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Spurious regressions between I(1) processes with long memory errors
Author(s) -
Cappuccio Nunzio,
Lubian Diego
Publication year - 1997
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00054
Subject(s) - spurious relationship , mathematics , limit (mathematics) , central limit theorem , regression , long memory , zero (linguistics) , statistical physics , statistics , regression analysis , econometrics , linear regression , asymptotic analysis , mathematical analysis , volatility (finance) , linguistics , philosophy , physics
In this paper we develop the asymptotic distribution theory for spurious regression between I(1) processes with long‐memory stationary errors. Our result departs from the standard results of Phillips (Understanding spurious regression in econometrics. J. Economet. 33 (1986), 311–40) in two respects. First, the limit theory we apply is based on a functional central limit theorem for stationary linear processes whose spectral density at frequency zero may diverge or collapse to zero. Second, different limit distributions may apply depending on the form of long memory exhibited by the error term. We also discuss the extension of our analyis to spurious regression with fitted intercept.