Fractional integration and cointegration in US financial time series data

This paper examines several US monthly financial time series 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$d > 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>d</mi> <mo>></mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>, 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 might exist many (fractionally) cointegrated bivariate relationships among the variables examined, for some of which only standard cointegration tests had previously been carried out. Copyright The Author(s) 2014