Center for Computational Finance and Economic Systems (CoFES)

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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.
A Bayesian Multivariate Functional Dynamic Linear Model
(Taylor & Francis, 2017) Kowal, Daniel R.; Matteson, David S.; Ruppert, David
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data—functional, time dependent, and multivariate components—we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time–frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online.
A Bayesian approach for capturing daily heterogeneity in intra-daily durations time series
(De Gruyter, 2013) Brownlees, Christian T.; Vannucci, Marina
Intra-daily financial durations time series typically exhibit evidence of long range dependence. This has motivated the introduction of models able to reproduce this stylized fact, like the Fractionally Integrated Autoregressive Conditional Duration Model. In this work we introduce a novel specification able to capture long range dependence. We propose a three component model that consists of an autoregressive daily random effect, a semiparametric time-of-day effect and an intra-daily dynamic component: the Mixed Autoregressive Conditional Duration (Mixed ACD) Model. The random effect component allows for heterogeneity in mean reversal within a day and captures low frequency dynamics in the duration time series. The joint estimation of the model parameters is carried out using MCMC techniques based on the Bayesian formulation of the model. The empirical application to a set of widely traded US tickers shows that the model is able to capture low frequency dependence in duration time series. We also find that the degree of dependence and dispersion of low frequency dynamics is higher in periods of higher financial distress.
Beating the House: Identifying Inefficiencies in Sports Betting Markets
(arXiv, 2019) Ramesh, Sathya; Mostofa, Ragib; Bornstein, Marco; Dobelman, John; Center for Computational Finance and Economic Systems
Inefficient markets allow investors to consistently outperform the market. To demonstrate that inefficiencies exist in sports betting markets, we created a betting algorithm that generates above market returns for the NFL, NBA, NCAAF, NCAAB, and WNBA betting markets. To formulate our betting strategy, we collected and examined a novel dataset of bets, and created a non-parametric win probability model to find positive expected value situations. As the United States Supreme Court has recently repealed the federal ban on sports betting, research on sports betting markets is increasingly relevant for the growing sports betting industry.
Enterprise and Political Risk Management in Complex Systems
(International Research Center for Energy and Economic Development, 2007) Ensor, Katherine B.; Kyj, Lada; Marfin, Gary C.; Center for Computational Finance and Economic Systems
Modeling Covariates with Nonparametric Bayesian Methods
(SSRN, 2010) Cruz-Marcelo, Alejandro; Rosner, Gary L.; Mueller, Peter; Stewart, Clinton; Center for Computational Finance and Economic Systems
A research problem that has received increased attention in recent years is extending Bayesian nonparametric methods to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. First, analyzing how the performance of such extensions differs, and second, understanding which features are worthwhile in order to produce better results. This article proposes answers to those questions focusing on predictive inference and continuous covariates. Specifically, we show that 1) nonparametric models using different strategies for modeling continuous covariates can show noteworthy differences when they are being used for prediction, even though they produce otherwise similar posterior inference results, and 2) when the predictive density is a mixture, it is convenient to make the weights depend on the covariates in order to produce sensible estimators. Such claims are supported by comparing the Linear DDP (an extension of the Sethuraman representation) and the Conditional DP (which augments the nonparametric distribution to include the covariates). Unlike the Conditional DP, the weights in the predictive mixture density of the Linear DDP are not covariate-dependent. This results in poor estimators of the predictive density. Specifically, in a simulation example, the Linear DDP wrongly introduces an additional mode into the predictive density, while in an application to a pharmacokinetic study, it produces unrealistic concentration-time curves.
Effect on Prediction When Modeling Covariates in Bayesian Nonparametric Models
(Springer Nature, 2013) Cruz-Marcelo, Alejandro; Rosner, Gary L.; Müller, Peter; Stewart, Clinton F.; Center for Computational Finance and Economic Systems
In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparamric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
Dynamic jump intensities and news arrival in oil futures markets
(Springer Nature, 2020) Ensor, Katherine B.; Han, Yu; Ostdiek, Barbara; Turnbull, Stuart M.; Center for Computational Finance and Economic Systems
We introduce a new class of discrete-time models that explicitly recognize the impact of news arrival. The distribution of returns is governed by three factors: dynamics volatility and two Poisson compound processes, one for negative news and one for positive news. We show in a model-free environment that the arrival of negative and positive news has an asymmetric effect on oil futures returns and volatility. Using the first 12 futures contracts, our empirical results confirm that the effects of negative and positive news are described by different processes, a significant proportion of volatility is explained by news arrival and the impact of negative news is larger than that of positive news.
