Summary This paper develops panel data tests for the null hypothesis of no error correction in a model with common stochastic trends. The asymptotic distributions of the new test statistics are derived and simulation results are provided to suggest that they perform well in small samples. Copyright © 2015 John Wiley & Sons, Ltd.

Panel unit-root and no-cointegration tests that rely on cross-sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, -91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unitroot tests using a common factor structure to model the cross-sectional dependence, but not much work has been done yet for panel nocointegration tests. This paper proposes a model for panel no-cointegration using an unobserved common factor structure, following the study by Bai panel unit roots. We distinguish two important cases: (i) the case when the non-stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing *Previous versions of this paper were presented at ]. Under the data-generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than ffiffiffiffi N p T as for independent panels. We then examine the possibilities of testing for various forms of no-cointegration by extracting the common factors and individual components from the observed data directly and then testing for no-cointegration using residual-based panel tests applied to the defactored data.

In this paper we derive permanent‐transitory decompositions of non‐stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose.

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions. JEL classifications: C14, C22.bootstrap samples with a smaller value for . Additionally, it provides a convenient framework for studying the theoretical properties of our method. Specifically, we need → ∞ as n → ∞, such that γ → 1. This is analogous to the block (and dependent wild) bootstrap, where the block size must increase to capture more dependence when the sample size increases. Assumption 7 postulates the formal conditions that needs to satisfy, which imply that γ → 1, but not too fast.Assumption 7. The bootstrap parameter = (n) satisfies → ∞ and / √ nh → 0 as n → ∞.Note that we propose to use a different bandwidthh in Step 1 of the algorithm. This is a common feature in the literature on bootstrap method for nonparametric regression, where by either selecting a larger (oversmoothing) or smaller bandwidth (undersmoothing) than used for the estimator, one can account for the asymptotic bias that is present in the local polynomial estimation, see Hall and Horowitz (2013, Section 1.4) for an extensive literature review. While undersmoothing, such as used in the related paper by Neumann and Polzehl (1998), aims at making the bias asymptotically negligible, oversmoothing aims at producing a consistent estimator of the (non-negligible) bias.Both have advantages and disadvantages, see the extensive discussion in Hall and Horowitz (2013).We follow Bühlmann (1998), also see Härdle and Marron (1991), and consider a solution based on oversmoothing, which we find to work well in practice. After presenting our theoretical results in Section 4, Remark 8 provides an intuition of why oversmoothing allows to consistently estimate the asymptotic bias. 1 We now state the formal conditions thath must satisfy in Assumption 8; one is that h/h → 0 as n → ∞, which ensures the oversmoothing. Assumption 8. The oversmoothing bandwidthh =h(n) satisfies max h , h/h, nh 5h4 → 0 and max h 4 , 1/nh → 0 as n → ∞. Remark 4. There are a number of ways to choose the AWB parameter γ in practice. Using the relation γ = θ 1/ , one can fix θ and choose as a deterministic function of the sample size. Smeekes and Urbain (2014) found in their simulation study that θ = 0.01 paired with = 1.75n ...