Luis A. Gil-Alana

Testing of unit root and other nonstationary hypotheses in macroeconomic time series

Abstract Recently proposed tests for unit root and other nonstationarity of Robinson (1994a) are applied to an extended version of the data set used by Nelson and Plosser (1982). Unusually, the tests are efficient (against appropriate parametric alternatives), the null can be any member of the I(d) class, and the null limit distribution is chi-squared. The conclusions vary substantially across the 14 series, and across different models for the disturbances (which, also unusually, include the Bloomfield spectral model). Overall, the consumer price index and money stock seem the most nonstationary, while industrial production and unemployment rate seem the closest to stationarity.

Mean reversion in the real exchange rates

Abstract Robinson’s [J. Am. Stat. Assoc. 89 (1994) 1420] fractionally-based tests for unit roots and other hypotheses are applied to real exchange rate data between U.S. and five industrialized countries. The results indicate that the series are fractionally integrated with mean reversion if the disturbances are autocorrelated.

Testing Stochastic Cycles in Macroeconomic Time Series

A particular version of the tests of Robinson (1994) for testing stochastic cycles in macroeconomic time series is proposed in this article. The tests have a standard limit distribution and are easy to implement in raw time series. A Monte Carlo experiment is conducted, studying the size and the power of the tests against different alternatives, and the results are compared with those based on other tests. An empirical application using historical U.S. annual data is also carried out at the end of the article.

Seasonal long memory in the aggregate output

Abstract The quarterly structure of the GDP series in Germany, Denmark and Italy is investigated in this article by means of new statistical techniques that allow simultaneously testing different orders of integration for each of the frequencies. The results indicate that the long run or zero frequency plays the most important role, especially for Denmark, while the biannual frequency π also appears important in the cases of Germany and Italy.

Fractional integration and mean reversion in stock prices

Abstract The Efficient Market Hypothesis (EMH) is frequently tested by measuring the degree of mean reversion in stock prices, since highly predictable changes might indicate that investors are not fully rational. Existing studies often rely on statistical tests which impose too restrictive assumptions on the time series behavior of the series of interest, and have very low power. This paper uses a test for unit roots and other nonstationary (and stationary) hypotheses—recently developed by Robinson (1994) —which allows for fractional alternatives and outperforms rival statistics. Its application to U.S. real stock returns suggests that there is no permanent component in stock prices, since the series examined is close to being I(0). The key question then becomes whether there exists an autocorrelated structure, which would imply that the series is perfectly predictable, and hence that the market might not be efficient.

A fractionally integrated model with a mean shift for the US and the UK real oil prices

In this article we model the log of the U.S. and the U.K. real oil prices in terms of fractionally integrated processes with a mean shift. We use different versions of the tests of Robinson (1994), which have standard null and local limit distributions. The results indicate that if we model the series without a mean shift, they are both nonstationary I(1). However, allowing for a mean shift during the oil crises, they become fractionally integrated with an order of integration smaller than one and thus, showing mean reverting behaviour.

A mean shift break in the US interest rate

Abstract We model in this article the monthly structure of the US interest rate in terms of a fractionally integrated process with a deterministic structural change. We show that the order of integration of the series is reduced when a mean shift is included in the regression model to describe the turbulence period at the beginning of the 1980s. In fact, the series appears to be I (0.61) in contrast to the I (0.79) process obtained when the mean shift is not considered. Thus, the series is still nonstationary but the mean reversion property of the process is accelerated when the break is taken into account.

Unemployment and input prices: A fractional cointegration approach

This paper examines the relationship between unemployment, real oil price and real interest rates in Canada. Instead of following the classical approach based on I(0) stationarity or I(1) cointegrating relationships, fractional integration/cointegration techniques are used which allow for the possibility that unemployment is highly persistent. In line with other studies, it is found that all three variables are I(1). But only cointegration is found in the presence of autocorrelated disturbances, which means that the relationship between these variables also has a dynamic component. Furthermore, there is evidence of fractional (as opposed to classical) cointegration, which implies long memory and slow reversion to equilibrium. This suggests that an equilibrium model with highly persistent shocks might be adequate to account for the observed behaviour of unemployment.

Semiparametric Estimation of the Fractional Differencing Parameter ofMeasures of the U.K. Unemployment

The order of integration of different measures of the U.K. unemployment is investigated in this paper by means of semiparametric techniques. Several methods, such as the R\S statistic, along with others proposed by Robinson in a number of papers are applied in this article. The methods perform poorly when using the time domain approaches, however, when using the frequency domain procedures, the results are fairly conclusive, with the order of integration of the series fluctuating around 1.50.

Confidence intervals for fractionally integrated hypotheses in the real output across Europe

Confidence intervals for the fractional differencing parameter are established in this article for the real output in several European countries. They are based on a testing procedure due to Robinson (Journal of the American Statistical Association, 89, 1420–37, 1994) and the results indicate that these confidence intervals are relatively wide, the unit root null hypothesis being rejected in practically all cases.