Resuscitating the co-fractional model of Granger (1986)

Federico Carlini () and Paolo Santucci de Magistris ()
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Federico Carlini: Università della Svizzera italiana, Postal: Università della Svizzera italiana, Institute of Finance, Via Buffi 13, 6900 Lugano, Switzerland
Paolo Santucci de Magistris: LUISS University and Aarhus University and CREATES, Postal: Department of Economics and Finance, LUISS University, Viale Romania 32, 00197, Roma, Italy

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We study the theoretical properties of the model for fractional cointegration proposed by Granger (1986), namely the FVECM_{d,b}. First, we show that the stability of any discretetime stochastic system of the type Pi(L)Y_t = e_t can be assessed by means of the argument principle under mild regularity condition on Pi(L), where L is the lag operator. Second, we prove that, under stability, the FVECM_{d,b} allows for a representation of the solution that demonstrates the fractional and co-fractional properties and we find a closed-form expression for the impulse response functions. Third, we prove that the model is identified for any combination of number of lags and cointegration rank, while still being able to generate polynomial co-fractionality. In light of these properties, we show that the asymptotic properties of the maximum likelihood estimator reconcile with those of the FCVAR_{d,b} model studied in Johansen and Nielsen (2012). Finally, an empirical illustration is provided.

Keywords: Fractional cointegration; Granger representation theorem; Stability; Identification; Impulse Response Functions; Profile Maximum Likelihood (search for similar items in EconPapers)
JEL-codes: C01 C02 C58 G12 G13 (search for similar items in EconPapers)
Pages: 43
Date: 2019-01-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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