arXiv subjects

Žikica Lukić

Publications and source records attributed to Žikica Lukić.

5 recordsLinked to original sources

arXiv2026

Change-point analysis: a new perspective for unstable financial markets

We introduce two new classes of nonparametric change-point tests for sequences of univariate non-negative random variables. The proposed procedures are based on the empirical modified Hankel transform and the Laplace transform, respectively, and provide new transform-based tools for detecting distributional changes. We derive the asymptotic null distributions of the corresponding test statistics and use a permutation bootstrap procedure to obtain $p$-values, since the limiting null distributions are not distribution-free. Through a finite-sample simulation study, we show that the proposed tests are well calibrated, generally more powerful than empirical-characteristic-function-based competitors, and capable of accurately estimating the change-point location, particularly in asymmetric settings. The usefulness of the proposed methodology is further demonstrated through applications to Argentina rainfall data, as well as U.S. GNP and S\&P 500 absolute log-returns. The real-data examples illustrate that the proposed Hankel- and Laplace-transform-based tests are effective tools for detecting meaningful distributional changes in non-negative data.

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arXiv2024

A Laplace transform-based test for the equality of positive semidefinite matrix distributions

In this paper, we present a novel test for determining equality in distribution of matrix distributions. Our approach is based on the integral squared difference of the empirical Laplace transforms with respect to the noncentral Wishart measure. We conduct an extensive power study to assess the performance of the test and determine the optimal choice of parameters. Furthermore, we demonstrate the applicability of the test on financial and non-life insurance data, illustrating its effectiveness in practical scenarios.

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arXiv2023

Change point analysis -- the empirical Hankel transform approach

In this study, we introduce the first-of-its-kind class of tests for detecting change points in the distribution of a sequence of independent matrix-valued random variables. The tests are constructed using the weighted square integral difference of the empirical orthogonal Hankel transforms. The test statistics have a convenient closed-form expression, making them easy to implement in practice. We present their limiting properties and demonstrate their quality through an extensive simulation study. We utilize these tests for change point detection in cryptocurrency markets to showcase their practical use. The detection of change points in this context can have various applications in constructing and analyzing novel trading systems.

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arXiv2023

A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance

This paper introduces a novel two-sample test for a broad class of orthogonally equivalent positive definite symmetric matrix distributions. Our test is the first of its kind and we derive its asymptotic distribution. To estimate the test power, we use a warp-speed bootstrap method and consider the most common matrix distributions. We provide several real data examples, including the data for main cryptocurrencies and stock data of major US companies. The real data examples demonstrate the applicability of our test in the context closely related to algorithmic trading. The popularity of matrix distributions in many applications and the need for such a test in the literature are reconciled by our findings.

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arXiv2023

Characterization-based approach for construction of goodness-of-fit test for Lévy distribution

The Lévy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the Lévy distribution. In this paper, two novel classes of goodness-of-fit tests for the Lévy distribution are proposed. Both tests are based on V-empirical Laplace transforms. New tests are scale free under the null hypothesis, which makes them suitable for testing the composite hypothesis. The finite sample and limiting properties of test statistics are obtained. In addition, a generalization of the recent Bhati-Kattumannil goodness-of-fit test to the Lévy distribution is considered. For assessing the quality of novel and competitor tests, the local Bahadur efficiencies are computed, and a wide power study is conducted. Both criteria clearly demonstrate the quality of the new tests. The applicability of the novel tests is demonstrated with two real-data examples.

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