Using Subspace Methods for Estimating ARMA Models for Multivariate Time Series with Conditionally Heteroskedastic Innovations

This paper deals with the estimation of linear dynamic models of the ARMA type for the conditional mean for time series with conditionally heteroskedastic innovation process widely used in modelling financial time series. Estimation is performed using subspace methods which are known to have computational advantages as compared to prediction error methods based on criterion minimization. These advantages are especially strong for high dimensional time series. The subspace methods are shown to provide consistent estimators. Moreover asymptotic equivalence to prediction error estimators in terms of the asymptotic variance is proved. Also order estimation techniques are proposed and analyzed. The estimators are not efficient as they do not model the conditional variance. Nevertheless, they can be used to obtain consistent estimators of the innovations. In a second step these estimated residuals can be used in order to levitate the problem of specifying the variance model in particular in the multi-output case. This is demonstrated in an ARCH setting, where it is proved that the estimated innovations can be used in place of the true innovations for testing in a linear least squares context in order to specify the structure of the ARCH model without changing the asymptotic distribution.Multivariate models, conditional heteroskedasticity, ARMA systems, subspace methods

Parameter Estimation in Nonlinear AR-GARCH Models

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.AR-GARCH, asymptotic normality, consistency, nonlinear time series, quasi maximum likelihood estimation

Parameter estimation in nonlinear AR–GARCH models

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.Nonlinear Autoregression, Generalized Autoregressive Conditional Heteroskedasticity, Nonlinear Time Series Models, Quasi-Maximum Likelihood Estimation, Strong Consistency, Asymptotic Normality

Euro area inflation persistence in an estimated nonlinear DSGE model

We estimate the approximate nonlinear solution of a small DSGE model on euro area data, using the conditional particle filter to compute the model likelihood. Our results are consistent with previous findings, based on simulated data, suggesting that this approach delivers sharper inference compared to the estimation of the linearised model. We also show that the nonlinear model can account for richer economic dynamics: the impulse responses to structural shocks vary depending on initial conditions selected within our estimation sample. JEL Classification: C11, C15, E31, E32, E52Bayesian estimation, DSGE Models, Inflation persistence, second order approximations, sequential Monte Carlo

Estimation and forecasting in large datasets with conditionally heteroskedastic dynamic common factors

We propose a new method for multivariate forecasting which combines Dynamic Factor and multivariate GARCH models. The information contained in large datasets is captured by few dynamic common factors, which we assume being conditionally heteroskedastic. After presenting the model, we propose a multi-step estimation technique which combines asymptotic principal components and multivariate GARCH. We also prove consistency of the estimated conditional covariances. We present simulation results in order to assess the finite sample properties of the estimation technique. Finally, we carry out two empirical applications respectively on macroeconomic series, with a particular focus on different measures of inflation, and on financial asset returns. Our model outperforms the benchmarks in fore-casting the inflation level, its conditional variance and the volatility of returns. Moreover, we are able to predict all the conditional covariances among the observable series. JEL Classification: C52, C53Conditional Covariance, Dynamic Factor Models, Inflation forecasting, multivariate GARCH, Volatility Forecasting

Bayesian analysis of FIAPARCH model: an application to São Paulo stock market

In this paper, we develop a Bayesian analysis of a FIAPARCH(p,d,q) model for parameter estimation and conditional variance prediction. In order to study the inference problem we use the Metropolis-Hastings algorithm.This methodology is illustrated in a simulation study and it is applied to a set of observations concerning the returns of IBOVESPA value

Modelling Heterogeneity and Dynamics in the Volatility of Individual Wages

This paper presents a model for the heterogeneity and dynamics of the conditional mean and the conditional variance of standardized individual wages. In particular, a heteroskedastic autoregressive model with multiple individual fixed effects is proposed. The expression for a modified likelihood function is obtained for estimation and inference in a fixed-T context. Using a bias-corrected likelihood approach makes it possible to reduce the estimation bias to a term of order 1/T². The small sample performance of the bias corrected estimator is investigated in a Monte Carlo simulation study. The simulation results show that the bias of the maximum likelihood estimator is substantially corrected for designs that are broadly calibrated to the data used in the empirical analysis, drawn from the 1968-1993 Panel Study of Income Dynamics. The empirical results show that it is important to account for individual unobserved heterogeneity and dynamics in the variance, and that the latter is driven by job mobility. The model also explains the non-normality observed in logwage data.panel data, dynamic nonlinear models, conditional heteroskedasticity, fixed effects, individual wages, bias reduction

Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach

This paper proposes a general formulation of a nonparametric frontier model introducingexternal environmental factors that might influence the production process butare neither inputs nor outputs under the control of the producer. A representation isproposed in terms of a probabilistic model which defines the data generating process.Our approach extends the basic ideas from Cazals, Florens and Simar (2002) to thefull multivariate case. We introduce the concepts of conditional efficiency measure andof conditional efficiency measure of order-m. Afterwards we suggest a practical wayfor computing the nonparametric estimators. Finally, a simple methodology to investigatethe influence of these external factors on the production process is proposed.Numerical illustrations through some simulated examples and through a real data seton Mutual Funds show the usefulness of the approach.production function, frontier, nonparametric estimation, environmental factors,robust estimation.