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on Econometric Time Series |
| By: | Canepa, Alessandra (University of Turin) |
| Abstract: | In this article, we employ a time-varying GARCH-type speci?cation to model in?ation and in- vestigate the behaviour of its persistence. Speci?cally, by modelling the in?ation series as AR(1)- APARCH(1,1)-in-mean-level process with breaks, we show that persistence is transmitted from the conditional variance to the conditional mean. Hence, by studying the conditional mean/variance independently, one will obtain a biased estimate of the true degree of persistence. Accordingly, we propose a new measure of time-varying persistence, which not only distinguishes between changes in the dynamics of in?ation and its volatility but also allows for feedback between the two variables. Analysing the in?ation series for a number of countries, we ?nd evidence that in?ation uncertainty plays an important role in shaping expectations, and a higher level of uncertainty increases in?ation persistence. We also consider a number of unit root tests and present the results of a Monte Carlo experiment to investigate the size and power properties of these tests in the presence of breaks in the mean and the variance equation of an AR(1)-APARCH(1,1)-in-mean-level data generating process. The Monte Carlo experiment reveals that if the model is misspeci?ed, then commonly used unit root tests will misclassify in?ation as a nonstationary, rather than a stationary process. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:uto:dipeco:202211&r= |
| By: | Fengler, Matthias; Polivka, Jeannine |
| Abstract: | In this paper, we make three contributions to the volatility impulse response function (VIRF) developed by Hafner and Herwartz (2006), the most widely applied impulse response function in the context of multivariate volatility models. First, we derive its law for multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models of the BEKK type. Second, we present a structural embedding of the VIRF by relying on recent developments concerning identification of MGARCH models. This broadens the use cases of the VIRF, which has previously been limited to historical analyses, by allowing for counterfactual and out-of-sample scenario analyses of volatility responses. Third, we show how to endow the VIRF with a causal interpretation. We illustrate the merits of a structural VIRF analysis by investigating the impacts of historical shock events as well as the consequences of well-defined future shock scenarios on the U.S. equity, government bond and foreign exchange markets. Our findings suggest that it is vital to be able to assess the statistical significance of volatility impulse responses. |
| Keywords: | causality in volatility, multivariate GARCH models, proxy identification, structural identification, volatility impulse response functions |
| JEL: | C32 C58 G17 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2022:11&r= |
| By: | Xu, Haotian (Université catholique de Louvain, LIDAM/ISBA, Belgium); Wang, Daren; Zhao, Zifeng; Yu, Yi |
| Abstract: | This paper concerns about the limiting distributions of change point estimators, in a high- dimensional linear regression time series context, where a regression object (yt, Xt) ∈ R × Rp is observed at every time point t ∈ {1, . . . , n}. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in l2-norm. We provide limiting distributions of the change point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change point localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package changepoints (Xu et al., 2021). |
| Keywords: | High-dimensional linear regression ; Change point inference ; Functional dependence ; Long-run variance ; Confidence interval |
| Date: | 2022–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2022027&r= |
| By: | Lukas Hoesch; Adam Lee; Geert Mesters |
| Abstract: | All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non-Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a robust semi-parametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non-Gaussianity when it is present, but yields correct size / coverage regardless of the distance to the Gaussian distribution. Empirically we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012) we find that non-Gaussianity can robustly identify reasonable confidence sets, whereas for the labour supply-demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to asses estimation uncertainty when using non-Gaussianity for identification. |
| Keywords: | weak identification, semi-parametric inference, hypothesis testing, impulse responses, independent component analysis |
| JEL: | C32 C39 C51 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1847&r= |
| By: | Ramis Khabibullin; Sergei Seleznev |
| Abstract: | This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at the first stage, and then a flexible model is trained to predict the variables of interest. In contrast to those proposed earlier, the procedure described in this paper makes it possible to train estimators for hidden states by concentrating only on certain characteristics of the marginal posterior distributions and introducing inductive bias. Illustrations using the examples of the stochastic volatility model, nonlinear dynamic stochastic general equilibrium model, and seasonal adjustment procedure with breaks in seasonality show that the algorithm has sufficient accuracy for practical use. Moreover, after pretraining, which takes several hours, finding the posterior distribution for any dataset takes from hundredths to tenths of a second. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.07154&r= |
| By: | Lambert, Philippe (Université catholique de Louvain, LIDAM/ISBA, Belgium); Gressani, Oswaldo (Université catholique de Louvain, LIDAM/ISBA, Belgium) |
| Abstract: | Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables and the Bernstein-von Mises theorem typically ensure a razor-sharp accuracy of the Laplace approximation to the posterior distribution of these variables. This accuracy can be seriously compromised for some unpenalized parameters, especially when the information synthesized by the prior and the likelihood is sparse. We propose a refined version of the LPS methodology by splitting the latent space in two subsets. The first set involves latent variables for which the joint posterior distribution is approached from a non-Gaussian perspective with an approximation scheme that is particularly well tailored to capture asymmetric patterns, while the posterior distribution for parameters in the complementary latent set undergoes a traditional treatment with Laplace approximations. As such, the dichotomization of the latent space provides the necessary structure for a separate treatment of model parameters, yielding improved estimation accuracy as compared to a setting where posterior quantities are uniformly handled with Laplace. In addition, the proposed enriched version of LPS remains entirely sampling-free, so that it operates at a computing speed that is far from reach to any existing Markov chain Monte Carlo approach. The methodology is illustrated on the additive proportional odds model with an application on ordinal survey data. |
| Keywords: | Additive model ; P-splines ; Laplace approximation ; Skewness |
| Date: | 2022–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2022030&r= |
| By: | H. Peter Boswijk; Roger J. A. Laeven; Evgenii Vladimirov |
| Abstract: | We develop a novel filtering and estimation procedure for parametric option pricing models driven by general affine jump-diffusions. Our procedure is based on the comparison between an option-implied, model-free representation of the conditional log-characteristic function and the model-implied conditional log-characteristic function, which is functionally affine in the model's state vector. We formally derive an associated linear state space representation and establish the asymptotic properties of the corresponding measurement errors. The state space representation allows us to use a suitably modified Kalman filtering technique to learn about the latent state vector and a quasi-maximum likelihood estimator of the model parameters, which brings important computational advantages. We analyze the finite-sample behavior of our procedure in Monte Carlo simulations. The applicability of our procedure is illustrated in two case studies that analyze S&P 500 option prices and the impact of exogenous state variables capturing Covid-19 reproduction and economic policy uncertainty. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.06217&r= |