Kernel Two-Sample and Independence Tests for Nonstationary Random Processes

Laumann, Felix; Kügelgen, Julius von; Barahona, Mauricio

doi:10.3390/engproc2021005031

Cited by 2 publications

(4 citation statements)

References 16 publications

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“…The application of kernel MMD two-sample testing has to date focused on problems such as evaluating the performance of models [ 52 , 53 ] and two-sample tests for nonstationary random processes [ 54 ]. [ 52 ] introduced a method to select kernels that maximize the power of a test.…”

Section: Methodsmentioning

confidence: 99%

Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening

Gudmundarson,

Peters

2024

PLoS ONE

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In this work we seek to enhance the frameworks practitioners in asset management and wealth management may adopt to asses how different screening rules may influence the diversification benefits of portfolios. The problem arises naturally in the area of Environmental, Social, and Governance (ESG) based investing practices as practitioners often need to select subsets of the total available assets based on some ESG screening rule. Once a screening rule is identified, one constructs a dynamic portfolio which is usually compared with another dynamic portfolio to check if it satisfies or outperforms the risk and return profile set by the company. Our study proposes a novel method that tackles the problem of comparing diversification benefits of portfolios constructed under different screening rules. Each screening rule produces a sequence of graphs, where the nodes are assets and edges are partial correlations. To compare the diversification benefits of screening rules, we propose to compare the obtained graph sequences. The method proposed is based on a machine learning hypothesis testing framework called the kernel two-sample test whose objective is to determine whether the graphs come from the same distribution. If they come from the same distribution, then the risk and return profiles should be the same. The fact that the sample data points are graphs means that one needs to use graph testing frameworks. The problem is natural for kernel two-sample testing as one can use so-called graph kernels to work with samples of graphs. The null hypothesis of the two-sample graph kernel test is that the graph sequences were generated from the same distribution, while the alternative is that the distributions are different. A failure to reject the null hypothesis would indicate that ESG screening does not affect diversification while rejection would indicate that ESG screening does have an effect. The article describes the graph kernel two-sample testing framework, and further provides a brief overview of different graph kernels. We then demonstrate the power of the graph two-sample testing framework under different realistic scenarios. Finally, the proposed methodology is applied to data within the SnP500 to demonstrate the workflow one can use in asset management to test for structural differences in diversification of portfolios under different ESG screening rules.

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Section: Methodsmentioning

confidence: 99%

Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening

Gudmundarson,

Peters

2024

PLoS ONE

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“…Aim of the paper: Here, we use kernels to embed finite-dimensional distributions of the d stochastic processes falsefalse{Xtjfalsefalse} and design tests for joint independence of time series thereof. Recent work has used HSIC to test for independence of pairs of stationary [27,34] and non-stationary [28] time series. Here, we extend this work to d > 2 time series using tests based on dHSIC.…”

Section: Preliminariesmentioning

confidence: 99%

“…Hence, there is a need for independence tests that apply to both stationary and non-stationary processes. Recently, pairwise HSIC has been extended to non-stationary random processes by using random permutations over independent realizations of each time series, when available [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we show how dHSIC can be applied to reject joint independence in the case of both stationary and non-stationary multivariate random processes. Following recent work [ 28 ], we adapt dHSIC so that it can be applied to stationary and non-stationary time-series data when multiple realizations are present. Additionally, we develop a new bootstrap method inspired by [ 26 ], which uses ‘shifting’ to deal with stationary time-series data when only one realization is available.…”

Section: Introductionmentioning

confidence: 99%

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Kernel-based joint independence tests for multivariate stationary and non-stationary time series

Liu,

Peach,

Laumann

et al. 2023

R. Soc. open sci.

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Multivariate time-series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the d -variable Hilbert–Schmidt independence criterion to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate, neuroscience and socio-economic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.

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Kernel Two-Sample and Independence Tests for Nonstationary Random Processes

Cited by 2 publications

References 16 publications

Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening

Assessing portfolio diversification via two-sample graph kernel inference. A case study on the influence of ESG screening

Kernel-based joint independence tests for multivariate stationary and non-stationary time series

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