Related papers: Estimators of Long-Memory: Fourier versus Wavelets

This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to…

Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local…

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…

In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is characterized by the memory parameter d and by…

We present a local Fourier slice equation that enables local and sparse projection of a signal. Our result exploits that a slice in frequency space is an iso-parameter set in spherical coordinates. Therefore, the projection of suitable…

An exact form of the local Whittle likelihood is studied with the intent of developing a general-purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local…

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…

Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…

This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…

We investigate minimax results for the anisotropic functional deconvolution model when observations are affected by the presence of long-memory. Under specific conditions about the covariance matrices of the errors, we follow a standard…

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 proposes a wavelet-based method for analysing periodic autoregressive moving average (PARMA) time series. Even though Fourier analysis provides an effective method for analysing periodic time series, it requires the estimation of…

A long memory process has self-similarity or scale-invariant properties in low frequencies. We prove that the log of the scale-dependent wavelet variance for a long memory process is asymptotically proportional to scales by using the Taylor…

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…

We develop a wavelet like representation of functions in $L^p(\mathbb{R})$ based on their Fourier--Hermite coefficients; i.e., we describe an expansion of such functions where the local behavior of the terms characterize completely the…

Functional magnetic resonance imaging (fMRI) time series are known to exhibit long-range temporal dependencies that challenge traditional modeling approaches. In this study, we propose a novel computational pipeline to characterize and…

Researchers have used many different methods to detect the possibility of long-term dependence (long memory) in stock market returns, but evidence is in general mixed. In this paper, three different tests, (namely Rescaled Range (R/S), its…

We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…

We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…

Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…