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We develop an LM test for Granger causality in high-dimensional (HD) vector autoregressive (VAR) models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity. We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in HD compared to standard low-dimensional VARs.

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.

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Reproduction permitted only if source is stated.ISBN 978-3-95729-217-9 (Printversion) Non-technical summary Research QuestionWhen dealing with time series sampled at various frequencies it has become common practice to directly incorporate high-frequency information into the econom(etr)ic model at hand. These specifications were first restricted to the single regression case; with the development of the (stacked) mixed-frequency vector autoregressive (MF-VAR) system (Ghysels, 2015) it is now possible to treat all series similarly and investigate causal effects between them. However, if the difference in frequencies between the series involved is large (as, e.g., in a month/working day scenario), estimation accuracy of the system coefficients is exacerbated, implying the detection of causal effects to be potentially inaccurate. To overcome this issue various parameter reduction techniques are introduced and analyzed. These methods are then evaluated in terms of their ability to detect causality patterns between the series under consideration in the resulting restricted model. ContributionTwo parameter reduction techniques are discussed in detail: three reduced rank regression (RRR) model variants and a Bayesian MF-VAR. Using a Monte Carlo experiment both approaches are compared in terms of their Granger causality testing behavior with an unrestricted VAR, a (time-aggregated) low-frequency VAR and the max-test (Ghysels, Motegi, and Hill, 2015a). To further enhance their finite sample properties we develop and evaluate (whenever possible) two bootstrap variants of these tests. Finally, the methods are applied to U.S. data by investigating channels of causality between the monthly growth rate of the industrial production index (IPI) and daily bipower variation (BV) of the S&P500 index. ResultsWe find that, depending on the direction of causality under consideration, a different set of tests results in the best Granger non-causality testing behavior. For the direction from the high-to the low-frequency series, standard testing within the Bayesian MF-VAR, the max-test and the restricted bootstrap version of the Wald test in two RRR model versions performs best. For the reverse direction, the unrestricted bootstrap variants of the Bonferroni-corrected Wald tests within the unrestricted VAR and the RRR models dominate. As far as our application is concerned, Granger causality from BV to IPIgrowth is clearly supported by the data; evidence for causality in the reverse direction, however, only comes from a subset of tests. Maastricht UniversityAbstract We analyze Granger causality testing in a mixed-frequency VAR, where the difference in sampling frequencies of the variables is large. Given a realistic sample size, the number of high-frequency observations per low-frequency period leads to parameter proliferation problems in case we attempt to estimate the model unrestrictedly. We propose several tests based on reduced rank restrictions, and implement bootstrap versions to account for the uncertainty when estimating fac...

This paper investigates one-step ahead density forecasts of mixed causalnoncausal models. We compare the sample-based and the simulations-based approaches respectively developed by Gouriéroux and Jasiak (2016) and Lanne, Luoto, and Saikkonen (2012). We focus on explosive episodes and therefore on predicting turning points of bubbles bursts. We suggest the use of both methods to construct investment strategies based on how much probabilities are induced by the assumed model and by past behaviours. We illustrate our analysis on Nickel prices series.

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.