Browsing by Author "Raath, Kim C."

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    Denoising Non-Stationary Signals via Dynamic Multivariate Complex Wavelet Thresholding
    (MDPI, 2023) Raath, Kim C.; Ensor, Katherine B.; Crivello, Alena; Scott, David W.
    Over the past few years, we have seen an increased need to analyze the dynamically changing behaviors of economic and financial time series. These needs have led to significant demand for methods that denoise non-stationary time series across time and for specific investment horizons (scales) and localized windows (blocks) of time. Wavelets have long been known to decompose non-stationary time series into their different components or scale pieces. Recent methods satisfying this demand first decompose the non-stationary time series using wavelet techniques and then apply a thresholding method to separate and capture the signal and noise components of the series. Traditionally, wavelet thresholding methods rely on the discrete wavelet transform (DWT), which is a static thresholding technique that may not capture the time series of the estimated variance in the additive noise process. We introduce a novel continuous wavelet transform (CWT) dynamically optimized multivariate thresholding method (WaveL2E). Applying this method, we are simultaneously able to separate and capture the signal and noise components while estimating the dynamic noise variance. Our method shows improved results when compared to well-known methods, especially for high-frequency signal-rich time series, typically observed in finance.
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    Denoising Non-Stationary Signals via Dynamic Multivariate Complex Wavelet Thresholding
    (MDPI, 2023) Raath, Kim C.; Ensor, Katherine B.; Crivello, Alena; Scott, David W.
    Over the past few years, we have seen an increased need to analyze the dynamically changing behaviors of economic and financial time series. These needs have led to significant demand for methods that denoise non-stationary time series across time and for specific investment horizons (scales) and localized windows (blocks) of time. Wavelets have long been known to decompose non-stationary time series into their different components or scale pieces. Recent methods satisfying this demand first decompose the non-stationary time series using wavelet techniques and then apply a thresholding method to separate and capture the signal and noise components of the series. Traditionally, wavelet thresholding methods rely on the discrete wavelet transform (DWT), which is a static thresholding technique that may not capture the time series of the estimated variance in the additive noise process. We introduce a novel continuous wavelet transform (CWT) dynamically optimized multivariate thresholding method (𝑊𝑎𝑣𝑒𝐿2𝐸). Applying this method, we are simultaneously able to separate and capture the signal and noise components while estimating the dynamic noise variance. Our method shows improved results when compared to well-known methods, especially for high-frequency signal-rich time series, typically observed in finance.
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    Time-varying wavelet-based applications for evaluating the Water-Energy Nexus
    (Frontiers, 2020) Raath, Kim C.; Ensor, Katherine B.
    This paper quantifies the rising global dynamic, interconnected relationship between energy and water commodities. Over the last decade, increased international concern has emerged about the water-energy nexus. However, recent research still lacks a quantified understanding of the role of water within a financial-economic view of the nexus. The complexity of commodity markets contributes to this lack of understanding. These markets consist of a wide variety of participants having different objectives, resulting in non-stationary time series. Wavelets are mathematical functions that detect common time-localized oscillations in non-stationary time series. The novelty of our analysis lies in applying wavelet techniques to better quantify the financial implications and understand opportunities of the dynamic relationship that exists in the water-energy nexus. Using daily water and energy commodity ETF price data from 2007 to 2017 we deconstruct each of the time series into different horizon components and evaluate their respective wavelet transforms. Comparing the wavelet squared coherence (WSC) and the windowed scalogram difference (WSD) allows us to specify nexus similarities and differences. We further analyze the wavelet local multiple correlations (WLMC) by including S&P500 ETF price data to conditionally eliminate market effects. Previous studies heavily focused on the qualitative relationships between water and energy. Whereas, the analysis in this paper, to the best of our knowledge, is the first to confirm the time-varying relationship in a quantitative manner. The most significant financial-economic result from our analysis is that water prices, at certain time horizons, lead energy prices during specific localized economic events.