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on Econometric Time Series |
| By: | Eduardo Abi Jaber (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique); Omar El Euch (Ecole Polytechnique - X) |
| Abstract: | Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting. |
| Keywords: | Rough volatility models,rough Heston models,stochastic Volterra equations,affine Volterra processes,fractional Riccati equations,limit theorems |
| Date: | 2018–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01697117&r=ets |
| By: | Bensalma, Ahmed |
| Abstract: | This article is devoted to study the e¤ects of the S-periodical fractional di¤erencing filter (1-L^S)^Dt . To put this e¤ect in evidence, we have derived the periodic auto-covariance functions of two distinct univariate seasonally fractionally di¤erenced periodic models. A multivariate representation of periodically correlated process is exploited to provide the exact and approximated expression auto-covariance of each models. The distinction between the models is clearly obvious through the expression of periodic auto-covariance function. Besides producing di¤erent autocovariance functions, the two models di¤er in their implications. In the first model, the seasons of the multivariate series are separately fractionally integrated. In the second model, however, the seasons for the univariate series are fractionally co-integrated. On the simulated sample, for each models, with the same parameters, the empirical periodic autocovariance are calculated and graphically represented for illustrating the results and support the comparison between the two models. |
| Keywords: | Periodically correlated process, Fraction integration, seasonal fractional integration, Periodic fractional integration |
| JEL: | C1 C15 C2 C22 C5 C51 C52 C6 |
| Date: | 2018–03–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:84969&r=ets |
| By: | Bruce E. Hansen; Jeffrey S. Racine |
| Abstract: | Classical unit root tests are known to suffer from potentially crippling size distortions, and a range of procedures have been proposed to attenuate this problem, including the use of bootstrap procedures. It is also known that the estimating equation’s functional form can affect the outcome of the test, and various model selection procedures have been proposed to overcome this limitation. In this paper, we adopt a model averaging procedure to deal with model uncertainty at the testing stage. In addition, we leverage an automatic model-free dependent bootstrap procedure where the null is imposed by simple differencing (the block length is automatically determined using recent developments for bootstrapping dependent processes). Monte Carlo simulations indicate that this approach exhibits the lowest size distortions among its peers in settings that confound existing approaches, while it has superior power relative to those peers whose size distortions do not preclude their general use. The proposed approach is fully automatic, and there are no nuisance parameters that have to be set by the user, which ought to appeal to practitioners. |
| Keywords: | inference, model selection, size distortion, time series. |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2018-09&r=ets |
| By: | Priyanga Dilini Talagala; Rob J Hyndman; Kate Smith-Miles; Sevvandi Kandanaarachchi; Mario A Munoz |
| Abstract: | This article proposes a framework that provides early detection of anomalous series within a large collection of non-stationary streaming time series data. We define an anomaly as an observation that is very unlikely given the recent distribution of a given system. The proposed framework first forecasts a boundary for the system's typical behavior using extreme value theory. Then a sliding window is used to test for anomalous series within a newly arrived collection of series. The model uses time series features as inputs, and a density-based comparison to detect any significant changes in the distribution of the features. Using various synthetic and real world datasets, we demonstrate the wide applicability and usefulness of our proposed framework. We show that the proposed algorithm can work well in the presence of noisy non-stationarity data within multiple classes of time series. This framework is implemented in the open source R package oddstream. R code and data are available in the supplementary materials. |
| Keywords: | concept drift, extreme value theory, feature-based time series analysis, kernel-based density estimation, multivariate time series, outlier detection. |
| JEL: | C38 C60 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2018-4&r=ets |
| By: | Takaki Sato; Yasumasa Matsuda |
| Abstract: | This study proposes a spatial extension of time series generalized autoregressive conditional heteroscedasticity (GARCH) models. We call the spatial extended GARCH models as spatial GARCH (S-GARCH) models. S-GARCH models specify conditional variances given simultaneous observations, which constitutes a good contrast with time series GARCH models that specify conditional variances given past observations. The S-GARCH model are transformed into a spatial autoregressive moving-average (SARMA) model and the parameters of the S-GARCH model are estimated by a two step procedure. First step estimation is the quasi maximum likelihood (QML) estimation method and consistency and asymptotic normality of the proposed QML estimators are given. Second step is estimation of an intercept term by the estimator derived from another QML to avoid bias in first step and consistency of the estimator is shown. We demonstrate empirical properties of the model by simulation studies and real data analyses of land price data in Tokyo areas. We find the estimators have small bias regardless of distributions of error terms from simulation studies and real data analyses show that spatial volatility in land price has global spillover and volatility clustering, namely units with higher spatial volatility are clustered in some specific districts like time series financial data. |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:toh:dssraa:78&r=ets |
| By: | Silvia Miranda-Agrippino (Bank of England; Centre for Macroeconomics (CFM)); Giovanni Ricco (OFCE SciencesPo; University of Warwick) |
| Abstract: | This article reviews Bayesian inference methods for Vector Autoregression models, commonly used priors for economic and financial variables, and applications to structural analysis and forecasting. |
| Keywords: | Bayesian inference, Vector Autoregression models, BVAR, SVAR, forecasting |
| JEL: | C30 C32 E00 |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:cfm:wpaper:1808&r=ets |
| By: | Stefan Bruder |
| Abstract: | Conditional heteroskedasticity can be exploited to identify the structural vector autoregressions (SVAR) but the implications for inference on structural impulse responses have not been investigated in detail yet. We consider the conditionally heteroskedastic SVAR-GARCH model and propose a bootstrap-based inference procedure on structural impulse responses. We compare the finite-sample properties of our bootstrap method with those of two competing bootstrap methods via extensive Monte Carlo simulations. We also present a three-step estimation procedure of the parameters of the SVAR-GARCH model that promises numerical stability even in scenarios with small sample sizes and/or large dimensions. |
| Keywords: | Bootstrap, conditional heteroskedasticity, multivariate GARCH, structural impulse responses, structural vector autoregression |
| JEL: | C12 C13 C32 |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:281&r=ets |
| By: | Luisa Bisaglia (Department of Statistics, University of Padova); Margherita Gerolimetto (Department of Economics, University Of Venice Cà Foscari) |
| Abstract: | In this paper we analyse some bootstrap techniques to make inference in INAR(p) models. First of all, via Monte Carlo experiments we compare the performances of these methods when estimating the thinning parameters in INAR(p) models. We state the superiority of sieve bootstrap approaches on block bootstrap in terms of low bias and Mean Square Error (MSE). Then we apply the sieve bootstrap methods to obtain coherent predictions and confidence intervals in order to avoid difficulty in deriving the distributional properties. |
| Keywords: | INAR(p) models, estimation, forecast, bootstrap |
| JEL: | C22 C53 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2018:06&r=ets |