We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. show that this method provides simple estimates such important quantities as integrated volatility or quarticity. Under mild conditions the consistency is proven. further assumptions we prove stable convergence our optimal rate $n^{−1/4}$. Moreover, construct which are robust to finite activity jumps.

This paper presents some limit theorems for certain functionals of moving averages semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634–658, Stochastic Process. Appl. 119 2249–2276]) and provides consistent estimates various characteristics general semimartingales. Furthermore, we prove associated multidimensional (stable) central theorems. As expected, find with a convergence rate n−1/4, if n is...

This paper presents a short survey on limit theorems for certain functionals of semimartingales that are observed at high frequency. Our aim is to explain the main ideas theory broader audience. We introduce concept stable convergence, which crucial our purpose. show some laws large numbers (for continuous and discontinuous case) most interesting from practical point view, demonstrate associated central theorems. Moreover, we state simple sketch proofs give examples.

In this article we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate L2-distance between spectral density process and its best approximation by process. An explicit expression minimal distance derived, which depends only integrals square. These can be estimated directly without estimating density, as consequence, estimation measure does not require specification smoothing bandwidth. We show weak...

In this paper, we are concerned with nonparametric inference on the volatility of process in stochastic models. We construct several estimators for its integrated version a high-frequency setting, all based increments spot estimators. Some those positive by construction, others bias corrected order to attain optimal rate $n^{-1/4}$. Associated central limit theorems proven which can be widely used practice, as they key essentially tools model validation As an illustration give brief idea...

Abstract In this article we study the theoretical properties of simultaneous multiscale change point estimator (SMUCE) in piecewise‐constant signal models with dependent error processes. Empirical studies suggest that case estimate is inconsistent, but it not known if alternatives suggested literature for correlated data are consistent. We propose a modification SMUCE scaling basic statistic by long run variance process, which estimated difference‐type calculated from local means different...

Abstract. Properties of a specification test for the parametric form variance function in diffusion processes are discussed. The is based on estimation certain integrals volatility function. If does not depend variable x it known that corresponding statistics have an asymptotic normal distribution. However, most models mathematical finance use which depends state . In this paper we prove general case, where σ also estimates converge stably law to random variables with non‐standard limit...

We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. show that this method provides simple estimates such important quantities as integrated volatility or quarticity. Under mild conditions the consistency is proven. further assumptions we prove stable convergence our optimal rate n-1/4. Moreover, construct which are robust to finite activity.

In this paper we investigate the problem of testing assumption stationarity in locally stationary processes. The test is based on an estimate a Kolmogorov-Smirnov type distance between true time varying spectral density and its best approximation through density. Convergence empirical process indexed by class certain functions proved, furthermore consistency bootstrap procedure shown which used to approximate limiting distribution statistic. Compared other methods proposed literature for new...

A practical system is described for making single-path phase measurements at X-band over ranges up to about 20 miles with instrumental noise of the order a fraction one degree. The techniques obtaining necessary transmitter frequency stability 1:109 are described. use such form simple microwave repeater power gain 50 db discussed.

We characterize the microwave loss in coplanar waveguides (CPWs) on AlGaN/GaN high-electron mobility transistor (HEMT) buffer layers high-resistivity silicon (HR-Si) substrates, up to 110 GHz. To our knowledge, this is first broadband characterization of CPWs GaN-on-Si. Conventional commercially available HR-Si HEMT show a as low 0.8 dB/mm at Losses are further reduced by etching trenches between CPW conductors, reaching 0.47 The work shows that GaN-on-Si exhibit performances comparable...

In this paper nonparametric methods to assess the multivariate Lévy measure are introduced. Starting from high-frequency observations of a process $\mathbf{X} $, we construct estimators for its tail integrals and Pareto–Lévy copula prove weak convergence these in certain function spaces. Given $n$ increments over intervals length $\Delta_{n}$, rate is $k_{n}^{-1/2}$ $k_{n}=n\Delta_{n}$ which natural concerning inference on measure. Besides extensions nonequidistant sampling schemes analytic...

In this work, we develop change-point methods for statistics of high-frequency data. The main interest is in the volatility an Itô semimartingale, latter being discretely observed over a fixed time horizon. We construct minimax-optimal test to discriminate continuous paths from with jumps, and it shown that can be embedded into more general theory infer smoothness volatilities. setting, prove weak convergence statistic under hypothesis extreme value distribution. Moreover, changes Hurst...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. also provides consistent estimators of other powers volatility - in particular, it gives feasible ways to consistently estimate asymptotic variance estimator We show that our approach, which possess an intuitive transparency, can generate rate optimal (with convergence n-1/4).

In this article, new tests for non-parametric hypotheses in stationary processes are proposed. Our approach is based on an estimate of the L2-distance between spectral density matrix and its best approximation under null hypothesis. We explain main idea problem testing a constant comparing densities several correlated time series. The method direct estimation integrals does not require specification smoothing parameters. show that limit distribution proposed test statistic normal investigate...

Abstract. In this study we are concerned with inference on the correlation parameter ρ of two Brownian motions, when only high‐frequency observations from one‐dimensional continuous Itô semimartingales, driven by these particular available. Estimators for constructed in situations: either both components observed (at same time), or one component is and other represents its volatility process thus has to be estimated data as well. first case it shown that our estimator asymptotic behaviour...

A microwave refractometer has been developed in which a calibrated servo-controlled tunable cavity resonator is made to follow the variations resonant frequency of sampling resonator. Considerable improvement realized calibration stability and simplicity operation over earlier instruments. Accuracy 1 ppm or better obtained periods weeks.