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This paper proposes concepts and methods to investigate whether the bubble patterns observed in individual time series are common among them. Having established the conditions under which common bubbles are present within the class of mixed causal–noncausal vector autoregressive models, we suggest statistical tools to detect the common locally explosive dynamics in a Student t-distribution maximum likelihood framework. The performances of both likelihood ratio tests and information criteria were investigated in a Monte Carlo study. Finally, we evaluated the practical value of our approach via an empirical application on three commodity prices. [ABSTRACT FROM AUTHOR]

We propose a model selection criterion to detect purely causal from purely noncausal models in the framework of quantile autoregressions (QAR). We also present asymptotics for the i.i.d. case with regularly varying distributed innovations in QAR. This new modelling perspective is appealing for investigating the presence of bubbles in economic and financial time series, and is an alternative to approximate maximum likelihood methods. We illustrate our analysis using hyperinflation episodes of Latin American countries. [ABSTRACT FROM AUTHOR]

Summary: Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non‐Gaussian densities. For a Student t likelihood, closed‐form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices. [ABSTRACT FROM AUTHOR]

We analyze Granger causality (GC) testing in mixed‐frequency vector autoregressions (MF‐VARs) with possibly integrated or cointegrated time series. It is well known that conducting inference on a set of parameters is dependent on knowing the correct (co)integration order of the processes involved. Corresponding tests are, however, known to often suffer from size distortions and/or a loss of power. Our approach works for MF variables that are stationary, integrated of an arbitrary order, or cointegrated. As it only requires the estimation of a MF‐VAR in levels with appropriately adjusted lag length, after which GC tests can be conducted using simple standard Wald tests, it is of great practical appeal. In addition, we show that the presence of non‐stationary and trivially cointegrated high‐frequency regressors leads to standard distributions when testing for causality on a subset of parameters, sometimes even without any need to augment the VAR order. Monte Carlo simulations and two applications involving the oil price and consumer prices as well as GDP and industrial production in Germany illustrate our approach. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of common non‐causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co‐movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non‐causal (i.e. forward‐looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non‐causal VAR processes of order P>1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward‐ or forward‐looking dynamics of the series. The proposed definitions of co‐movements are also valid for the mixed causal—non‐causal VAR, with the exception that a non‐Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co‐movements are found in a conventional causal VAR, but they are detected when considering a purely non‐causal VAR. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper proposes a mixed-frequency error correction model for possibly cointegrated non-stationary time series sampled at different frequencies. We highlight the impact, in terms of model specification, of the choice of the particular high-frequency explanatory variable to be included in the cointegrating relationship, which we call a dynamic mixed-frequency cointegrating relationship. The forecasting performance of aggregated models and several mixed-frequency regressions are compared in a set of Monte Carlo experiments. In particular, we look at both the unrestricted mixed-frequency model and at a more parsimonious MIDAS regression. Whereas the existing literature has only investigated the potential improvements of the MIDAS framework for stationary time series, our study emphasizes the need to include the relevant cointegrating vectors in the non-stationary case. Furthermore, it is illustrated that the choice of dynamic mixed-frequency cointegrating relationship does not matter as long as the short-run dynamics are adapted accordingly. Finally, the unrestricted model is shown to suffer from parameter proliferation for samples of relatively small size, whereas MIDAS forecasts are robust to over-parameterization. We illustrate our results for the US inflation rate. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the concept of separability in multiple nonstationary time series displaying both common stochastic trends and common stochastic cycles. When modeling the dynamics of multiple time series for a panel of several entities such as countries, sectors, firms, imposing some form of separability and commonalities is often required to restrict the dimension of the parameter space. For this purpose we introduce the concept of common feature separation and investigate the relationships between separation in cointegration and separation in serial correlation common features. Loosely speaking we investigate whether a set of time series can be partitioned into subsets such that there are serial correlation common features within the sub-groups only. The paper investigates three issues. First, it provides conditions for separating joint cointegrating vectors into marginal cointegrating vectors as well as separating joint short-term dynamics into marginal short-term dynamics. Second, conditions for making permanenttransitory decompositions based on marginal systems are given. Third, issues of weak exogeneity are considered. Likelihood ratio type tests for the different hypotheses under study are proposed. An empirical analysis of the link between economic fluctuations in the United States and Canada shows the practical relevance of the approach proposed in this paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to derive permanent-transitory decompositions of nonstationary multiple times series generated by a finite order Gaussian VAR(p) model with both cointegration and serial correlation common features. For cointegrated processes, several permanent-transitory decompositions have been extensively used in empirical and theoretical analyses. These include the multivariate extension of the Beveridge-Nelson decomposition proposed by researcher J.H. Stock and M.W. Watson, the observable permanent-transitory decomposition of researcher J. Gonzalo and C.W.J. Granger where the components are identified as being combinations of the observable series. It proposes a permanent-transitory decomposition which satisfies three criteria. Firstly, the decomposition studied in the paper is expressed in terms of observable variables and only involves quantities already available from the vector error correction model and the estimation of common features and cointegrating vectors. Secondly, the decomposition takes into account cointegrating and common cyclical feature restrictions. Thirdly, this decomposition should not only be a permanent-transitory decomposition but also a common trend-common cycle decomposition.