A unified framework to derive the distribution of conventional statistics under a unit root is presented. It is based on formulae which can generate (analytically as well as numerically) the densities and distributions of statistics such as the t ratio, the normalized autocorrelation...

We present a method of estimating density-related functionals, without prior knowledge of the density's functional form. The approach revolves around the specification of an explicit formula for a new class of distributions which encompasses many of the known cases in statistics, including the...

We provide a methodology to disentangle the long-run relation between variables from their own dynamics. Macroeconomic and aggregate financial series have a high degree of inertia. If this persistence is not properly accounted for, spurious correlations will give rise to paradoxes. Our procedure...

Two variables are said to be cointegrated when they move closely together over time, after proper scaling. Cointegration was taken to be the statistical expression of the notion of equilibrium in economics. But is it still possible to talk of cointegration when 'disequilibrium' economics...

It is shown that the bias of estimated parameters in autoregressive models can increase as the sample size grows. This bias is also a nonmonotonic function of the largest autoregressive root, contrary to what asymptotic approximations had indicated so far in the literature. These unusual results...

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is...