High-Dimensional Multivariate Time Series With Additional Structure
(Taylor & Francis, 2017) Schweinberger, Michael; Babkin, Sergii; Ensor, Katherine B.; Center for Computational Finance and Economic Systems
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with statistical error. We consider high-dimensional vector autoregressive processes with spatial structure, a simple and common form of additional structure. We propose novel high-dimensional methods that take advantage of such structure without making model assumptions about how distance affects dependence. We provide nonasymptotic bounds on the statistical error of parameter estimators in high-dimensional settings and show that the proposed approach reduces the statistical error. An application to air pollution in the USA demonstrates that the estimation approach reduces both computing time and prediction error and gives rise to results that are meaningful from a scientific point of view, in contrast to high-dimensional methods that ignore spatial structure. In practice, these high-dimensional methods can be used to decompose high-dimensional multivariate time series into lower-dimensional multivariate time series that can be studied by other methods in more depth.
Discussion on an approach for identifying and predicting economic recessions in real-time using time-frequency functional models
(Wiley, 2012) Ensor, Katherine B.; Center for Computational Finance and Economic Systems
Filtering and Estimation for a Class of Stochastic Volatility Models with Intractable Likelihoods
(Project Euclid, 2019) Vankov, Emilian R.; Guindani, Michele; Ensor, Katherine B.
We introduce a new approach to latent state filtering and parameter estimation for a class of stochastic volatility models (SVMs) for which the likelihood function is unknown. The α-stable stochastic volatility model provides a flexible framework for capturing asymmetry and heavy tails, which is useful when modeling financial returns. However, the α-stable distribution lacks a closed form for the probability density function, which prevents the direct application of standard Bayesian filtering and estimation techniques such as sequential Monte Carlo and Markov chain Monte Carlo. To obtain filtered volatility estimates, we develop a novel approximate Bayesian computation (ABC) based auxiliary particle filter, which provides improved performance through better proposal distributions. Further, we propose a new particle based MCMC (PMCMC) method for joint estimation of the parameters and latent volatility states. With respect to other extensions of PMCMC, we introduce an efficient single filter particle Metropolis-within-Gibbs algorithm which can be applied for obtaining inference on the parameters of an asymmetric α-stable stochastic volatility model. We show the increased efficiency in the estimation process through a simulation study. Finally, we highlight the necessity for modeling asymmetric α-stable SVMs through an application to propane weekly spot prices.
Denoising Non-stationary Signals by Dynamic Multivariate Complex Wavelet Thresholding
(SSRN, 2020) Raath, Kim; Ensor, Katherine B.; Scott, David W.; Crivello, Alena
Over the past few years, we have seen an increased need for analyzing 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 transforms (DWT), 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. 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. Supplementary materials for your article are available online.
Multivariate Modeling of Natural Gas Spot Trading Hubs Incorporating Futures Market Realized Volatility
(SSRN, 2019) Weylandt, Michael; Han, Yu; Ensor, Katherine B.
Financial markets for Liquified Natural Gas (LNG) are an important and rapidly-growing segment of commodities markets. Like other commodities markets, there is an inherent spatial structure to LNG markets, with different price dynamics for different points of delivery hubs. Certain hubs support highly liquid markets, allowing efficient and robust price discovery, while others are highly illiquid, limiting the effectiveness of standard risk management techniques. We propose a joint modeling strategy, which uses high-frequency information from thickly-traded hubs to improve volatility estimation and risk management at thinly-traded hubs. The resulting model has superior in- and out-of-sample predictive performance, particularly for several commonly used risk management metrics, demonstrating that joint modeling is indeed possible and useful. To improve estimation, a Bayesian estimation strategy is employed and data-driven weakly informative priors are suggested. Our model is robust to sparse data and can be effectively used in any market with similar irregular patterns of data availability.
WRDS Index Data Extraction Methodology
(Rice University, 2014) Dobelman, J.A.; Kang, H.B.; Park, S.W.
This paper provides and validates an automatic procedure to generate accurate CRSP PERMNOs from Compustat GVKEYs for historical index constituents. We then validate the resulting PERMNO lists and examine some of the many pitfalls in other attempts to accomplish this, and provide cautionary guidance for WRDS index data researchers.
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.
