Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate

Testing hypotheses in an 1(2) model with
applications to the persistent long swings in the

Dmk/$ rate

S0ren Johansen* Economics Department, University of Copenhagen
Katarina Juselius, Economics Department, University of Copenhagen

Roman Frydman, Economics Department, New York University
Michael Goldberg, Economics Department, University of New Hampshire

December 18, 2007

Abstract

This paper discusses a number of likelihood ratio tests on long-run relations
and common trends in the I(2) model and provide new results on the test of
overidentifying restrictions on β'x_t and the asymptotic variance for the stochas-
tic trends parameters, ɑɪɪ. How to specify deterministic components in the 1(2)
model is discussed at some length. Model specification and tests are illustrated
with an empirical analysis of long and persistent swings in the foreign exchange
market between Germany and USA. The data analyzed consist of nominal ex-
change rates, relative prices, US inflation rate, two long-term interest rates and
two short-term interest rates over the 1975-1999 period. One important aim of
the paper is to demonstrate that by structuring the data with the help of the
I(2) model one can achieve a better understanding of the empirical regularities
underlying the persistent swings in nominal exchange rates, typical in periods of
floating exchange rates.

JEL:C32, C52, F41

Keywords: PPP puzzle, Forward premium puzzle, Cointegrated VAR. Like-
lihood inference.

1 Introduction

This paper discusses a number of likelihood ratio tests on long-run relations and com-
mon trends in the I(2) model and provides new results on the test of overidentifying

*Support from Center for Research in Econometric Analysis of Time Series, CREATES, funded by
the Danish National Research Foundation is gratefully acknowledged by the first author.

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