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We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the…
Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…
This paper proposes a new integrated variance estimator based on order statistics within the framework of jump-diffusion models. Its ability to disentangle the integrated variance from the total process quadratic variation is confirmed by…
We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with realized range-based variance -- a statistic that replaces every squared return of realized variance with a normalized squared…
In this paper, we present a realized range-based multipower variation theory, which can be used to estimate return variation and draw jump-robust inference about the diffusive volatility component, when a high-frequency record of asset…
In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent…
We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity.…
This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most…
We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the…
Several studies have focused on the Realized Range Volatility, an estimator of the quadratic variation of financial prices, taking into account the impact of microstructure noise and jumps. However, none has considered direct modeling and…
We propose a new estimator for the integrated covariance of two Ito semimartingales observed at a high-frequency. This new estimator, which we call the pre-averaged truncated Hayashi-Yoshida estimator, enables us to separate the sum of the…
With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed…
Quantum metrology aims to use quantum resources to improve the precision of measurement. Quantum criticality has been presented as a novel and efficient resource. Generally, protocols of criticality-based quantum metrology often work…
We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an…
We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic…
Realized statistics based on high frequency returns have become very popular in financial economics. In recent years, different non-parametric estimators of the variation of a log-price process have appeared. These were developed by many…
With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum…
Constructing valid prediction intervals rather than point estimates is a well-established approach for uncertainty quantification in the regression setting. Models equipped with this capacity output an interval of values in which the ground…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…