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on Econometric Time Series |
| By: | Matyas Barczy; Mohamed Ben Alaya; Ahmed Kebaier; Gyula Pap |
| Abstract: | We consider a jump-type Cox-Ingersoll-Ross (CIR) process driven by a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak consistency and asymptotic normality, and, under an additional moment assumption, strong consistency as well. In the supercritical case, we prove strong consistency and mixed normal (but non-normal) asymptotic behavior, while in the critical case, weak consistency and non-standard asymptotic behavior are described. We specialize our results to so-called basic affine jump-diffusions as well. Concerning the asymptotic behavior of the MLE in the supercritical case, we derive a stochastic representation of the limiting mixed normal distribution containing a jump-type supercritical CIR process, which is a new phenomena, compared to the critical case, where a diffusion-type critical CIR process comes into play. |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1609.05865&r=ets |
| By: | Henry Penikas |
| Abstract: | An approach is proposed to determine structural shift in time-series assuming non-linear dependence of lagged values of dependent variable. Copulas are used to model non-linear dependence of time series components. |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1609.05056&r=ets |
| By: | Maheu, John M; Shamsi, Azam |
| Abstract: | This paper derives a dynamic conditional beta representation using a Bayesian semiparametric multivariate GARCH model. The conditional joint distribution of excess stock returns and market excess returns are modeled as a countably infinite mixture of normals. This allows for deviations from the elliptic family of distributions. Empirically we find the time-varying beta of a stock nonlinearly depends on the contemporaneous value of excess market returns. In highly volatile markets, beta is almost constant, while in stable markets, the beta coefficient can depend asymmetrically on the market excess return. The model is extended to allow nonlinear dependence in Fama-French factors. |
| Keywords: | GARCH, Dirichlet process mixture, slice sampling |
| JEL: | C32 C58 G10 G17 |
| Date: | 2016–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:73764&r=ets |
| By: | Vanessa Berenguer-Rico (Dept of Economics, Mansfield College and Programme for Economic Modelling, Oxford University); Bent Nielsen (Dept of Economics, Nuffield College, Institute Programme for Economic Modelling, Oxford University) |
| Abstract: | We show that the cumulated sum of squares test has a standard Brownian bridge-type asymptotic distribution in non-linear regression models with non-stationary regressors. This contrasts with cumulated sum tests which have been studied previously and where the asymptotic distribution involves nuisance quantities. Through simulation we show that the power is comparable in a wide of range of situations. |
| Keywords: | Cumulated sum of squares, Non-linear Least Squares, Non-stationarity, Specification tests. |
| JEL: | C01 C22 |
| Date: | 2015–08–03 |
| URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:1509&r=ets |
| By: | Manabu Asai (Faculty of Economics Soka University, Japan.); Michael McAleer (Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute, Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute, The Netherlands and Department of Quantitative Economics Complutense University of Madrid, Spain.) |
| Abstract: | The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties. |
| Keywords: | Multivariate conditional volatility, Vector random coefficient autoregressive process, Asymmetry, Long memory, Dynamic conditional correlations, Regularity conditions, Asymptotic properties. |
| JEL: | C13 C32 C58 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1614&r=ets |
| By: | Manabu Asai (Faculty of Economics Soka University, Japan.); Chia-Lin Chang (Department of Applied Economics Department of Finance National Chung Hsing University Taichung, Taiwan.); Michael McAleer (Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute, Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute, The Netherlands and Department of Quantitative Economics Complutense University of Madrid, Spain.) |
| Abstract: | The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model). The matrix exponential transformation guarantees the positivedefiniteness of the dynamic covariance matrix. The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988, 39(1-2), 69–104), especially for developing tests for leverage and spillover effects in the covariance dynamics. Efficient importance sampling is used to maximize the likelihood function of RMESV-ALM, and the finite sample properties of the quasi-maximum likelihood estimator of the parameters are analysed. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. The volatility and co-volatility spillovers are examined via the news impact curves and the impulse response functions from returns to volatility and co-volatility. |
| Keywords: | Matrix-exponential transformation, Realized stochastic covariances, Realized conditional covariances, Asymmetry, Long memory, Spillovers, Dynamic covariance matrix, Finite sample properties, Forecasting performance. |
| JEL: | C22 C32 C58 G32 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1615&r=ets |
| By: | Heni Boubaker (IPAG Lab); Giorgio Canarella (University of Nevada, Las Vegas); Rangan Gupta (University of Pretoria); Stephen M. Miller (University of Nevada, Las Vegas and University of Connecticut) |
| Abstract: | We propose a new long-memory model with a time-varying fractional integration parameter, evolving non-linearly according to a Logistic Smooth Transition Autoregressive (LSTAR) specification. To estimate the time-varying fractional integration parameter, we implement a method based on the wavelet approach, using the instantaneous least squares estimator (ILSE). The empirical results show the relevance of the modeling approach and provide evidence of regime change in inflation persistence that contributes to a better understanding of the inflationary process in the US. Most importantly, these empirical findings remind us that a "one-size-fits-all" monetary policy is unlikely to work in all circumstances. |
| Keywords: | Time-varying long-memory, LSTAR model, MODWT algorithm, ILSE estimator |
| JEL: | C13 C22 C32 C54 E31 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:uct:uconnp:2016-09&r=ets |
| By: | Sylvia Kaufmann (Study Center Gerzensee) |
