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Book ChapterDOI

Restoring Corrupted Cross-Recurrence Plots Using Matrix Completion: Application on the Time-Synchronization Between Market and Volatility Indexes

01 Jan 2016-Vol. 180, pp 241-263
TL;DR: In this paper, a matrix completion based approach is proposed to restore the corrupted cross-recurrence plot (CRP) prior to the estimation of the time-synchronization relationship.
Abstract: The success of a trading strategy can be significantly enhanced by tracking accurately the implied volatility changes, which refers to the amount of uncertainty or risk about the degree of changes in a market index. This fosters the need for accurate estimation of the time-synchronization profile between a given market index and its associated volatility index. In this chapter, we advance existing solutions, which are based widely on the typical correlation, for identifying this temporal interdependence. To this end, cross-recurrence plot (CRP) analysis is exploited for extracting the underlying dynamics of a given market and volatility indexes pair, along with their time-synchronization profile. However, CRPs of degraded quality, for instance due to missing information, may yield a completely erroneous estimation of this profile. To overcome this drawback, a restoration stage based on the concept of matrix completion is applied on a corrupted CRP prior to the estimation of the time-synchronization relationship. A performance evaluation on the S&P 500 index and its associated VIX volatility index reveals the superior capability of our proposed approach in restoring accurately their CRP and subsequently estimating a temporal relation between the two indexes even when \(80\,\%\) of CRP values are missing.
Citations
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Journal ArticleDOI
TL;DR: In this article, a method that combines the adaptive signal decomposition with the recurrence analysis is proposed to solve the difficulty of testing nonlinearity and non-stationarity of bridge structure signals.
Abstract: To test the nonlinearity and non-stationarity of measured dynamic signals from a bridge structure with high-level noise and dense modal characteristics, a method that combines the adaptive signal decomposition with the recurrence analysis is proposed to solve the difficulty of testing nonlinearity and non-stationarity of bridge structure signals. A novel white noise assistance and cluster analysis are introduced to the ensemble empirical mode decomposition to alleviate mode-mixing issues and generate single-mode intrinsic mode functions. Combining the hypothesis-testing scheme of nonstationary and nonlinear synchronization and surrogate techniques, a data-driven recurrence quantification analysis method is proposed and a novel recurrence quantification measure pairs are set up. To demonstrate the efficacy of the proposed methodology, complex signals, which are collected from a carefully instrumented model of a cable-stayed bridge, are utilized as the basis for comparing with traditional nonlinear and non-stationary test methods. Results show that the proposed multiscale recurrence method is feasible and effective for applications to a nonlinear and non-stationary test for real complex civil structures.

9 citations


Additional excerpts

  • ...In recent years, RP and RQA or their variations, like cross recurrence plot [6], the ordinal patterns recurrence plot [7], the multivariate recurrence plot [8], and the recurrence network [9] have been widely and successfully applied to test the nonlinearity and non-stationarity of the signal from the real world in various branches of science and technology, such as in physiology [9–12], economy [13,14], chemistry [15,16], and engineering [17,18]....

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Journal ArticleDOI
TL;DR: The cross-recurrence plot analysis is used as a nonlinear method for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization.
Abstract: Cross-correlation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this end, we use the cross recurrence plot analysis as a nonlinear method for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization. We adopt a deep learning framework for methodologically addressing the prediction of the synchronization state based on features extracted from dynamically sub-sampled cross recurrence plots. We provide extensive experiments on several stocks, major constituents of the S &P100 index, to empirically validate our approach. We find that the task of predicting the state of synchronization of two time series is in general rather difficult, but for certain pairs of stocks attainable with very satisfactory performance (84% F1-score, on average).
Journal ArticleDOI
Kopp, Fabian1
TL;DR: In this paper , a cross-correlation analysis is used for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization.
Abstract: Abstract Cross-correlation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this end, we use the cross recurrence plot analysis as a nonlinear method for quantifying the multidimensional coupling in the time domain of two time series and for determining their state of synchronization. We adopt a deep learning framework for methodologically addressing the prediction of the synchronization state based on features extracted from dynamically sub-sampled cross recurrence plots. We provide extensive experiments on several stocks, major constituents of the S &P100 index, to empirically validate our approach. We find that the task of predicting the state of synchronization of two time series is in general rather difficult, but for certain pairs of stocks attainable with very satisfactory performance (84% F1-score, on average).
References
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Book
01 Jan 1987
TL;DR: This work states that maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse and large-Sample Inference Based on Maximum Likelihood Estimates is likely to be high.
Abstract: Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse.Large-Sample Inference Based on Maximum Likelihood Estimates.Bayes and Multiple Imputation.PART III: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA: APPLICATIONS TO SOME COMMON MODELS.Multivariate Normal Examples, Ignoring the Missing-Data Mechanism.Models for Robust Estimation.Models for Partially Classified Contingency Tables, Ignoring the Missing-Data Mechanism.Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missing-Data Mechanism.Nonignorable Missing-Data Models.References.Author Index.Subject Index.

18,201 citations

Journal ArticleDOI
TL;DR: This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.
Abstract: This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem and arises in many important applications as in the task of recovering a large matrix from a small subset of its entries (the famous Netflix problem). Off-the-shelf algorithms such as interior point methods are not directly amenable to large problems of this kind with over a million unknown entries. This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative, produces a sequence of matrices $\{\boldsymbol{X}^k,\boldsymbol{Y}^k\}$, and at each step mainly performs a soft-thresholding operation on the singular values of the matrix $\boldsymbol{Y}^k$. There are two remarkable features making this attractive for low-rank matrix completion problems. The first is that the soft-thresholding operation is applied to a sparse matrix; the second is that the rank of the iterates $\{\boldsymbol{X}^k\}$ is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal storage space and keep the computational cost of each iteration low. On the theoretical side, we provide a convergence analysis showing that the sequence of iterates converges. On the practical side, we provide numerical examples in which $1,000\times1,000$ matrices are recovered in less than a minute on a modest desktop computer. We also demonstrate that our approach is amenable to very large scale problems by recovering matrices of rank about 10 with nearly a billion unknowns from just about 0.4% of their sampled entries. Our methods are connected with the recent literature on linearized Bregman iterations for $\ell_1$ minimization, and we develop a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.

5,276 citations

Journal ArticleDOI
TL;DR: It is proved that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries, and that objects other than signals and images can be perfectly reconstructed from very limited information.
Abstract: We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys $$m\ge C\,n^{1.2}r\log n$$ for some positive numerical constant C, then with very high probability, most n×n matrices of rank r can be perfectly recovered by solving a simple convex optimization program. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Similar results hold for arbitrary rectangular matrices as well. Our results are connected with the recent literature on compressed sensing, and show that objects other than signals and images can be perfectly reconstructed from very limited information.

5,274 citations