Related papers: Nonparametric estimation of the volatility functio…
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…
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…
Based on discrete observations, we develop a test to infer if the volatility function $\sigma(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = \sigma(t)dW_t$ is constant. The testing procedure is shown to be…
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…
We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent.…
Volatility estimation based on high-frequency data is key to accurately measure and control the risk of financial assets. A L\'{e}vy process with infinite jump activity and microstructure noise is considered one of the simplest, yet…
This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and…
We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at a high temporal frequency, we use limit theorems for multipower variations and…
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…
In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to…
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our…
We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, Z=X+\sigma\epsilon$, involving independent and unobserved random variables $X,\xi,\epsilon$. The density $g$ of…
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…
We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…
This paper studies a Bayesian approach to non-asymptotic minimax adaptation in nonparametric estimation. Estimating an input function on the basis of output functions in a Gaussian white-noise model is discussed. The input function is…
In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…
High frequency based estimation methods for a semiparametric pure-jump subordinated Brownian motion exposed to a small additive microstructure noise are developed building on the two-scales realized variations approach originally developed…
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…
Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…