169,301 research outputs found

    Fractional Integration and Cointegration in US Financial Time Series Data

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    This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with dfractional integration, long-range dependence, fractional cointegration, financial data

    Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation

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    A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized for giving a new geometric and physical interpretation of more general convolution integrals of the Volterra type. Besides this, a new physical interpretation is suggested for the Stieltjes integral.Comment: 18 pages, 7 figures, 1 tabl

    Fractional Integration and Cointegration in US Financial Time Series Data

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    This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with dFractional integration, long-range dependence, fractional cointegration, financial data

    Fractional integration and cointegration in US financial time series data

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    This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with d < 1, which implies mean reversion. The multivariate framework exploiting recent developments in fractional cointegration allows to investigate in greater depth the relationships between financial series. We show that there exist many (fractionally) cointegrated bivariate relationships among the variables examined

    An Integral Equation Involving Legendre Functions

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    Rodrigues’s formula can be applied also to (1.1) and (1.3) but here the situation is slightly more involved in that the integrals with respect to σ^2 are of fractional order and their inversion requires the knowledge of differentiation and integration of fractional order. In spite of this complication the method has its merits and seems more direct than that employed in [1] and [3]. Moreover, once differentiation and integration of fractional order are used, it seems appropriate to allow a derivative of fractional order with respect to σ^-1 to appear so that the ultraspherical polynomial in (1.3) may be replaced by an (associated) Legendre function. This will be done in the present paper

    A novel approach to fractional calculus: utilizing fractional integrals and derivatives of the Dirac delta function

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    While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants of integration in their results. An elimination of constants of integration opens the door to an operator that reconciles all known fractional derivatives and shows surprising results in areas unobserved before, including the appearance of the Riemann Zeta Function and fractional Laplace and Fourier Transforms. A new class of functions, known as Zero Functions and closely related to the Dirac Delta Function, are necessary for one to perform elementary operations of functions without using constants. The operator also allows for a generalization of the Volterra integral equation, and provides a method of solving for Riemann's "complimentary" function introduced during his research on fractional derivatives

    How did the Sovereign debt crisis affect the Euro financial integration? A fractional cointegration approach.

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    This paper examines financial integration among stock markets in the Eurozone using the prices from each stock index. Monthly time series are constructed for four major stock indices for the period between 1998 and 2016. A fractional cointegrated vector autoregressive model is estimated at an international level. Our results show that there is a perfect and complete Euro financial integration. Considering the possible existence of structural breaks, this paper also examines the fractional cointegration within each regime, showing that Euro financial integration is very robust. However, in the financial and sovereign debt crisis regime, IBEX 35 appears to be the weak link in Euro financial integration, unless Euro financial integration recovers when this period ends
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