We consider the incidental parameters problem in this paper, i.e. the estimation for a small number of parameters of interest in the presence of a large number of nuisance parameters. By assuming that the observations are taken from a multiple strictly stationary process, the two estimation...

We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible ARMA time series models, which were initially established by Hannan (1973) via the asymptotic properties of a Whittle's estimator. This also paves the way to...

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has proved particularly valuable in modelling time series with time varying volatility. These include financial data, which can be particularly heavy tailed. It is well understood now that the tail heaviness of...

For a set of spatially dependent dynamical models, we propose a method for estimating parameters that control temporal dynamics by spatial smoothing. The new approach is particularly relevant for analyzing spatially distributed panels of short time series. The asymptotic results show that...

It is increasingly important in financial economics to estimate volatilities of asset returns. However, most of the available methods are not directly applicable when the number of assets involved is large, due to the lack of accuracy in estimating high-dimensional matrices. Therefore it is...

We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable, nonstationary factors are identified by expanding the white noise space step by step, thereby...

This paper examines the Gaussian maximum likelihood estimator (GMLE) in the context of a general form of spatial autoregressive and moving average (ARMA) processes with finite second moment. The ARMA processes are supposed to be causal and invertible under the half-plane unilateral order, but...

In this paper, we study three different types of estimates for the noise-to signal ratios in a general stochastic regression setup. The locally linear and locally quadratic regression estimators serve as the building blocks in our approach. Under the assumption that the observations are strictly...

For autoregressive moving average (ARMA) models with infinite variance innovations, quasi-likelihood-based estimators (such as Whittle estimators) suffer from complex asymptotic distributions depending on unknown tail indices. This makes statistical inference for such models difficult. In...

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least...