression is by now a standard procedure to start the examination of long memory in a time series. A popular model with long memory is the ARFIMA(p; d; q) model: \Phi(L)(1 \Gamma L) d y t = \Theta(L)AE t , t = 1; 2; : : : with \Phi(L) and \Theta (L) polynomials of orders p and q in the lag operator L : L k y t = y t\Gammak and (1 \Gamma L) d = 1 \Gamma dL \Gamma d(1\Gammad) 2 L 2 \Gamma...