This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T ), and the cross section dimension (N) are relatively large. It distinguishes between the first generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might...

This paper develops the large sample theory for econometric models with time series having roots in proximity of unity. In particular, a special attention is given to the time series with roots outside the n−1-neighborhood of unity, called the weak unit roots. They are the processes with roots approaching to unity as sample size increases, but not too fastly. It is shown that the weak unit root...

This paper considers a class of parametric models with nonparametric autoregressive errors. A new test is proposed and studied to deal with the parametric specification of the nonparametric autoregressive errors with either stationarity or nonstationarity. Such a test procedure can initially avoid misspecification through the need to parametrically specify the form of the errors. In other words...

The maintenance of plane trees (Platanus acerfolia Wild) by regular curtain-like pruning during the vegetative period induced modifications in the distribution and seasonal patterns of carbohydrate reserves in the perennial parts. The unpruned trees were characterized by high and fairly constant concentrations of starch in roots > 5 cm in diameter and a decreasing gradient of starch from the ba...

This paper considers a class of parametric models with nonparametric autoregressive errors. A new test is proposed and studied to deal with the parametric specification of the nonparametric autoregressive errors with either stationarity or nonstationarity. Such a test procedure can initially avoid misspecification through the need to parametrically specify the form of the errors. In other words...

F tests which test jointly for a unit root and a zero intercept, and so compete against Dickey−Fuller t tests, are shown not to enhance power because they are invariant to the intercept value in the absence of a unit root. Monte Carlo results in the literature that indicate otherwise are shown to have resulted from the use of special starting values. Testing procedures that employ these F tests...

Contents Abstract 1. Introduction 2. Models and preliminary asymptotic theory 2.1. Basic concepts and notation 2.2. The functional central limit theorem and related tools 2.3. Examples and preliminary results 2.4. Generalizations and additional references

This chapter investigates the robustness of impulse response estimators to near unit roots and near cointegration in VAR models. We compare estimators based on VAR specifications determined by pre-tests for unit roots and cointegration as well as unrestricted VAR specifications in levels. Our main finding is that the impulse response estimators obtained from the levels specification tend to be ...

Some statistical tests of randomness are made of the first 88062 binary digits (or equivalent in other bases) of Jn in various bases b, 2 g n g 15 (n square-free) with b = 2,4, 8, 16 and n = 2, 3, 5 with b = 3,5, 6, 7, and 10. The statistical tests are the y2 test for cumulative frequency distribution of the digits, the lead test, and the gap test. The lead test is an examination of the distanc...

A length k Newman polynomial is any polynomial of the form za1 + · · ·+zak (where a1 < · · · < ak). Some Newman polynomials are reducible over the rationals, and some are not. Some Newman polynomials have roots on the unit circle, and some do not. Defining, in a natural way, what we mean by the “proportion” of length k Newman polynomials with a given property, we prove that • 1/4 of length 3 Ne...