arXiv subjects

Maryam Movahedifar

Publications and source records attributed to Maryam Movahedifar.

3 recordsLinked to original sources

arXiv2025

Utilizing Multiple Testing for Grouping in Singular Spectrum Analysis

A key step in separating signal from noise in time series by means of singular spectrum analysis (SSA) is grouping. We present a multiple testing method for the grouping step in SSA. As separability criterion, we utilize the weighted correlation between the signal and the noise component of the (reconstructed) time series, and we test whether this weighted correlation is equal to zero. This test has to be performed for several possible groupings, resulting in a multiple test problem. The null distributions of the corresponding test statistics are approximated by a wild bootstrap procedure. The performance of our proposed method is assessed in a simulation study, and we illustrate its practical application with an analysis of real world data.

stat.ME↗

arXiv2023

On the closed-loop Volterra method for analyzing time series

The main focus of this paper is to approximate time series data based on the closed-loop Volterra series representation. Volterra series expansions are a valuable tool for representing, analyzing, and synthesizing nonlinear dynamical systems. However, a major limitation of this approach is that as the order of the expansion increases, the number of terms that need to be estimated grows exponentially, posing a considerable challenge. This paper considers a practical solution for estimating the closed-loop Volterra series in stationary nonlinear time series using the concepts of Reproducing Kernel Hilbert Spaces (RKHS) and polynomial kernels. We illustrate the applicability of the suggested Volterra representation by means of simulations and real data analysis. Furthermore, we apply the Kolmogorov-Smirnov Predictive Accuracy (KSPA) test, to determine whether there exists a statistically significant difference between the distribution of estimated errors for concurring time series models, and secondly to determine whether the estimated time series with the lower error based on some loss function also has exhibits a stochastically smaller error than estimated time series from a competing method. The obtained results indicate that the closed-loop Volterra method can outperform the ARFIMA, ETS, and Ridge regression methods in terms of both smaller error and increased interpretability.

stat.ME↗

arXiv2022

Combining Multiple Testing with Multivariate Singular Spectrum Analysis

Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The purpose of this paper is to apply a nonparametric preprocessing method, called Singular Spectrum Analysis (SSA), to a variety of datasets which are subsequently analyzed by means of multiple statistical hypothesis tests. SSA is a nonparametric preprocessing method which has recently been utilized in the context of many life science problems. In the present work, SSA is compared with three other state-of-the-art preprocessing methods in terms of goodness of denoising and in terms of the statistical power of the subsequent multiple test. These other methods are either parametric or nonparametric. Our findings demonstrate that (multivariate) SSA can be taken into account as a promising method to reduce noise, to extract the main signal from noisy data, and to detect statistically significant signal components.

stat.ME↗