3,330 research outputs found
Wavelet Estimation of Time Series Regression with Long Memory Processes
This paper studies the estimation of time series regression when both regressors and disturbances have long memory. In contrast with the frequency domain estimation as in Robinson and Hidalgo (1997), we propose to estimate the same regression model with discrete wavelet transform (DWT) of the original series. Due to the approximate de-correlation property of DWT, the transformed series can be estimated using the traditional least squares techniques. We consider both the ordinary least squares and feasible generalized least squares estimator. Finite sample Monte Carlo simulation study is performed to examine the relative efficiency of the wavelet estimation.Discrete Wavelet Transform
Wavelet analysis of the multivariate fractional Brownian motion
The work developed in the paper concerns the multivariate fractional Brownian
motion (mfBm) viewed through the lens of the wavelet transform. After recalling
some basic properties on the mfBm, we calculate the correlation structure of
its wavelet transform. We particularly study the asymptotic behavior of the
correlation, showing that if the analyzing wavelet has a sufficient number of
null first order moments, the decomposition eliminates any possible long-range
(inter)dependence. The cross-spectral density is also considered in a second
part. Its existence is proved and its evaluation is performed using a von
Bahr-Essen like representation of the function \sign(t) |t|^\alpha. The
behavior of the cross-spectral density of the wavelet field at the zero
frequency is also developed and confirms the results provided by the asymptotic
analysis of the correlation
Locally stationary long memory estimation
There exists a wide literature on modelling strongly dependent time series
using a longmemory parameter d, including more recent work on semiparametric
wavelet estimation. As a generalization of these latter approaches, in this
work we allow the long-memory parameter d to be varying over time. We embed our
approach into the framework of locally stationary processes. We show weak
consistency and a central limit theorem for our log-regression wavelet
estimator of the time-dependent d in a Gaussian context. Both simulations and a
real data example complete our work on providing a fairly general approach
A Review of Fault Diagnosing Methods in Power Transmission Systems
Transient stability is important in power systems. Disturbances like faults need to be segregated to restore transient stability. A comprehensive review of fault diagnosing methods in the power transmission system is presented in this paper. Typically, voltage and current samples are deployed for analysis. Three tasks/topics; fault detection, classification, and location are presented separately to convey a more logical and comprehensive understanding of the concepts. Feature extractions, transformations with dimensionality reduction methods are discussed. Fault classification and location techniques largely use artificial intelligence (AI) and signal processing methods. After the discussion of overall methods and concepts, advancements and future aspects are discussed. Generalized strengths and weaknesses of different AI and machine learning-based algorithms are assessed. A comparison of different fault detection, classification, and location methods is also presented considering features, inputs, complexity, system used and results. This paper may serve as a guideline for the researchers to understand different methods and techniques in this field
Large scale reduction principle and application to hypothesis testing
Consider a non--linear function where is a stationary Gaussian
sequence with long--range dependence. The usual reduction principle states that
the partial sums of behave asymptotically like the partial sums of the
first term in the expansion of in Hermite polynomials. In the context of
the wavelet estimation of the long--range dependence parameter, one replaces
the partial sums of by the wavelet scalogram, namely the partial sum
of squares of the wavelet coefficients. Is there a reduction principle in the
wavelet setting, namely is the asymptotic behavior of the scalogram for
the same as that for the first term in the expansion of in Hermite
polynomial? The answer is negative in general. This paper provides a minimal
growth condition on the scales of the wavelet coefficients which ensures that
the reduction principle also holds for the scalogram. The results are applied
to testing the hypothesis that the long-range dependence parameter takes a
specific value
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