In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that...

Fractional cointegration imposes restrictions on the zero-frequency behavior of a time series. In a multivariate time series, integrated of order d epsilon (1/2, 3/2) and cointegrating to order d - b epsilon (-1/2, 1/2), we derive these restrictions in terms of the (reduced) rank of the spectral...

Cointegration imposes restrictions on the frequency domain behavior of a time series at the zero-frequency. We derive these restrictions for a multivariate fractionally cointegrated system. In particular, we consider a p-vector time series integrated of order d with r cointegrating relations,...

We study measures of foreign exchange rate volatility based on high-frequency (5-minute) $/DM exchange rate returns using recent nonparametric statistical techniques to compute realized return volatility and its separate continuous sample path and jump components, and measures based on prices of...

Seemingly absent from the arsenal of currently available "nearly efficient" testing procedures for the unit root hypothesis, i.e. tests whose local asymptotic power functions are indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We...