Related papers: Inference of seasonal long-memory aggregate time s…
The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general…
In the general setting of long-memory multivariate time series, the long-memory characteristics are defined by two components. The long-memory parameters describe the autocorrelation of each time series. And the long-run covariance measures…
This paper explores seasonal and long-memory time series properties by using the seasonal fractional ARIMA model when the seasonal data has one and two seasonal periods and short-memory counterparts. The stationarity and invertibility…
Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
Empirical likelihood method has been applied to short-memory time series models by Monti (1997) through the Whittle's estimation method. Yau (2012) extended this idea to long-memory time series models. Asymptotic distributions of the…
In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be…
Long memory in the sense of slowly decaying autocorrelations is a stylized fact in many time series from economics and finance. The fractionally integrated process is the workhorse model for the analysis of these time series. Nevertheless,…
Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed and the usual…
We study the aggregation/disaggregation problem of random parameter AR(1) processes and its relation to the long memory phenomenon. We give a characterization of a subclass of aggregated processes which can be obtained from simpler,…
The approximation of a stationary time-series by finite order autoregressive (AR) and moving averages (MA) is a problem that occurs in many applications. In this paper we study asymptotic behavior of the spectral density of finite order…
We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…
Since with massive data growth, the need for autonomous and generic anomaly detection system is increased. However, developing one stand-alone generic anomaly detection system that is accurate and fast is still a challenge. In this paper,…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The…
Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] introduced the generalized filtered method-of-moments approach to simultaneously estimate singularity…
In this paper, we consider the Whittle estimator for the parameters of a stationary solution of a continuous-time linear state space model sampled at low frequencies. In our context the driving process is a L\'evy process which allows…