Dimension of the minimal cover and fractal analysis of time series

Dubovikov, M. M.; Starchenko, N.V; Dubovikov, M. S.

doi:10.1016/j.physa.2004.03.025

Cited by 57 publications

(36 citation statements)

References 24 publications

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“…This method has been recently introduced [4], and, in its original version, it relates the minimal area necessary to cover a given plane curve, at a specified scale, to a power-law behavior.…”

Section: Minimal-cover Analysismentioning

confidence: 99%

Fractal Analysis of Weld Defect Patterns Obtained by Radiographic Tests

Tesser¹,

Lopes²,

Vieira³

et al. 2007

AIP Conference Proceedings

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Abstract. This paper presents a fractal analysis of radiographic patterns obtained from specimens with three types of inserted welding defects: lack of fusion, lack of penetration, and porosity. The study focused on patterns of carbon steel beads from radiographs of the International Institute of Welding (IIW). The radiographs were scanned using a greyscale with 256 levels, and the fractal features of the surfaces constructed from the radiographic images were characterized by means of Hurst, detrended-fluctuation, and minimal-cover analyses. A Karhunen-Loève transformation was then used to classify the curves obtained from the fractal analyses of the various images, and a study of the classification errors was performed. The obtained results indicate that fractal analyses can be an effective additional tool for pattern recognition of weld defects in radiographic tests.

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Section: Minimal-cover Analysismentioning

confidence: 99%

Fractal Analysis of Weld Defect Patterns Obtained by Radiographic Tests

Tesser¹,

Lopes²,

Vieira³

et al. 2007

AIP Conference Proceedings

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“…Our research builds upon and further extends results reported in [16], [17], [18]. We use the following notation, adopted in previous works.…”

Section: Dynamic Volatility Componentsmentioning

confidence: 58%

“…According to results previously reported in [16], [18] shown that the dynamics of these variables is determined by the behavior of the price series P t ( ) .…”

Section: Dynamic Volatility Componentsmentioning

confidence: 88%

“…The approach for computing fractal dimension using sequence of the minimal covers with decreasing scale (proposed in [1]) is used to decompose volatility into two dynamic components: specific , based on different principles and capable of catching long uptrends in volatility. To test statistical significance of its abilities we introduce several estimators of conditional and unconditional probabilities of reversals in observed and predicted dynamic components of volatility.…”

Section: Introductionmentioning

confidence: 99%

“…Next session introduces an algorithm to unbundle structural (scale-specific) dynamic component of multiscale volatility from time-specific dynamic component using fractal measure introduced by Dubovikov in [1]. Sections 3 introduces two separate models for these dynamic components, addressing mentioned issues (i. e. ability to predict volatility reversals on many scales simultaneously).…”

Section: Introductionmentioning

confidence: 99%

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Forecasting Coherent Volatility Breakouts

Didenko

Dubovikov²,

Poutko

2014

SSRN Journal

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ДуБОВИКОВ МИхАИЛ МИхАЙЛОВИЧ заместитель генерального директора, оАо «индекс-xx», Москва, россияПуТКО БОРИС АЛЕКСАНДРОВИЧ преподаватель кафедры «Математика-1», Финансовый университет, Москва, россия АННОТАЦИЯ Разработана методика долгосрочного (до нескольких месяцев) прогнозирования разворотной динамики во-латильности с использованием свойств длинной памяти финансовых временных рядов. Предложенный в [1] алгоритм вычисления фрактальной размерности через покрытие предфракталами используется для декомпо-зиции волатильности на удельнуюПредложены модели динамических компонент волатильности, способные предсказывать длинные восходящие в ней тренды. Для проверки статистической значимости прогнозов введены функции оценки условных и безусловных вероятностей для наблюдаемых и прогнозируемых компонент. Наши результаты могут быть использованы для предсказания точек перехода рынка в нестабильное состояние. Ключевые слова: фондовый рынок; ценовой риск; фрактальная размерность; крахи рынка; ARCH-GARCH мо-дель; модели волатильности как амплитуды; многомасштабная волатильность; развороты волатильности; тех-нический анализ. FORECASTING COHERENT vOLATILITY BREAKOUTS ALExANDER S. DIDENKO financial university under the Government of Russian federation Email: alexander.didenko@gmail.com MIKHAIL M. DuBOVIKOV deputy ceo, «index-xx» company BORIS A. POuTKO lecturer, department of mathematics, financial university under the Government of Russian federation ABSTRACTThe paper develops an algorithm for making long-term (up to three months ahead) predictions of volatility reversals based on long memory properties of financial time series. The approach for computing fractal dimension using sequence of the minimal covers with decreasing scale (proposed in [1]) is used to decompose volatility into two dynamic components: specific , based on different principles and capable of catching long uptrends in volatility. To test statistical significance of its abilities we introduce several estimators of conditional and unconditional probabilities of reversals in observed and predicted dynamic components of volatility. Our results could be used for forecasting points of market transition to an unstable state.

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