Using high-frequency data on deutschemark and yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only model-free, 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 normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of long-memory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.

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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 long-memory 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 long-memory properties in the volatility and co-volatility 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 long-memory in a non-standard data generating process is then assessed.

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, ϕ(λ) � by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a “local polynomial Whittle ” (LPW) estimator. We specify a data-dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of ϕ(λ) at zero and selects the bandwidth. The resulting “adaptive LPW ” estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of ϕ(λ) at zero, up to a logarithmic factor.

This paper investigates if component GARCH models introduced by Engle and Lee (1999) and Ding and Granger (1996) can capture the long-range dependence observed in measures of time-series volatility. Long-range dependence is assessed through the sample autocorrelations, two popular semiparametric estimators of the long-memory parameter, and the parametric fractionally integrated GARCH (FI-GARCH) model. Monte Carlo methods are used to characterize the finite sample distributions of these statistics when data are generated from GARCH(1,1), component GARCH and FIGARCH models. For several daily financial return series we find that a two-component GARCH model captures the shape of the autocorrelation function of volatility, and is consistent with long-memory based on semiparametric and parametric estimates. Therefore, GARCH models can in some circumstances account for the long-range dependence found in financial market volatility. JEL classification: C22,C52

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter d ∈ [0, 1/2) to ensure that the corresponding counting process N(t) satisfies VarN(t) ∼ Ct 2d+1 (C> 0) as t → ∞, with the same memory parameter d ∈ [0, 1/2) that was assumed for the durations. Thus, these conditions ensure that the memory in durations propagates to the same memory parameter in counts and therefore in realized volatility. We then show that any Autoregressive Conditional Duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, while any Long Memory Stochastic Duration model with d> 0 and all finite moments yields long memory in counts, with the same d. Finally, we present a result implying that the only way for a series of counts aggregated over a long time period to have nontrivial autocorrelation is for the short-term counts to have long memory. In other words, aggregation ultimately destroys all autocorrelation in counts, if and only if the counts have short memory.

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Nonlinear statistical modelling of high frequency ground ozone data

This paper utilizes the log-periodogram regression to volatility measures of a large set of emerging markets. Evidence for long memory in these volatility series is very signi…cant and these results are very robust to various speci…cations. This has the rami…cation that the creation of derivative markets, more speci…cally options markets in these respective countries would be very pro…table, as the value of an option increases with the volatility of the underlying price process. It is concluded that these emerging markets should establish such option markets due to pro…t incentives and hedging opportunities that arise from them. Such …nancial instruments may also increase foreign investors sentiments and risk perceptions towards these markets and provide these countries with much needed capital. 1