Robust to noise and outliers estimator of correlation dimension

Dhifaoui, Zouhaier

doi:10.1016/j.chaos.2016.10.017

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…Recall that the model given by Eq. ( 9) is used, for unidimensional process, in [20] and [21] to testing the robustness of a proposed estimator of correlation dimension for deterministic dynamics corrupted by outliers observations. The advantage of the model given by Eq.…”

Section: Resultsmentioning

confidence: 99%

Robustness of Detrended Cross-correlation Analysis Method Under Outliers Observations

Dhifaoui

2022

Fluct. Noise Lett.

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The computation of the bivariate Hurst exponent constitutes an important technique to test the power-law cross-correlation of time series. For this objective, the detrended cross-correlation analysis (DCCA) method represents the most used one. In this paper, we prove the robustness of the DCCA method, where the trend is estimated using the polynomial fitting, to estimate the bivariate Hurst exponent when time series are corrupted by outliers observations. On the other hand, we give the exact polynomial order and a regression region for computing a detrended cross-correlation function to obtain a least square estimator of bivariate Hurst exponent. Our theoretical results are shown by a simulation study on a two-fractional Gaussian noise process corrupted by outliers observations. Additionally, our results are applied to financial time series. The empirical findings results are accompanied by interpretations.

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Section: Resultsmentioning

confidence: 99%

Robustness of Detrended Cross-correlation Analysis Method Under Outliers Observations

Dhifaoui

2022

Fluct. Noise Lett.

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“…In forthcoming research, investigators have an intriguing opportunity to delve deeper into the dynamics underpinning the observed patterns within the studied time series. A prospective avenue involves the implementation of the robust correlation dimension estimator proposed by [80], utilizing the Gaussian kernel correlation integral [81]. This innovative approach promises a meticulous exploration into whether the examined time series might manifest chaotic behavior.…”

Section: Discussionmentioning

confidence: 99%

The Nexus between Climate Change and Geopolitical Risk Index in Saudi Arabia Based on the Fourier-Domain Transfer Entropy Spectrum Method

Dhifaoui,

Ncibi,

Gasmi

et al. 2023

Sustainability

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Geopolitical risks have recently escalated due to increased disputes and tensions between nations worldwide. Additionally, “climate change” describes the prolonged alteration of regular weather patterns, mainly due to human activities on Earth, leading to disastrous consequences for human livelihoods, the economy, and natural ecology. This study employs a novel transfer entropy spectrum-based Fourier domain to dynamically analyze the geopolitical risk index and specific climate change factors in Saudi Arabia. Our comprehensive investigation reveals a robust bidirectional causal relationship between the geopolitical risk index and key climate change variables, including total precipitation, relative humidity, temperature, and wind speed and direction. These findings provide compelling evidence of the intricate and complex links between geopolitical concerns and climate change in the region. The study offers policymakers and scholars crucial new insights into addressing the challenges posed by geopolitical instability and climate change by uncovering these causal relationships.

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“…The correlation dimension can be estimated from Gaussian kernel correlation integral C m (h) (see Dhifaoui (2016, 2018) and references therein for more details) which is characterized, in the presence of Gaussian noise and when h2+σ2→0 and m → +∞, by following scale: …”

Section: Methodsmentioning

confidence: 99%

“…is computed for a series of discrete bandwidth values {h k }, k = 0,1,2,... ,N b and fitting to the scaling relation given by Equation (2) using non-linear least squares method. The principal problem of this procedure is how to choose the best bandwidth region (values of h k ) for doing the regression to obtain D. In Dhifaoui (2016), the author proposes a new estimator of correlation dimension, that is independent of regression region and is highly robust to the presence of variety of types of noise and also to outliers observations in time series. This estimator, for any embedding dimension m, is given by: ( )…”

Section: Robust Estimator Of Correlation Dimensionmentioning

confidence: 99%

“…But the problem of this estimation method is how to choose a good range of bandwidths values for doing a non-linear regression. To overcome this problem a robust estimator of correlation dimension is proposed by Dhifaoui (2016). This method is based on similarity between the curve of correlation integral proposed by Diks (1996) and that of modified Boltzman sigmoidal function.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determinism and Non-linear Behaviour of Log-return and Conditional Volatility: Empirical Analysis for 26 Stock Markets

Dhifaoui

2021

South Asian Journal of Macroeconomics and Public Finance

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Determinism and non-linear behaviour in log-return and conditional volatility time series of the stock market index is examined for twenty-six countries. For this goal, the principal statistical techniques used in this study are a robust estimator of correlation dimension, a normalized non-linear prediction error, and pseudo-periodic surrogate data method. The proposed approach indicates, first, the stochastic behaviour of all log-return time series. Second, the inability of local linear, ARMA, or state- dependent noise models (such as ARCH, GARCH, and EGARCH) to describe its structure for the frontier, emerging, and developed markets. The same stochastic behaviour of conditional volatility time series, estimated by the stochastic volatility model with moving average innovations, is detected. This finding proves the efficiency of the stochastic volatility model compared with some analysed types of GARCH models for all studied markets. JEL Classification: C12, C52, D53, E44

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Robust to noise and outliers estimator of correlation dimension

Cited by 7 publications

References 11 publications

Robustness of Detrended Cross-correlation Analysis Method Under Outliers Observations

Robustness of Detrended Cross-correlation Analysis Method Under Outliers Observations

The Nexus between Climate Change and Geopolitical Risk Index in Saudi Arabia Based on the Fourier-Domain Transfer Entropy Spectrum Method

Determinism and Non-linear Behaviour of Log-return and Conditional Volatility: Empirical Analysis for 26 Stock Markets

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