Results 1  10
of
86
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 ..."
Abstract

Cited by 167 (19 self)
 Add to MetaCart
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.
A biasreduced logperiodogram regression estimator for the longmemory parameter. Cowles Foundation Discussion Paper No
, 1999
"... COWLES FOUNDATION DISCUSSION PAPER NO. 1263 ..."
Nonlinear LogPeriodogram Regression for Perturbed Fractional Processes
, 2002
"... This paper studies fractional processes that may be perturbed by weakly dependent time series. The model for a perturbed fractional process has a components framework in which there may be components of both long and short memory. All commonly used estimates of the long memory parameter (such as log ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
This paper studies fractional processes that may be perturbed by weakly dependent time series. The model for a perturbed fractional process has a components framework in which there may be components of both long and short memory. All commonly used estimates of the long memory parameter (such as log periodogram (LP) regression) may be used in a components model where the data are affected by weakly dependent perturbations, but these estimates can suffer from serious downward bias. To circumvent this problem, the present paper proposes a new procedure that allows for the possible presence of additive perturbations in the data. The new estimator resembles the LP regression estimator but involves an additional (nonlinear) term in the regression that takes account of possible perturbation effects in the data. Under some smoothness assumptions at the origin, the bias of the new estimator is shown to disappear at a faster rate than that of the LP estimator, while its asymptotic variance is inflated only by a multiplicative constant. In consequence, the optimal rate of convergence to zero of the asymptotic MSE of the new estimator is faster than that of the LP estimator. Some simulation results demonstrate the viability and the biasreducing feature of the new estimator relative to the LP estimator in finite samples. A
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 ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
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...
Residual logperiodogram inference for long run relationships
, 2002
"... We assume that some consistent estimator bβ 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) residual ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
We assume that some consistent estimator bβ 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. Provided bβ 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 superconsisten tbβ, 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.
The Long Range Dependence Paradigm for Macroeconomics and Finance
, 2002
"... The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of u ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of unanticipated shocks, yet exhibiting mean reversion. Whereas linear long range dependent time series models have been extensively used in macroeconomics, empirical evidence from financial time series prompted the development of nonlinear long range dependent time series models, in particular models of changing volatility. We discuss empirical evidence of long range dependence as well as the theoretical issues, both for economics and econometrics, such evidence has stimulated
An analytical evaluation of the log–periodogram estimate in the presence of level shift and its implications for stock returns volatility
 Department of Economics, Boston University
, 2004
"... Recently, there has been an upsurge of interest on the possibility of confusing long memory and structural changes in level. Many studies have shown that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away from z ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Recently, there has been an upsurge of interest on the possibility of confusing long memory and structural changes in level. Many studies have shown that when a stationary short memory process is contaminated by level shifts the estimate of the fractional differencing parameter is biased away from zero and the autocovariance function exhibits a slow rate of decay, akin to a long memory process. We analyze the properties of the log periodogram estimate of the memory parameter when the jump component is specified by a simple mixture model. Our theoretical results explain many findings reported and uncover new features. Simulations are presented to highlight the properties of the distributions and to assess the adequacy of our approximations. We also show the usefulness of our results to distinguish between long memory and level shifts via an application to the volatility of daily returns for wheat commodity futures. JEL Classification Number: C22.