Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity

This paper draws attention to the limitations of the standard unit root/cointegration approach to economic and financial modelling, and to some of the alternatives based on the idea of fractional integration, long memory models, and the random field regression approach to nonlinearity. Following brief explanations of fractional integration and random field regression, and the methods of applying them, selected techniques are applied to a demand for money dataset. Comparisons of the results from this illustrative case study are presented, and conclusions are drawn that should aid practitioners in applied time-series econometrics.

Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study

This paper draws attention to the limitations of the standard unit root/cointegration approach to economic and financial modelling, and to some of the alternatives based on the idea of fractional integration, long memory models, and the random field regression approach to nonlinearity. Following brief explanations of fractional integration and random field regression, and the methods of applying them, selected techniques are applied to a demand for money dataset. Comparisons of the results from this illustrative case study are presented, and conclusions are drawn that should aid practitioners in applied time-series econometrics.

Purchasing Power Parity: The Irish Experience Re-visited

This paper looks at issues surrounding the testing of purchasing power parity using Irish data. Potential difficulties in placing the analysis in an I(1)/I(0) framework are highlighted. Recent tests for fractional integration and nonlinearity are discussed and used to investigate the behaviour of the Irish exchange rate against the United Kingdom and Germany. Little evidence of fractionality is found but there is strong evidence of nonlinearity from a variety of tests. Importantly, when the nonlinearity is modelled using a random field regression, the data conform well to purchasing power parity theory, in contrast to the findings of previous Irish studies, whose results were very mixed.

Exploring Long Memory and Nonlinearity in Irish Real Exchange Rates using Tests based on Semiparametric Estimation

Deciding whether a time series that appears nonstationary is in fact fractionally integrated or subject to structural change is a difficult task. However, various tests have recently been introduced for distinguishing long memory from level shifts and nonlinearity. In this paper, three testing approaches based on the properties of semiparametric estimators of the fractional differencing parameter, d, are described and applied to the (log) Ireland-United Kingdom and Ireland-Germany real exchange rates. The two exchange rates behave quite differently over time and the new tests give different results for each; but overall the results provide fairly strong support for the possibility of nonlinearity rather than long memory.Fractional integration, long memory, nonlinearity, real exchange rates, struc- tural change

Modelling Ireland’s exchange rates: from EMS to EMU

This paper attempts to model the nominal and real exchange rate for Ireland, relative to Germany and the UK from 1975 to 2003. It offers an overview of the theory of purchasing power parity (PPP), focusing particularly on likely sources of nonlinearity. Potential difficulties in placing the analysis in the standard I(1)/I(0) framework are highlighted and comparisons with previous Irish studies are made. Tests for fractional integration and nonlinearity, including random field regressions, are discussed and applied. The results obtained highlight the likely inadequacies of the standard cointegration and STAR approaches to modelling, and point instead to multiple structural changes models. Using this approach, both bilateral nominal exchange rates are effectively modelled, and in the case of Ireland and Germany, PPP is found to be valid not only in the long run, but also in the medium term. JEL Classification: C22, C51, F31, F41fractional Dickey-Fuller tests, multiple structural changes models, purchasing power parity, random field regression, smooth transition autoregression

Some Empirical Observations on the Forward Exchange Rate Anomaly

This paper looks at issues surrounding the testing of fractional integration and nonlinearity in relation to the forward exchange rate anomaly of Fama (1984). Recent tests for fractional integration and nonlinearity are discussed and used to investigate the behaviour of three exchange rates and premiums. The findings provide some support for I(1) exchange rates but suggest fractionality for premiums, mixed evidence on cointegration, and a strong possibility of time-wise nonlinearity. Significantly, when the nonlinearity is modelled using a random field regression, the forward anomaly disappears.