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on Econometric Time Series |
| By: | Abdelkamel Alj; Rajae Azrak; Guy Melard |
| Abstract: | The paper is concerned with vector autoregressive-moving average (VARMA) models with time-dependent coe_cients (td) to represent some non-stationary time series. The coe_cients depend on time but can also depend on the length of the series n, hence the name tdVARMA(n) for the models. As a consequence of dependency of the model on n, we need to consider array processes instead of stochastic processes. Generalizing results for univariate time series combined with new results for array models, under appropriate assumptions, it is shown that a Gaussian quasi-maximum likelihood estimator is consistent in probability and asymptotically normal. The theoretical results are illustrated using two examples of bivariate processes, both with marginal heteroscedasticity. The first example is a tdVAR(n)(1) process while the second example is a tdVMA(n)(1) process. It is shown that the assumptions underlying the theoretical results apply. In the two examples, the asymptotic information matrix is obtained, not only in the Gaussian case. Finally, the finite-sample behaviour is checked via a Monte Carlo simulationstudy. The results con_rm the validity of the asymptotic properties even for small n and reveal that the asymptotic information matrix deduced from thetheory is correct. |
| Keywords: | Non-stationary process; multivariate time series; timevarying models; array process. |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/348492&r= |
| By: | Nishi, Mikihito; 西, 幹仁; Kurozumi, Eiji; 黒住, 英司 |
| Keywords: | random coefficient model, local to unity, moderate deviation, LBI test, power envelope |
| JEL: | C12 C22 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2022-02&r= |
| By: | Danilo Cascaldi-Garcia |
| Abstract: | The onset of the COVID-19 pandemic and the great lockdown caused macroeconomic variables to display complex patterns that hardly follow any historical behavior. In the context of Bayesian VARs, an off-the-shelf exercise demonstrates how a very low number of extreme pandemic observations bias the estimated persistence of the variables, affecting forecasts and giving a myopic view of the economic effects after a structural shock. I propose an easy and straightforward solution to deal with these extreme episodes, as an extension of the Minnesota Prior with dummy observations by allowing for time dummies. The Pandemic Priors succeed in recovering these historical relationships and the proper identification and propagation of structural shocks. |
| Keywords: | Bayesian VAR; Minnesota Prior; COVID-19; Structural shocks |
| JEL: | C32 E32 E44 |
| Date: | 2022–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgif:1352&r= |
| By: | Patrice Abry (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS Lyon - École normale supérieure - Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Yannick Malevergne (PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne); Herwig Wendt (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS Lyon - École normale supérieure - Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - CNRS - Centre National de la Recherche Scientifique); Stéphane Jaffard (LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - Fédération de Recherche Bézout - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique); Marc Senneret; Laurent Jaffrès |
| Abstract: | After Mandelbrot's seminal work, scale-free and multifractal temporal dynamics have been recognized as classical stylized facts for financial time series and massively documented. Multifractal analysis in finance has however mainly remained univariate (one time series at a time) when multivariate (or basket) properties are critical for financial applications. This is mostly due to a lack of theoretical foundations and practical tools for multivariate multifractal analysis. Expanding on a theoretically-grounded recently proposed multivariate multifractal formalism, the present work performs an original multivariate analysis for a basket of six Foreign Exchange rate time series. Beyond confirming multifractality for each component independently, the definition of cross-multifractalities amongst components is introduced, assessing cross-dependencies in temporal dynamics not already accounted for by cross-correlations. The key practical outcome is to show that, essentially, one same multifractal time governs jointly the temporal dynamics of all the Foreign Exchange time series studied here. |
| Keywords: | Financial times series,Foreign exchange,basket properties,multivariate multifractal analysis,wavelet leaders |
| Date: | 2022–08–29 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03735497&r= |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Ekaterina Seregina (Colby College) |
| Abstract: | In this paper we develop a novel method of combining many forecasts based on a machine learning algorithm called Graphical LASSO. We visualize forecast errors from different forecasters as a network of interacting entities and generalize network inference in the presence of common factor structure and structural breaks. First, we note that forecasters often use common information and hence make common mistakes, which makes the forecast errors exhibit common factor structures. We propose the Factor Graphical LASSO (Factor GLASSO), which separates common forecast errors from the idiosyncratic errors and exploits sparsity of the precision matrix of the latter. Second, since the network of experts changes over time as a response to unstable environments such as recessions, it is unreasonable to assume constant forecast combination weights. Hence, we propose Regime-Dependent Factor Graphical LASSO (RD-Factor GLASSO) and develop its scalable implementation using the Alternating Direction Method of Multipliers (ADMM) to estimate regime-dependent forecast combination weights. The empirical application to forecasting macroeconomic series using the data of the European Central Bank’s Survey of Professional Forecasters (ECB SPF) demonstrates superior performance of a combined forecast using Factor GLASSO and RD-Factor GLASSO. |
| Keywords: | Common Forecast Errors, Regime Dependent Forecast Combination, Sparse Precision Matrix of Idiosyncratic Errors, Structural Breaks. |
| JEL: | C13 C38 C55 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:202213&r= |
| By: | Christian K. Wolf; Alisdair McKay |
| Abstract: | We show that, in a general family of linearized structural macroeconomic models, knowledge of the empirically estimable causal effects of contemporaneous and news shocks to the prevailing policy rule is sufficient to construct counterfactuals under alternative policy rules. If the researcher is willing to postulate a loss function, our results furthermore allow her to recover an optimal policy rule for that loss. Under our assumptions, the derived counterfactuals and optimal policies are robust to the Lucas critique. We then discuss strategies for applying these insights when only a limited amount of empirical causal evidence on policy shock transmission is available. |
| JEL: | E32 E61 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30358&r= |