Institute of Information Theory and Automation

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Long-range cross-correlations: Tests,estimators and applications

Ladislav Krištoufek
Defense type: 
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Fsv Uk - Opletalova - m.č. 314
We provide the essentials and framework for understanding and treating long range cross-correlated processes. Starting from the definition of long-range cross-correlated processes as jointly stationary processes with asymptotically power-law decaying cross-correlation function, we follow the steps of the standard univariate long-range dependence texts to show that such definition implies a divergent at origin cross-power spectrum and power-law scaling of covariances of partial sums of the long-range cross-correlated processes. Chapter 2 describes these and other basic definitions and propositions together with necessary proofs. Chapter 3 then introduces several processes which posses long-range cross-correlated series properties. Apart from cases when the memory parameter of the bivariate memory is a simple average of the parameters of the separate processes, we also introduce a new kind of process, which we call the mixed-correlated ARFIMA process, which allows to control both for the bivariate and univariate memory parameters. Chapter 4 deals with tests for a presence of long-range cross-correlations. Apart from one already existent test, we develop three new tests, and the statistical power and size of the tests is compared. The newly introduced tests strongly surpass the other one. In Chapter 5, we cover the estimators of long-range cross-correlation parameter - the bivariate Hurst exponent. The estimators are split into two groups based on their domain of operation-time domain and frequency domain. Apart from four already existing estimators, one of which has been introduced by the author of this thesis, we present additional two estimators. As another novelty, we reconfigure the estimators so that the power law coherency can be estimated as well. Statistical properties (bias, variance and mean squared error) of the estimators are compared for various specifications. In Chapter 6, we apply the proposed methodology to analyze the leverage effect between financial returns and volatility. The dissertation thesis thus provides quite a complex study on long-range cross-correlated processes and proposes a guide how to treat them.
2018-05-03 08:01