# Martin Wagner

#### 3 packages on CRAN

We propose a consistent monitoring procedure to detect a structural change from a cointegrating relationship to a spurious relationship. The procedure is based on residuals from modified least squares estimation, using either Fully Modified, Dynamic or Integrated Modified OLS. It is inspired by Chu et al. (1996) <DOI:10.2307/2171955> in that it is based on parameter estimation on a pre-break "calibration" period only, rather than being based on sequential estimation over the full sample. See the discussion paper <DOI:10.2139/ssrn.2624657> for further information. This package provides the monitoring procedures for both the cointegration and the stationarity case (while the latter is just a special case of the former one) as well as printing and plotting methods for a clear presentation of the results.

Cointegration methods are widely used in empirical macroeconomics and empirical finance. It is well known that in a cointegrating regression the ordinary least squares (OLS) estimator of the parameters is super-consistent, i.e. converges at rate equal to the sample size T. When the regressors are endogenous, the limiting distribution of the OLS estimator is contaminated by so-called second order bias terms, see e.g. Phillips and Hansen (1990) <DOI:10.2307/2297545>. The presence of these bias terms renders inference difficult. Consequently, several modifications to OLS that lead to zero mean Gaussian mixture limiting distributions have been proposed, which in turn make standard asymptotic inference feasible. These methods include the fully modified OLS (FM-OLS) approach of Phillips and Hansen (1990) <DOI:10.2307/2297545>, the dynamic OLS (D-OLS) approach of Phillips and Loretan (1991) <DOI:10.2307/2298004>, Saikkonen (1991) <DOI:10.1017/S0266466600004217> and Stock and Watson (1993) <DOI:10.2307/2951763> and the new estimation approach called integrated modified OLS (IM-OLS) of Vogelsang and Wagner (2014) <DOI:10.1016/j.jeconom.2013.10.015>. The latter is based on an augmented partial sum (integration) transformation of the regression model. IM-OLS is similar in spirit to the FM- and D-OLS approaches, with the key difference that it does not require estimation of long run variance matrices and avoids the need to choose tuning parameters (kernels, bandwidths, lags). However, inference does require that a long run variance be scaled out. This package provides functions for the parameter estimation and inference with all three modified OLS approaches. That includes the automatic bandwidth selection approaches of Andrews (1991) <DOI:10.2307/2938229> and of Newey and West (1994) <DOI:10.2307/2297912> as well as the calculation of the long run variance.

Model-based linear model trees adjusting for spatial correlation using a simultaneous autoregressive spatial lag, Wagner and Zeileis (2019) <doi:10.1111/geer.12146>.