Orthonormal Transforms of Time Series

Percival, Donald B.; Walden, A. T.

doi:10.1017/cbo9780511841040.004

Cited by 187 publications

(334 citation statements)

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“…Also, more importantly, the MODWT is invariant to circular shifting of the time series under study, while the DWT is not. Furthermore, both the DWT and MODWT can be used to analyze variance based on wavelet and scaling coefficients, but the MODWT wavelet variance estimator of the wavelet coefficients is asymptotically more efficient than the equivalent estimator based on DWT [13,14,22]. The MODWT is used to compute wavelet variances, wavelet correlations (WC) and cross-correlations (WCC) of bivariate time series [13,14].…”

Section: The Wavelet Methodologymentioning

confidence: 99%

“…Discrete Wavelet Transform (DWT) [13,14] is a mathematical tool that can handle non-stationary time series and which works in the combined time-and-scale domain. There are various algorithms for computing the DWT.…”

Section: The Wavelet Methodologymentioning

confidence: 99%

“…Furthermore, both the DWT and MODWT can be used to analyze variance based on wavelet and scaling coefficients, but the MODWT wavelet variance estimator of the wavelet coefficients is asymptotically more efficient than the equivalent estimator based on DWT [13,14,22]. The MODWT is used to compute wavelet variances, wavelet correlations (WC) and cross-correlations (WCC) of bivariate time series [13,14]. Several applications of the DWT and MODWT can be found in economic and financial literature (see e.g., [8,13,23,24]) and to a lesser extent in energy studies [25][26][27].…”

Section: The Wavelet Methodologymentioning

confidence: 99%

“…The maximum decomposition level J is given by log 2 (N) [13,14], which in this case is J = 8, so the MODWT produces eight wavelet coefficients and one scaling coefficient, that is, w 1,t , . .…”

Section: The Wavelet Methodologymentioning

confidence: 99%

“…By contrast, from a practical point of view, oil time series can be not stationary and involve heterogeneous agents who make decisions over different time horizons and operate on different time scales (frequencies) [9][10][11][12]. A mathematical tool that can handle non-stationaries time series, study interrelationships between time series and it is able to work in the combined time-and-scale domain, it is the wavelet cross-correlation via the Maximal Overlap Discrete Wavelet Transform (MODWT) [13,14]. Furthermore, the MODWT obtain an overview of the temporal changes in spectral dynamics of a time series under study.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analyzing Crude Oil Spot Price Dynamics versus Long Term Future Prices: A Wavelet Analysis Approach

Polanco-Martínez

Abadie

2016

Energies

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Abstract:The West Texas Intermediate (WTI) spot price shows high volatility and in 2014 and 2015 when quoted prices declined sharply, long-term prices in future markets were less volatile. These prices are different and diverge depending on how they process fundamental and transitory factors. US tight oil production has been a major innovation with significant macroeconomic effects. In this paper we use WTI spot prices and long-term futures prices, the latter calculated as the expected value with a stochastic model calibrated with the futures quotes of each sample day. These long-term prices are the long-term equilibrium value under risk neutral measurement. In order to analyze potential time-scale relationships between spots and future, we perform a wavelet cross-correlation analysis using a novel wavelet graphical tool recently proposed. To check the direction of the causality, we apply non-linear causality tests to raw data and log returns as well as to the wavelet transform of the spot and futures prices. Our results show that in the spot and futures markets for the period 24 February 2006-2 April 2016 there is a bi-directional causality effect for most time scales (from intra-week to biannual). This suggests that spot and futures prices react simultaneously to new information.

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Section: The Wavelet Methodologymentioning

confidence: 99%

Section: The Wavelet Methodologymentioning

confidence: 99%

Section: The Wavelet Methodologymentioning

confidence: 99%

Section: The Wavelet Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analyzing Crude Oil Spot Price Dynamics versus Long Term Future Prices: A Wavelet Analysis Approach

Polanco-Martínez

Abadie

2016

Energies

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Land‐surface controls on near‐surface soil moisture dynamics: Traversing remote sensing footprints

Mohanty

2016

Water Resources Research

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In this new era of remote-sensing based hydrology, a major unanswered question is how to incorporate the impact of land-surface based heterogeneity on soil moisture dynamics at remote sensing scales. The answer to this question is complicated since (1) soil moisture dynamics that vary with support, extent, and spacing scales are dependent on land-surface based heterogeneity and (2) land-surface based heterogeneity itself is scale-specific and varies with hydroclimates. Land-surface factors such as soil, vegetation, and topography affect soil moisture dynamics by redistributing the available soil moisture on the ground. In this study, we determined the contribution of these biophysical factors to redistribution of near-surface soil moisture across a range of remote sensing scales varying from an (airborne) remote sensor footprint (1.6 km) to a (satellite) footprint scale (25.6 km). Two-dimensional nondecimated wavelet transform was used to extract the support scale information from the spatial signals of the land-surface and soil moisture variables. The study was conducted in three hydroclimates: humid (Iowa), subhumid (Oklahoma), and semiarid (Arizona). The dominance of soil on soil moisture dynamics typically decreased from airborne to satellite footprint scales whereas the influence of topography and vegetation increased with increasing support scale for all three hydroclimates. The distinct effect of hydroclimate was identifiable in the soil attributes dominating the soil moisture dynamics. The near-surface soil moisture dynamics in Arizona (semiarid) can be attributed more to the clay content which is an effective limiting parameter for evaporation whereas in Oklahoma (humid), sand content (limiting parameter for drainage) was the dominant soil attribute. The findings from this study can provide a deeper understanding of the impact of heterogeneity on soil moisture dynamics and the potential improvement of hydrological models operating at footprints' scales.

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Combining Multiscale Filtering and Neural Networks for Local Rainfall Forecast

Buendía

Moya

Andina

2017

Biomedical Applications Based on Natural and Artificial Computing

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Abstract. Rainfall is one of the most important events of human life and society. Some rainfall phenomena like floods or hailstone are a threat to agriculture, business and even life. Predicting the weather has emerged as one of the most important areas of scientific endeavour. Nowadays, there is a big effort and great developments in long and mid-term rainfall forecasts, where qualitative improvements have been obtained both in forecasts and verification. This work proposes a diverse local rainfall forecasting system, using a long term local measurements registry. The forecast is performed estimating pressure time series and processing them with multispectral wavelet analysis and Neural Networks. The aim of the study is to provide complementary criteria based on the observed pressure wave pattern repetition. This method was proposed by expert meteorologists after observing these events during 40 years.

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Orthonormal Transforms of Time Series

Cited by 187 publications

References 0 publications

Analyzing Crude Oil Spot Price Dynamics versus Long Term Future Prices: A Wavelet Analysis Approach

Analyzing Crude Oil Spot Price Dynamics versus Long Term Future Prices: A Wavelet Analysis Approach

Land‐surface controls on near‐surface soil moisture dynamics: Traversing remote sensing footprints

Combining Multiscale Filtering and Neural Networks for Local Rainfall Forecast

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