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on Econometric Time Series |
| By: | Frédérique Bec (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique); Heino Bohn Nielsen (Department of Economics - University of Copenhagen - KU - University of Copenhagen = Københavns Universitet); Sarra Saïdi (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | This paper stresses the bimodality of the widely used Student's t likelihood function applied in modelling Mixed causal-noncausal AutoRegressions (MAR). It first shows that a local maximum is very often to be found in addition to the global Maximum Likelihood Estimator (MLE), and that standard estimation algorithms could end up in this local maximum. It then shows that the issue becomes more salient as the causal root of the process approaches unity from below. The consequences are important as the local maximum estimated roots are typically interchanged , attributing the noncausal one to the causal component and vice-versa, which severely changes the interpretation of the results. The properties of unit root tests based on this Student's t MLE of the backward root are obviously affected as well. To circumvent this issues, this paper proposes an estimation strategy which i) increases noticeably the probability to end up in the global MLE and ii) retains the maximum relevant for the unit root test against a MAR stationary alternative. An application to Brent crude oil price illustrates the relevance of the proposed approach. Keywords: Mixed autoregression, non-causal autoregression, maximum likelihood estimation, unit root test, Brent crude oil price. |
| Date: | 2019–07–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02175760&r=all |
| By: | Yao, Qiwei; Zhang, Rongmao; Robinson, Peter |
| Abstract: | We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain non-negative definite matrix. Our setting is model-free, and we allow the integer-valued integration orders of the observable series to be unknown, and to possibly differ. Consistency of estimates of the cointegration space and cointegration rank is established both when the dimension of the observable time series is fixed as sample size increases, and when it diverges slowly. The proposed methodology is also extended and justified in a fractional setting. A Monte Carlo study of finite-sample performance, and a small empirical illustration, are reported. |
| Keywords: | cointegration; eigenanalysis; i(d); nonstationary processes; cector time series; ES/J007242/1; EP/L01226X/1 |
| JEL: | C1 |
| Date: | 2018–07–11 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:87431&r=all |
| By: | Bucci, Andrea |
| Abstract: | Accurately forecasting multivariate volatility plays a crucial role for the financial industry. The Cholesky-Artificial Neural Networks specification here presented provides a twofold advantage for this topic. On the one hand, the use of the Cholesky decomposition ensures positive definite forecasts. On the other hand, the implementation of artificial neural networks allows to specify nonlinear relations without any particular distributional assumption. Out-of-sample comparisons reveal that Artificial neural networks are not able to strongly outperform the competing models. However, long-memory detecting networks, like Nonlinear Autoregressive model process with eXogenous input and long shortterm memory, show improved forecast accuracy respect to existing econometric models. |
| Keywords: | Neural Networks; Machine Learning; Stock market volatility; Realized Volatility |
| JEL: | C22 C45 C53 G17 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95137&r=all |
| By: | Angela Bitto-Nemling; Annalisa Cadonna; Sylvia Fr\"uhwirth-Schnatter; Peter Knaus |
| Abstract: | Time-varying parameter (TVP) models are widely used in time series analysis to flexibly deal with processes which gradually change over time. However, the risk of overfitting in TVP models is well known. This issue can be dealt with using appropriate global-local shrinkage priors, which pull time-varying parameters towards static ones. In this paper, we introduce the R package shrinkTVP (Knaus, Bitto-Nemling, Cadonna, and Fr\"uhwirth-Schnatter 2019), which provides a fully Bayesian implementation of shrinkage priors for TVP models, taking advantage of recent developments in the literature, in particular that of Bitto and Fr\"uhwirth-Schnatter (2019). The package shrinkTVP allows for posterior simulation of the parameters through an efficient Markov Chain Monte Carlo (MCMC) scheme. Moreover, summary and visualization methods, as well as the possibility of assessing predictive performance through log predictive density scores (LPDSs), are provided. The computationally intensive tasks have been implemented in C++ and interfaced with R. The paper includes a brief overview of the models and shrinkage priors implemented in the package. Furthermore, core functionalities are illustrated, both with simulated and real data. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.07065&r=all |
| By: | Marcel Bräutigam (LabEx MME-DII - UCP - Université de Cergy Pontoise - Université Paris-Seine, ESSEC Business School - Essec Business School, LPSM UMR 8001 - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique); Marie Kratz (SID - Information Systems, Decision Sciences and Statistics Department - Essec Business School, LabEx MME-DII - UCP - Université de Cergy Pontoise - Université Paris-Seine) |
| Abstract: | In this note, we build upon the asymptotic theory for GARCH processes, considering the general class of augmented GARCH(p, q) processes. Our contribution is to complement the well-known univariate asymptotics by providing a bivariate functional central limit theorem between the sample quantile and the r-th absolute centred sample moment. This extends existing results in the case of identically and independently distributed random variables. We show that the conditions for the convergence of the estimators in the univariate case suffice even for the joint bivariate asymptotics. We illustrate the general results with various specific examples from the class of augmented GARCH(p, q) processes and show explicitly under which conditions on the moments and parameters of the process the joint asymptotics hold. |
| Keywords: | asymptotic distribution,(sample) variance,functional central limit theorem,(augmented) GARCH,correlation,(sample) quantile,measure of dispersion,(sample) mean absolute deviation |
| Date: | 2019–06–29 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02176276&r=all |
| By: | Escribano, Álvaro; Blazsek, Szabolcs; Ayala, Astrid |
| Abstract: | Dynamic conditional score (DCS) models with time-varying shape parameters provide a exible method for volatility measurement. The new models are estimated by using the maximum likelihood (ML) method, conditions of consistency and asymptotic normality of ML are presented, and Monte Carlo simulation experiments are used to study the precision of ML. Daily data from the Standard & Poor's 500 (S&P 500) for the period of 1950 to 2017 are used. The performances of DCS models with constant and dynamic shape parameters are compared. In-sample statistical performance metrics and out-of-sample value-at-risk backtesting support the use of DCS models with dynamic shape. |
| Keywords: | Outliers; Value-At-Risk; Score-Driven Shape Parameters; Dynamic Conditional Score Models |
| JEL: | C58 C52 C22 |
| Date: | 2019–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:28638&r=all |
| By: | Joshua C. C. Chan |
| Abstract: | Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at the expense of modelling exibility, as it rules out cross-variable shrinkage – i.e. shrinking coefficients on lags of other variables more aggressively than those on own lags. We develop a prior that has the best of both worlds: it can accommodate cross-variable shrinkage, while maintaining many useful analytical results, such as a closed-form expression of the marginal likelihood. This new prior also leads to fast posterior simulation - for a BVAR with 100 variables and 4 lags, obtaining 10,000 posterior draws takes less than half a minute on a standard desktop. In a forecasting exercise, we show that a data-driven asymmetric prior outperforms two useful benchmarks: a data-driven symmetric prior and a subjective asymmetric prior. |
| Keywords: | shrinkage prior, forecasting, marginal likelihood, optimal hyperparameters, structural VAR |
| JEL: | C11 C52 E37 E47 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2019-51&r=all |