Related papers: Sample autocovariances of long-memory time series
In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…
We consider a L\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the…
Let $(\varepsilon_{t})_{t>0}$ be a sequence of independent real random vectors of $p$-dimension and let $X_T= \sum_{t=s+1}^{s+T}\varepsilon_t\varepsilon^T_{t-s}/T$ be the lag-$s$ ($s$ is a fixed positive integer) auto-covariance matrix of…
In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized…
We study the asymptotic joint distribution of sample space--time covariance estimators of strictly stationary random fields. We do this without any marginal or joint distributional assumptions other than mild moment and mixing conditions.…
This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…
We consider the model selection problem for a large class of time series models, including, multivariate count processes, causal processes with exogenous covariates. A procedure based on a general penalized contrast is proposed. Some…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We consider a stochastic process model with time trend and measurement error. We establish consistency and derive the limiting distributions of the maximum likelihood (ML) estimators of the covariance function parameters under a general…
In $M$-estimation under standard asymptotics, the weak convergence combined with the polynomial type large deviation estimate of the associated statistical random field Yoshida (2011) provides us with not only the asymptotic distribution of…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time…
This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that…
Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…