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We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities. Next, we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more elusive to model than stationary processes in the sense that the proximity bounds are larger. By contrast, the bounds are of smaller order for models that are unidentified or nearly unidentified, so that lack or near lack of identification may not be as fatal to the use of a model in practice as some recent results on inference suggest. Finally, we look at one possible future of econometrics that involves the use of advanced econometric methods interactively by way of a web browser. With these methods users may access a suite of econometric methods and data sets online. They may also upload data to remote servers and by simple web browser selections initiate the implementation of advanced econometric software algorithms, returning the results online and by file and graphics downloads.

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This paper details the differential and numeric properties of two measures of entropy, Shannon entropy and Kullback-Leibler distance, applicable for the unit root hypothesis. It is found that they are differentiable functions of the degree of trending in any included deterministic component and of the correlation of the underlying innovations. Moreover, Shannon entropy is concave in these, and thus maximisable. Kullback-Leibler is instead convex, and thus minimizable. It is explicitly confirmed, therefore, that it is approximately linear trends and negative unit root moving average innovations which minimize the efficacy of unit root inferential tools. Moreover, applied to the Nelson and Plosser macroeconomic series the effect that the inclusion, Despite tremendous progress in understanding the properties of unit root time series and tests thereof, analytic results in closed form are extremely rare. Exceptions are the distributional results of Abadir (1993), Phillips and Ploberger (1994) and more recently, Phillips and Magdalinos (2007). To see why detailing analytic properties

miracle of the Septuagint and the promise of data mining in economics

Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity —in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence.

This paper overviews recent developments in series estimation of stochastic processes and some of their applications in econometrics. Underlying this approach is the idea that a stochastic process may under certain conditions be represented in terms of a set of orthonormal basis functions, giving a series representation that involves deterministic functions. Several applications of this series approximation method are discussed. The …rst shows how a continuous function can be approximated by a linear combination of Brownian motions (BMs), which is useful in the study of the spurious regressions. The second application utilizes the series representation of BM to investigate the e¤ect of the presence of deterministic trends in a regression on traditional unit-root tests. The third uses basis functions in the series approximation as instrumental variables (IVs) to perform e ¢ cient estimation of the parameters in cointegrated systems. The fourth application proposes alternative estimators of long-run variances in some econometric models with dependent data, thereby providing autocorrelation robust inference methods in these models.