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on Econometric Time Series |
| By: | Florian Huber; Gary Koop; Massimiliano Marcellino; Tobias Scheckel |
| Abstract: | Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on the autoregressive coefficients. Introducing shrinkage on the error covariance matrix is sometimes done but, in the vast majority of cases, without considering the network structure of the shocks and by placing the prior on the lower Cholesky factor of the precision matrix. In this paper, we propose a prior on the VAR error precision matrix directly. Our prior, which resembles a standard spike and slab prior, models variable inclusion probabilities through a stochastic block model that clusters shocks into groups. Within groups, the probability of having relations across group members is higher (inducing less sparsity) whereas relations across groups imply a lower probability that members of each group are conditionally related. We show in simulations that our approach recovers the true network structure well. Using a US macroeconomic data set, we illustrate how our approach can be used to cluster shocks together and that this feature leads to improved density forecasts. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.16349 |
| By: | Susana Campos-Martins (NIPE/Center for Research in Economics and Management, University of Minho; and Católica Lisbon School of Business & Economics); Cristina Amado (NIPE/Center for Research in Economics and Management, University of Minho, Portugal) |
| Abstract: | In this paper we propose a multivariate generalisation of the multiplicative decomposition of the volatility within the class of conditional correlation GARCH models. The GARCH variance equations are multiplicatively decomposed into a deterministic nonstationary component describing the long-run movements in volatility and a short-run dynamic component allowing for volatility spillover effects across markets or assets. The conditional correlations are assumed to be time-invariant in its simplest form or generalised into a flexible dynamic parameterisation. Parameters of the model are estimated equation-by-equation by maximum likelihood applying the maximisation by parts algorithm to the variance equations, and thereafter to the structure of conditional correlations. An empirical application using carbon markets data illustrates the usefulness of the model. Our results suggest that, after modelling the variance equations accordingly, we find evidence that the transmission mechanism of shocks persists which is supported by the presence of variance interactions robust to nonstationarity. |
| Keywords: | Variance interactions; Nonstationarity; Short- and long-term volatility; Lagrange multiplier test. |
| JEL: | C12 C13 C32 C51 |
| Date: | 2023 |
| URL: | https://d.repec.org/n?u=RePEc:nip:nipewp:13/2023 |
| By: | Astill, Sam; Harvey, David I; Leybourne, Stephen J; Taylor, AM Robert |
| Abstract: | The Bonferroni Q test of Campbell and Yogo (2006) is widely used in empirical studies investigating predictability in asset returns by strongly persistent and endogenous predictors. Its formulation, however, only allows for a constant mean in the predictor, seemingly at odds with many of the predictors used in practice. We establish the asymptotic size and local power properties of the Q test, and the corresponding Bonferroni t-test of Cavanagh, Elliott and Stock (1995), as operationalised for the constant mean case by Campbell and Yogo (2006), under a local-to-zero specification for a linear trend in the predictor, revealing that size and power depends on the magnitude of the trend for both. To rectify this we develop with-trend variants of the operational Bonferroni Q and t tests. However, where a trend is not present in the predictor we show that these tests lose (both finite sample and asymptotic local) power relative to the extant constant-only versions of the tests. In practice uncertainty will necessarily exist over whether a linear trend is genuinely present in the predictor or not. To deal with this, we also develop hybrid tests based on unionof- rejections and switching mechanisms to capitalise on the relative power advantages of the constant-only tests when a trend is absent (or very weak) and the with-trend tests otherwise. A further extension allows use of a conventional t-test where the predictor appears to be weakly persistent. We show that, overall, our recommended hybrid test can offer excellent size and power properties regardless of whether or not a linear trend is present in the predictor, or the predictor’s degrees of persistence and endogeneity. An empirical application to an updated Welch and Goyal (2008) dataset illustrates the practical relevance of our new approach. |
| Keywords: | predictive regression; linear trend; unknown regressor persistence; Bonferroni tests; hybrid tests; union of rejections |
| Date: | 2024–08–12 |
| URL: | https://d.repec.org/n?u=RePEc:esy:uefcwp:38947 |
| By: | Gabriel Montes-Rojas; Zacharias Psaradakis; Martín Sola |
| Abstract: | We consider models for conditional quantiles in which parameters are subject to discrete changes governed by an exogenous, unobservable Markov chain. We argue that all quantiles of the conditional distribution of the response variable should share the Markov regimes. This gives an unambiguous classification of regimes and allows the capture of quantile-specific characteristics conditionally on the hidden regimes. The potential of our approach is illustrated using a quantile autoregression for U.S. inflation. |
| Keywords: | Markov Switching; Quantile Regressions. |
| JEL: | C32 C52 C58 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:udt:wpecon:2024_05 |
| By: | Malte Londschien; Peter B\"uhlmann |
| Abstract: | We propose a weak-instrument-robust subvector Lagrange multiplier test for instrumental variables regression. We show that it is asymptotically size-correct under a technical condition. This is the first weak-instrument-robust subvector test for instrumental variables regression to recover the degrees of freedom of the commonly used Wald test, which is not robust to weak instruments. Additionally, we provide a closed-form solution for subvector confidence sets obtained by inverting the subvector Anderson-Rubin test. We show that they are centered around a k-class estimator. Also, we show that the subvector confidence sets for single coefficients of the causal parameter are jointly bounded if and only if Anderson's likelihood-ratio test rejects the hypothesis that the first-stage regression parameter is of reduced rank, that is, that the causal parameter is not identified. Finally, we show that if a confidence set obtained by inverting the Anderson-Rubin test is bounded and nonempty, it is equal to a Wald-based confidence set with a data-dependent confidence level. We explicitly compute this Wald-based confidence test. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.15256 |