Spectral Based Methods to Identify Common Trends and Common Cycles

19 Pages Posted: 20 Feb 2003

Date Written: April 2001

Abstract

The rank of the spectral density matrix conveys relevant information in a variety of modelling scenarios. Phillips (1986) showed that a necessary condition for cointegration is that the spectral density matrix of the innovation sequence at frequency zero is of a reduced rank. In a recent paper Forni and Reichlin (1998) suggested the use of generalized dynamic factor model to explain the dynamics of a large set of macroeconomic series. Their method relied also on the computation of the rank of the spectral density matrix. This paper provides formal tests to estimate the rank of the spectral density matrix at any given frequency. The tests of rank at frequency zero are tests of the null of 'cointegration', complementary to those suggested by Phillips and Ouliaris (1988) which test the null of 'no cointegration'.

Keywords: Tests of Rank, Spectral Density Matrix, Canonical Correlations

JEL Classification: C12, C15, C32

Suggested Citation

Camba-Mendez, Gonzalo and Kapetanios, George, Spectral Based Methods to Identify Common Trends and Common Cycles (April 2001). Available at SSRN: https://ssrn.com/abstract=356100

Gonzalo Camba-Mendez (Contact Author)

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany
0049 69 13440 (Phone)
0044 69 1344 6000 (Fax)

George Kapetanios

King's College, London ( email )

30 Aldwych
London, WC2B 4BG
United Kingdom
+44 20 78484951 (Phone)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
79
Abstract Views
918
rank
344,358
PlumX Metrics