Tail approximation of the asymptotic distribution of the log likelihood ratio test for cointegration in a vector autoregressive process is studied. In dimension 2, an approximation of weighted χ2 type is derived by applying multivariate saddlepoint approximation techniques to a Fourier inversion integral.

This paper deals with the estimation of unequally spaced panel data regression models with AR(1) remainder disturbances. A feasible generalized least squares (GLS) procedure is proposed as a weighted least squares that can handle a wide range of unequally spaced panel data patterns. This procedure is simple to compute and provides natural estimates of the serial correlation and variance components parameters. The paper also provides a locally best invariant test for zero first-order serial correlation against positive or negative serial correlation in case of unequally spaced panel data.

In this paper, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH(p,q) process is given and also an expression for the moment itself. Furthermore, the autocorrelation function of the centered and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as the GARCH(2,2) process and the ARCH(q) process.

In time series regression models with “short-memory” residual processes, the Durbin–Watson statistic (DW) has been used for the problem of testing for independence of the residuals. In this paper we elucidate the asymptotics of DW for “long-memory” residual processes. A standardized Durbin–Watson statistic (SDW) is proposed. Then we derive the asymptotic distributions of SDW under both the null and local alternative hypotheses. Based on this result we evaluate the local power of SDW. Numerical studies for DW and SDW are given.

Professor James Tobin is a figure of truly historic significance in the economics profession. He is one of the major developers of modern macroeconomic theory. He has contributed fundamental knowledge to the theory of investment, of consumption, of money and banking, and of economic growth. His theoretical work made possible the development of the capital asset pricing model that has been a central paradigm in modern finance. His work on limited-dependent variable models has started a field within econometrics.