Semiparametric estimation in perturbed long memory series

The estimation of the memory parameter in perturbed long memory series has recently attracted attention motivated especially by the strong persistence of the volatility in many financial and economic time series and the use of Long Memory in Stochastic Volatility (LMSV) processes to model such a behaviour. This paper discusses frequency domain semiparametric estimation of the memory parameter and proposes an extension of the log periodogram regression which explicitly accounts for the added noise, comparing it, asymptotically and in finite samples, with similar extant techniques. Contrary to the non linear log periodogram regression of Sun and Phillips, we do not use a linear approximation of the logarithmic term which accounts for the added noise. A reduction of the asymptotic bias is achieved in this way and makes possible a faster convergence by permitting a larger bandwidth. Monte Carlo results confirm this bias reduction in finite samples. An application to a series of returns of the Spanish Ibex35 stock index is finally included.long memory, stochastic volatility, semiparametric estimation

Trimming and tapering semi-parametric estimates in asymmetric long memory time series

This paper considers semi-parametric frequency domain inference for seasonal or cyclical time series with asymmetric long memory properties. It is shown that tapering the data reduces the bias caused by the asymmetry of the spectral density at the cyclical frequency. We provide a joint treatment of different tapering schemes and of the log-periodogram regression and Gaussian semi-parametric estimates of the memory parameters. Tapering allows for a less restrictive trimming of frequencies for the analysis of the asymptotic properties of both estimates when allowing for asymmetries. Simple rules for inference are feasible thanks to tapering and their validity in finite samples is investigated in a simulation exercise and for an empirical example.Publicad

Homogeneous spaces, algebraic KK-theory and cohomological dimension of fields

Let $q$ be a non-negative integer. We prove that a perfect field $K$ has cohomological dimension at most $q+1$ if, and only if, for any finite extension $L$ of $K$ and for any homogeneous space $Z$ under a smooth linear connected algebraic group over $L$, the $q$-th Milnor $K$-theory group of $L$ is spanned by the images of the norms coming from finite extensions of $L$ over which $Z$ has a rational point. We also prove a variant of this result for imperfect fields.Comment: Final accepted versio

Semiparametric inference in correlated long memory signal plus noise models

This paper proposes an extension of the log periodogram regression in perturbed long memory series that accounts for the added noise, also allowing for correlation between signal and noise, which represents a common situation in many economic and financial series. Consistency (for d < 1) and asymptotic normality (for d < 3/4) are shown with the same bandwidth restriction as required for the original log periodogram regression in a fully observable series, with the corresponding gain in asymptotic efficiency and faster convergence over competitors. Local Wald, Lagrange Multiplier and Hausman type tests of the hypothesis of no correlation between the latent signal and noise are also proposed.long memory, signal plus noise, semiparametric inference, log-periodogram regression

Gaussian Semiparametric Estimation in Long Memory in Stochastic Volatility and Signal Plus Noise Models

This paper considers the persistence found in the volatility of many financial time series by means of a local Long Memory in Stochastic Volatility model and analyzes the performance of the Gaussian semiparametric or local Whittle estimator of the memory parameter in a long memory signal plus noise model which includes the Long Memory in Stochastic Volatility as a particular case. It is proved that this estimate preserves the consistency and asymptotic normality encountered in observable long memory series and under milder conditions it is more efficient than the estimator based on a log-periodogram regression. Although the asymptotic properties do not depend on the signal-to-noise ratio the finite sample performance rely upon this magnitude and an appropriate choice of the bandwidth is important to minimize the influence of the added noise. I analyze the effect of the bandwidth via Monte Carlo. An application to a Spanish stock index is finally included.long memory, stochastic volatility, semiparametric estimation, frequency domain

Semiparametric estimation in perturbed long memory series

The estimation of the memory parameter in perturbed long memory series has recently attracted attention motivated especially by the strong persistence of the volatility in many financial and economic time series and the use of Long Memory in Stochastic Volatility (LMSV) processes to model such a behaviour. This paper discusses frequency domain semiparametric estimation of the memory parameter and proposes an extension of the log periodogram regression which explicitly accounts for the added noise, comparing it, asymptotically and in finite samples, with similar extant techniques. Contrary to the non linear log periodogram regression of Sun and Phillips (2003), we do not use a linear approximation of the logarithmic term which accounts for the added noise. A reduction of the asymptotic bias is achieved in this way and makes possible a faster convergence in long memory signal plus noise series by permitting a larger bandwidth. Monte Carlo results confirm the bias reduction but at the cost of a higher variability. An application to a series of returns of the Spanish Ibex35 stock index is finally included.long memory, stochastic volatility, semiparametric estimation

The Grunwald problem and approximation properties for homogeneous spaces

Given a group $G$ and a number field $K$, the Grunwald problem asks whether given field extensions of completions of $K$ at finitely many places can be approximated by a single field extension of $K$ with Galois group G. This can be viewed as the case of constant groups $G$ in the more general problem of determining for which $K$-groups $G$ the variety $\mathrm{SL}_n/G$ has weak approximation. We show that away from an explicit set of bad places both problems have an affirmative answer for iterated semidirect products with abelian kernel. Furthermore, we give counterexamples to both assertions at bad places. These turn out to be the first examples of transcendental Brauer-Manin obstructions to weak approximation for homogeneous spaces.Comment: 18 pages. Final version. Accepted for publication in Annales de l'Institut Fourie