| Abstract: | Markov models introduce persistence in the mixture distribution. In time series analysis, the mixture components relate to different persistent states characterizing the state-specific time series process. Model specification is discussed in a general form. Emphasis is put on the functional form and the parametrization of timeinvariant and time-varying specifications of the state transition distribution. The concept of mean-square stability is introduced to discuss the condition under which Markov switching processes have finite first and second moments in the indefinite future. Not surprisingly, a time series process may be mean-square stable even if it switches between bounded and unbounded state-specific processes. Surprisingly, switching between stable state-specific processes is neither necessary nor sufficient to obtain a mean-square stable time series process. Model estimation proceeds by data augmentation. We derive the basic forward-filtering backward-smoothing/sampling algorithm to infer on the latent state indicator in maximum likelihood and Bayesian estimation procedures. Emphasis is again laid on the state transition distribution. We discuss the specification of state-invariant prior parameter distributions and posterior parameter inference under either a logit or probit functional form of the state transition distribution. With simulated data, we show that the estimation of parameters under a probit functional form is more efficient. However, a probit functional form renders estimation extremely slow if more than two states drive the time series process. Finally, various applications illustrate how to obtain informative switching in Markov switching models with time-invariant and time-varying transition distributions. |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:szg:worpap:1606&r=ets |
| By: | Matthias Raddant; Friedrich Wagner |
| Abstract: | The problems related to the application of multivariate GARCH models to a market with a large number of stocks are solved by restricting the form of the conditional covariance matrix. It contains one component describing the market and a second simple component to account for the remaining contribution to the volatility. This allows the analytical calculation of the inverse covariance matrix. We compare our model with the results of other GARCH models for the daily returns from the S&P500 market. The description of the covariance matrix turns out to be similar to the DCC model but has fewer free parameters and requires less computing time. As applications we use the daily values of $\beta$ coefficients available from the market component to confirm a transition of the market in 2006. Further we discuss properties of the leverage effect. |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1609.07051&r=ets |
| By: | Michael Thornton; Marcus Chambers |
| Abstract: | This paper explores the representation and estimation of mixed continuous time ARMA (autoregressive moving average) systems of orders p, q. Taking the general case of mixed stock and flow variables, we discuss new state space and exact discrete time representations and demonstrate that the discrete time ARMA representations widely used in empirical work, based on differencing stock variables, are members of a class of observationally equivalent discrete time ARMA(p + 1, p) representations, which includes a more natural ARMA(p, p) representation. We compare and contrast two approaches to likelihood evaluation and computation, namely one based on an exact discrete time representation and another utilising astate space representation and the Kalman-Bucy filter. |
| Keywords: | Continuous time; ARMA process; state space; discrete time representation. |
| JEL: | C32 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:16/10&r=ets |
| By: | Antoine Mandel (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Amir Sani (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics) |
| Abstract: | Non-parametric forecast combination methods choose a set of static weights to combine over candidate forecasts as opposed to traditional forecasting approaches, such as ordinary least squares, that combine over information (e.g. exogenous variables). While they are robust to noise, structural breaks, inconsistent predictors and changing dynamics in the target variable, sophisticated combination methods fail to outperform the simple mean. Time-varying weights have been suggested as a way forward. Here we address the challenge to “develop methods better geared to the intermittent and evolving nature of predictive relations” in Stock and Watson (2001) and propose a data driven machine learning approach to learn time-varying forecast combinations for output, inflation or any macroeconomic time series of interest. Further, the proposed procedure “hedges” combination weights against poor performance to the mean, while optimizing weights to minimize the performance gap to the best candidate forecast in hindsight. Theoretical results are reported along with empirical performance on a standard macroeconomic dataset for predicting output and inflation. |
| Abstract: | Les méthodes non-paramétriques de combinaison de prédicteurs déterminent un vecteur statique de poids pour combiner les prédicteurs. Elles différent ainsi des méthodes de prévision traditionnelles qui visent à combiner l'information (i.e. les variables exogènes). Bien qu'elles soient très robustes, notamment au bruit, aux changements structurels ou à la présence de prédicteurs inconsistants, les méthodes de combinaison complexes n'offrent généralement pas une performance supérieure à celle de la simple moyenne. L'usage de poids variables dans le temps est considéré comme une nouvelle voie de recherche prometteuse face à ce dilemme. Dans cet article, nous développons cette approche en proposant une approche par l'apprentissage statistique du problème de la détermination de combinaisons de prédicteurs évoluant dans le temps pour l'inflation, le PIB ou tout autre série macro-économique. La méthode proposée permet en particulier de garantir, au pire, une performance proche de celle de la moyenne tout en optimisant les poids de telle sorte que la performance soit proche de celle de la meilleure combinaison à posteriori. Nous reportons à cet effet des résultats théoriques et empiriques sur un ensemble de données standard pour la prédiction macro-économique. |
| Keywords: | Forecast combinations,Machine Learning,Econometrics,Forecasting,Forecast Combination Puzzle,Apprentissage statistique,Combinaison de prédicteurs,Econométrie |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01317974&r=ets |
| By: | Papa Ousmane Cissé (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement - Université Gaston Bergé Sénégal); Abdou Kâ Diongue (LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement - Université Gaston Bergé Sénégal); Dominique Guegan (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | In this paper, we introduce a new model called Fractionally Integrated Separable Spatial Autoregressive processes with Seasonality and denoted Seasonal FISSAR for two-dimensional spatial data. We focus on the class of separable spatial models whose correlation structure can be expressed as a product of correlations. This new modelling allows taking into account the seasonality patterns observed in spatial data. We investigate the properties of this new model providing stationary conditions, some explicit expressions form of the autocovariance function and the spectral density function. We establish the asymptotic behaviour of the spectral density function near the seasonal frequencies and perform some simulations to illustrate the behaviour of the model. |
| Keywords: | spatial autocovariance,spatial stationary process,seasonality,spatial short memory,seasonal long memory,two-dimensional data,separable process |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01278126&r=ets |