A Comparative Study on Methods to Handle Wavelet Edge Distortion

AWSY Wickramasinghe¹ and WMND Basnayake^1,

¹Department of Statistics, University of Colombo, Sri Lanka

Cite this paper:
AWSY Wickramasinghe and WMND Basnayake. A Comparative Study on Methods to Handle Wavelet Edge Distortion. American Journal of Applied Mathematics and Statistics. 2022; 10(3):95-102. doi: 10.12691/ajams-10-3-4

Abstract

The discrete wavelet transformation (DWT) is of considerable use in the domain of time series analysis. A fundamental problem in DWT is the distortions occurring at the edges while utilizing finite-length series. Insufficient information at boundary regions can lead to questionable accuracies of the transformation at the edges which will thus make a profound effect on further applications. Since the generally used methods to handle edge distortion such as zero padding has their own drawbacks, there are studies that have been done to alleviate the problem using mathematical techniques. With the main objective of finding an evidence-based strategy to reduce the edge effect inherent to DWT using statistical terminologies, this research compares the effect of statistical and machine learning-based denoising and extrapolating techniques in reducing-edge distortion using daily catchment flow series. The most suitable mother wavelet function and the decomposition level for the given series were considered as “biorthogonal 3.1” and level 2 and the edge effect was quantified using MAPE metric. The extrapolating techniques outperformed the denoising methods resulting Vanilla LSTM model with the lowest MAPE values and according to the averaged results taken considering 10 different points of the series, the Vanilla-LSTM and the SARIMA-LSTM hybrid model convincingly alleviate the edge distortion of all coefficients in a more generalized manner.

Keywords:
discrete wavelet transformation neural networks LSTM time series

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