An MLE of the unknown parameters of co integrating vectors is presented for systems in which some variables exhibit higher orders of integration, in which there might be deterministic components, and in which the co integrating vector itself might involve variables of differing orders of...

In this paper we provide evidence on the presence of seasonal unit roots in aggregate U.S. data. The analysis is conducted using the approach developed by Hyllebcrg, Engle, Granger and Yoo (1990). We first derive the mechanics and asyrnptotics of the HEGY procedure for monthly data and use Monte...

It is well known that the distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice the order of integration is rarely blown. This paper examines two conventional approaches to this...

Recent empirical work in several economic fields, particularly environmental and energy economics, has adapted the regression discontinuity (RD) framework to applications where time is the running variable and treatment begins at a particular threshold in time. In this guide for practitioners,...

A number of recent studies have attempted to test propositions concerning "long runt" economic relationships by means of frequency-domain time series techniques that concentrate attention on low frequency co-movements of variables.The present paper emphasizes that many of these propositions...

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper discusses efficient low-frequency inference about cointegrating vectors that is robust...

Many questions in economics involve long-run or trend variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of...

High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuous-time model. In particular, we measure the additional effects of the...

We develop inference methods about long-run comovement of two time series. The parameters of interest are defined in terms of population second-moments of lowfrequency trends computed from the data. These trends are similar to low-pass filtered data and are designed to extract variability...