Ulrich K. Müller

We introduce a generalization of the popular local-to-unity model of time series persistence by allowing for p autoregressive roots and p-1 moving average roots close to unity. This generalized local-to-unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p-1) process on the unit interval. Our main theoretical result establishes the richness of this form of limiting processes, in the sense that they can well approximate a large class of stationary Gaussian processes in the total variation norm. We show that Campbell and Yogos's (2006) popular inference method for predictive regressions fails to controle size in the GLTU(2) model with empirically plausible parameter values, and we propose a limited information Bayesian framework for inference in the GLTU(p) model and apply it to quantify the uncertainty about the half-life of deviations from Purchasing Power Parity.

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the sum of the smaller summands. If the tail is well approximated by a Pareto density, then this new approximation has substantially smaller error rates compared to the usual normal approximation for underlying distributions with finite variance and less than three moments. It can also provide an accurate approximation for some infinite variance distributions.

We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is it assumed known that nearly all control coefficients are zero. We instead impose a bound on a weighted sum of squared control coefficients, which is interpretable as a bound on the sample variation in the dependent variable induced by the controls. We develop a simple testing procedure that exploits this additional information in general heteroskedastic models. We also show that under asymptotics where the number of controls is a non-negligible fraction of the number of observations, and the bound is not too large, our suggested test comes close to being weighted average power maximizing in the Gaussian homoskedastic model. We compare our procedure to a sparsity-based approach in a Monte Carlo study and by revisiting the empirical relationship between crime and abortion.  

We propose a Bayesian procedure for exploiting small, possibly long-lag linear predictability in the innovations of a finite order autoregression. We model the innovations as having a log-spectral density that is a continuous mean-zero Gaussian process of order 1/sqrt(T). This local embedding makes the problem asymptotically a normal-normal Bayes problem, resulting in closed-form solutions for the best forecast. When applied to data on 132 U.S. monthly macroeconomic time series, the method is found to improve upon autoregressive forecasts by an amount consistent with the theoretical and Monte Carlo calculations. 

     Nearly Weighted Risk Minimal Unbiased Estimation. Journal of Econometrics, 209 (2019), 18 – 34. (Joint with YULONG WANG.) Replication files.

     Long-Run Covariability. Econometrica 86 (2018), 775 – 804. Mark Watson’s Fisher-Schultz lecture 2016. (Joint with MARK WATSON.) Appendix and Replication files.

     Low-Frequency Econometrics. In Advances in Economics and Econometrics: Eleventh World Congress of the Econometric Society, Volume II, ed. by B. Honoré, and L. Samuelson, Cambridge University Press (2017), 53 – 94. (Joint with MARK WATSON.) Replication files.

     Fixed-k Asymptotic Inference about Tail Properties. Journal of the American Statistical Association, 112 (2017), 1334 – 1343. (Joint with YULONG WANG.) Replication files.

     Credibility of Confidence Sets in Nonstandard Econometric Problems. Econometrica 84 (2016), 2183 – 2213. (Joint with ANDRIY NORETS.) Supplementary Appendix.

     Measuring Uncertainty about Long-Run Predictions. Review of Economic Studies 83 (2016), 1711 – 1740. (Joint with MARK WATSON.) Supplementary Appendix. Replication files.

     Coverage Inducing Priors in Nonstandard Inference Problems. Journal of the American Statistical Association 111 (2016), 1233 – 1241. (Joint with ANDRIY NORETS.) Supplementary Appendix.

     Inference with Few Heterogenous Clusters. Review of Economics and Statistics 98 (2016), 83 – 96. (Joint with RUSTAM IBRAGIMOV.) Supplementary Appendix. Replication files.

     Nearly Optimal Tests when a Nuisance Parameter is Present Under the Null Hypothesis. Econometrica 83 (2015), 771 – 811. (Joint with GRAHAM ELLIOTT and MARK WATSON.)

      HAC Corrections for Strongly Autocorrelated Time Series. Journal of Business & Economic Statistics 32 (2014), 311 – 322. Comments and Rejoinder.

     Pre and Post Break Parameter Inference. Journal of Econometrics 180 (2014), 141 – 157. (Joint with GRAHAM ELLIOTT.) 2012 working paper version.

     Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix, Econometrica 81 (2013), 1805 – 1849.

     Low-Frequency Robust Cointegration Testing, Journal of Econometrics 174 (2013), 66 – 81. (Joint with MARK WATSON.)

      Measuring Prior Sensitivity and Prior Informativeness in Large Bayesian Models, Journal of Monetary Economics 59 (2012), 581 – 597.

     Efficient Tests under a Weak Convergence Assumption, Econometrica 79 (2011), 395 – 435. (Formerly circulated under the title "An Alternative Sense of Asymptotic Efficiency".)

     Efficient Estimation of the Parameter Path in Unstable Time Series Models, Review of Economic Studies 77 (2010), 1508 – 1539. Supplement. Correction. (Joint with PHILIPPE-EMMANUEL PETALAS.) 

     t-statistic Based Correlation and Heterogeneity Robust Inference, Journal of Business & Economic Statistics 28 (2010), 453 – 468. Supplement. (Joint with RUSTAM IBRAGIMOV.)

     Valid Inference in Partially Unstable GMM Models, Review of Economic Studies 76 (2009), 343 – 365. (Joint with HONG LI.) 

     Testing Models of Low-Frequency Variability, Econometrica 76 (2008), 979 – 1016. (Joint with MARK WATSON.) 

     The Impossibility of Consistent Discrimination between I(0) and I(1) Processes, Econometric Theory 24 (2008), 616 – 630.

     A Theory of Robust Long-Run Variance Estimation, Journal of Econometrics 141 (2007), 1331 – 1352. (Substantially different 2004 working paper).

     Confidence Sets for the Date of a Single Break in Linear Time Series Regressions, Journal of Econometrics 141 (2007), 1196 – 1218. (Joint with GRAHAM ELLIOTT.)

     Efficient Tests for General Persistent Time Variation in Regression Coefficients, Review of Economic Studies 73 (2006), 907 – 940. Formerly circulated under the title “Optimally Testing General Breaking Processes in Linear Time Series Models”. (Joint with GRAHAM ELLIOTT.)

     Are Forecasters Reluctant to Revise their Predictions? Some German Evidence, Journal of Forecasting 25 (2006), 401 – 413. (Joint with GEBHARD KIRCHGÄSSNER.)

     Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series, Journal of Econometrics 128 (2005), 195 – 213.

     Tests for Unit Roots and the Initial Condition, Econometrica 71 (2003), 1269 – 1286. (Joint with GRAHAM ELLIOTT.)

     Comment on “HAR Inference: Recommendations for Practice” by E. Lazarus, D. J. Lewis and J. H. Stock, Journal of Business & Economic Statistics 36 (2018), 563 – 564.

     Comment on “Unit Root Testing in Practice: Dealing with Uncertainty over the Trend and Initial Condition” by D. I. Harvey, S. J. Leybourne and A. M. R. Taylor, Econometric Theory 25 (2009), 643 – 648.