Testing fractional integration in macroeconomic time series
This thesis concentrates on testing fractional (and seasonally fractional) integration and cointegration in macroeconomic time series. Fractional integration has recently emerged in the literature as an alternative plausible way of modelling economic series, and here we focus mainly on some empirical applications of a testing procedure suggested by Robinson (1994c) for testing unit roots and other nonstationary hypotheses in raw time series. These tests, described in Chapter 2, are asymptotically most powerful against fractional alternatives, have asymptotic critical values given by a chi-squared distribution, and allow great flexibility in the choice of null and alternative hypotheses, which can entail one or more integer or fractional roots of arbitrary order anywhere on the unit circle in the complex plane. In Chapter 2 we also make some simulations, comparing the size-corrected versions of the tests with those based on asymptotic critical values, and other existing unit root tests. The tests of Robinson (1994c) are applied in Chapter 3 to an extended version of the data set used by Nelson and Plosser (1982). These are fourteen U.S. macroeconomic variables in annual data, and we focus here on cases where the root is located at zero frequency. In Chapter 4 we concentrate on seasonality. Robinson's (1994c) tests are now applied to quarterly U.K. and Japanese consumption and income series, using the same data as in Hylleberg, Engle, Granger and Yoo (HEGY, 1990) and Hylleberg, Engle, Granger and Lee (HEGY, 1993). We test for the presence of unit or fractional roots, not only at zero but also at seasonal frequencies. A multivariate version of the tests, based on the score, likelihood-ratio and Wald principles is obtained in Chapter 5 and some simulations, based on Monte Carlo experiments, are carried out at the end of the chapter. The multivariate tests of Chapter 5 are applied in Chapter 6 to some pairs of macroeconomic variables claimed to be cointegrated by many authors. Using the same data as in Engle and Granger (1987) and Campbell and Shiller (1987), we analyze the relationship between U.S. consumption and income, prices and wages, GNP and money and stock prices and dividends. A testing procedure to investigate if these pairs of variables are fractionally cointegrated is also described and applied in Chapter 6.