An Examination of Some Open Problems in Time Series Analysis
(Rice University, 2005) Davis, Ginger Michelle
We investigate two open problems in the area of time series analysis. The first is developing a methodology for multivariate time series analysis when our time series has components that are both continuous and categorical. Our specific contribution is a logistic smooth transition regression (LSTR) model whose transition variable is related to a categorical variable. This methodology is necessary for series that exhibit nonlinear behavior dependent on a categorical variable. The estimation procedure is investigated both with simulation and an economic example. The second contribution to time series analysis is examining the evolving structure in multivariate time series. The application area we concentrate on is financial time series. Many models exist for the joint analysis of several financial instruments such as securities due to the fact that they are not independent. These models often assume some type of constant behavior between the instruments over the time period of analysis. Instead of imposing this assumption, we are interested in understanding the dynamic covariance structure in our multivariate financial time series, which will provide us with an understanding of changing market conditions. In order to achieve this understanding, we first develop a multivariate model for the conditional covariance and then examine that estimate for changing structure using multivariate techniques. Specifically, we simultaneously model individual stock data that belong to one of three market sectors and examine the behavior of the market as a whole as well as the behavior of the sectors. Our aims are detecting and forecasting unusual changes in the system, such as market collapses and outliers, and understanding the issue of portfolio diversification in multivariate financial series from different industry sectors. The motivation for this research concerns portfolio diversification. The false assumption that investment in different industry sectors is uncorrelated is not made. Instead, we assume that the comovement of stocks within and between sectors changes with market conditions. Some of these market conditions include market crashes or collapses and common external influences.
Estimating Marginal Survival in the Presence of Dependent and Independent Censoring: With Applications to Dividend Initiation Policy
(Rice University, 2005) Fix, Gretchen Abigail
In many survival analysis settings, the assumption of non-informative (i.e. independent) censoring is not valid. Zheng and Klein (1995, 1996) develop a copula-based method for estimating the marginal survival functions of bivariate dependent competing risks data. We expand upon this earlier work and adapt their method to data in which there are three competing risks representing both dependent and independent censoring. Specifically, our extension allows for the estimation of the survival functions of dependent competing risks X and Y in the presence of a third independent competing risk Z. An application to dividend initiation data is presented.
Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds
(Taylor & Francis, 2011) Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.
The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material.
Covariance Estimation in Dynamic Portfolio Optimization: A Realized Single Factor Model*
(SSRN, 2009) Kyj, Lada; Ostdiek, Barbara; Ensor, Katherine
Realized covariance estimation for large dimension problems is little explored and poses challenges in terms of computational burden and estimation error. In a global minimum volatility setting, we investigate the performance of covariance conditioning techniques applied to the realized covariance matrices of the 30 DJIA stocks. We find that not only is matrix conditioning necessary to deliver the benefits of high frequency data, but a single factor model, with a smoothed covariance estimate, outperforms the fully estimated realized covariance in one-step ahead forecasts. Furthermore, a mixed-frequency single-factor model - with factor coefficients estimated using low-frequency data and variances estimated using high-frequency data performs better than the realized single-factor estimator. The mixed-frequency model is not only parsimonious but it also avoids estimation of high-frequency covariances, an attractive feature for less frequently traded assets. Volatility dimension curves reveal that it is difficult to distinguish among estimators at low portfolio dimensions, but for well-conditioned estimators the performance gain relative to the benchmark 1/N portfolio increases with N.
Computational finance: correlation, volatility, and markets
(Wiley, 2014) Ensor, Katherine Bennett; Koev, Ginger M.
Financial data by nature are inter-related and should be analyzed using multivariate methods. Many models exist for the joint analysis of multiple financial instruments. Early models often assumed some type of constant behavior between the instruments over the time period of analysis. But today, time-varying covariance models are a key component of financial time series analysis leading to a deeper understanding of changing market conditions. Models for covolatility of financial data quickly grow in their complexity and parameters, and 20 years of research offers a variety of solutions to this complexity. After a short introduction of univariate volatility models, this article begins with the basic multivariate formulation for time series covariance modeling and moves to leading time series tools that address this complexity. Coupling these models with regime switching via a Markov process extends the features that can be understood from market behavior. We ground this review in an example of modeling the covariance of securities within sectors and sectors within markets, with dynamics that allow for two different market regimes. Specifically, we simultaneously model individual daily stock data that belong to one of three market sectors and examine the behavior of the market as a whole as well as the behavior of the market sectors over time. A motivation for this characterization concerns portfolio diversification and stock anomalies, and we capture the changing comovement of stocks within and between sectors as market conditions change. For example, some of these market conditions include market crashes or collapses and common external influences.

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