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This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…
Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
We study the multivariate nonparametric change point detection problem, where the data are a sequence of independent $p$-dimensional random vectors whose distributions are piecewise-constant with Lipschitz densities changing at unknown…
This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned…
The problem of detecting change points in the parameters of a linear regression model with errors and covariates exhibiting heteroscedasticity is considered. Asymptotic results for weighted functionals of the cumulative sum (CUSUM)…
A change point detection procedure using the method of moment estimators is proposed. The test statistics is based on a suitable $Z$-process. The asymptotic behavior of this process is established under both the null and the alternative…
In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…
Change-point detection has been a classical problem in statistics and econometrics. This work focuses on the problem of detecting abrupt distributional changes in the data-generating distribution of a sequence of high-dimensional…
Change-point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large-scale, high-dimensional, and complex streaming data call for…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
A framework to establish response theory for a class of nonlinear stochastic partial differential equations (SPDEs) is provided. More specifically, it is shown that for a certain class of observables, the averages of those observables…
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
This paper offers a new approach to modeling and forecasting of nonstationary time series with applications to volatility modeling for financial data. The approach is based on the assumption of local homogeneity: for every time point, there…
We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency…
We propose a new statistical test to identify non-stationary frequency-modulated stochastic processes from time series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from…
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…