Wavelets in the Analysis of Autoregressive Conditional Heteroskedasticity (ARCH) Models Using Neural Network

Ataulla Nihal Zaidi

doi:10.11648/j.ajam.20160402.14

Abstract

In the paper, proposed a new method for the time frequency signal analysis, speech processing and other signal processing applications. Stationary signal components can be analyzed by a powerful tool called as Fourier transform. But it is fizzled for analysing the non-stationary signal whereas wavelet transform allows the components of a non-stationary signal to be analyzed. It is the improved version of Fourier transform. Wavelets allow complex information such as music, speech, images and patterns to be decomposed into elementary forms at different positions and scales and subsequently reconstructed with high precision. Here, for extracting the best features of non-stationary signal we use discrete wavelet transform. This can be decomposed into two components named as high frequency component and low frequency component. The decomposed output component is sent for regression analysis. This is done by passing through ARCH model which can characterize and model observed time series. An ARCH time series is the one in which the variance of the error in a period depends on upon size of the squared error in the previous period i.e. if a large error occurs in one period, the variance of the error in the next period will be even larger. The performance of the ARCH will be improved by predicting its co-efficient or cofactor using an artificial technique. The artificial technique presented in this paper is neural network, which is capable of handling sophisticated computations similar to the human brain. The proposed model algorithm will be implemented in MATLAB and the output performances are estimated.

Highlights

The power spectral density estimation is explained as, from a finite record of a stationary data sequence, estimate how the total power is distributed over frequencies, or more practically, over narrow spectral bands [1]
Discrete Wavelet Transform (DWT) was capable of decomposing the system input signal into two components called as high frequency component and low frequency component which could be referred as details and approximations of the signal information
In the paper, proposed method was used for time frequency signal analysis, speech processing and other signal processing applications

Summary

Introduction

The power spectral density estimation is explained as, from a finite record of a stationary data sequence, estimate how the total power is distributed over frequencies, or more practically, over narrow spectral bands (frequency bins) [1]. Spectral estimation methods are two types: Classical (Nonparametric) Methods for e.g., Pass the data through a set of band-pass filters and measure the filter output powers and Parametric (Modern) Approaches for e.g., Model the data as a sum of a few damped sinusoids and estimate their parameters. Parametric Methods may offer better estimates if data closely agrees with assumed model. In comparison to the STFT, wavelet analysis makes it possible to perform a multi-resolution analysis. It can be performed in several ways; a continuous wavelet transform, a discretized continuous wavelet transform and a true discrete wavelet transform [3]. One of the main advantages of wavelet analysis is the ability to perform local analysis [4] and is capable of decomposing a signal into component wavelets i.e., high frequency component and low frequency

Methods

Results

Conclusion