A Bootstrap Stationarity Test for Predictive Regression Invalidity

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid, and potentially also spurious, as both the finite sample and asymptotic size of the predictability tests can be significantly in ated. In response we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroskedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test by proving that the limit distribution of the bootstrap statistic, conditional on the data, is the same as the limit null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors and test statistics akin to ours the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have applications beyond the present context. An illustration is given by re-examining the results relating to U.S. stock returns data in Campbell and Yogo (2006)

Clustering and forecasting of dissolved oxygen concentration on a river basin

The aim of this contribution is to combine statistical methodologies to geographically classify homogeneous groups of water quality monitoring sites based on similarities in the temporal dynamics of the dissolved oxygen (DO) concentration, in order to obtain accurate forecasts of this quality variable. Our methodology intends to classify the water quality monitoring sites into spatial homogeneous groups, based on the DO concentration, which has been selected and considered relevant to characterize the water quality. We apply clustering techniques based on Kullback Information, measures that are obtained in the state space modelling process. For each homogeneous group of water quality monitoring sites we model the DO concentration using linear and state space models, which incorporate tendency and seasonality components in different ways. Both approaches are compared by the mean squared error (MSE) of forecasts

Panel stationary tests against changes in persistence

In this paper we propose new panel tests to detect changes in persistence. The test statistics are used to test the null hypothesis of stationarity against the alternative of a change in persistence from I(0) to I(1), from I(1) to I(0), and in an unknown direction. The limiting null distributions of the tests are derived and evaluated in small samples by means of Monte Carlo simulations. An empirical illustration is also provided.Wallenberg Academy Fellowship; The Jan Wallander and Tom Hedelius Foundatio