44 research outputs found
Inference for Noisy Long Run Component Process
This paper introduces a new approach to the modelling of a stationary long run component, which is an autoregressive process with near unit root and small sigma innovation. We show that a combination of a noise and a long run component can explain the long run predictability puzzle pointed out in Fama-French (1988). Moreover in the presence of a long run component, spurious regressions arise and misleading long run predictions are obtained when standard statistical approaches are applie
Structural Modelling of Dynamic Networks and Identifying Maximum Likelihood
This paper considers nonlinear dynamic models where the main parameter of
interest is a nonnegative matrix characterizing the network (contagion)
effects. This network matrix is usually constrained either by assuming a
limited number of nonzero elements (sparsity), or by considering a reduced rank
approach for nonnegative matrix factorization (NMF). We follow the latter
approach and develop a new probabilistic NMF method. We introduce a new
Identifying Maximum Likelihood (IML) method for consistent estimation of the
identified set of admissible NMF's and derive its asymptotic distribution.
Moreover, we propose a maximum likelihood estimator of the parameter matrix for
a given non-negative rank, derive its asymptotic distribution and the
associated efficiency bound
Inference for Noisy Long Run Component Process
This paper introduces a new approach to the modelling of a stationary long run component, which is an autoregressive process with near unit root and small sigma innovation. We show that a combination of a noise and a long run component can explain the long run predictability puzzle pointed out in Fama-French (1988). Moreover in the presence of a long run component, spurious regressions arise and misleading long run predictions are obtained when standard statistical approaches are applie
Nonlinear Persistence and Copersistence
In a nonlinear framework, temporal dependence of time series is sensitive to transformations. The aim of this paper is to examine in detail the relationships between various forms of persistence and nonlinear transformations of stationary and nonstationary processes. We introduce the concept of persistence space and use it to define the degrees of persistence of univariate or multivariate processes. For illustration, we examine and compare the persistence structure of a fractionally integrated process and a beta mixture of AR(1) processes. The study of multivariate processes is focused on nonlinear comovements between the components, called the copersistence directions, or cointegration directions in the nonstationary case. We nd that, in general, there is a multiplicity of such directions, causing an identication problem in the analysis of nonlinear cointegration.Nonlinear Autocorrelogram, Canonical Analysis, Persistence, Chaos, Unit Root, Cointegration
Local Likelihood Density Estimation and Value-at-Risk
This paper presents a new nonparametric method for computing the conditional Value-at-Risk, based on a local approximation of the conditional density function in a neighborhood of a predetermined
extreme value for univariate and multivariate series of portfolio returns. For illustration, the method is applied to intraday VaR estimation on portfolios of two stocks traded on the Toronto Stock Exchange. The performance of the new VaR
computation method is compared to the historical simulation, variance-covariance, and J. P. Morgan methods
Composite Likelihood for Stochastic Migration Model with Unobserved Factor
We introduce the conditional Maximum Composite Likelihood (MCL) estimation
method for the stochastic factor ordered Probit model of credit rating
transitions of firms. This model is recommended for internal credit risk
assessment procedures in banks and financial institutions under the Basel III
regulations. Its exact likelihood function involves a high-dimensional
integral, which can be approximated numerically before maximization. However,
the estimated migration risk and required capital tend to be sensitive to the
quality of this approximation, potentially leading to statistical regulatory
arbitrage. The proposed conditional MCL estimator circumvents this problem and
maximizes the composite log-likelihood of the factor ordered Probit model. We
present three conditional MCL estimators of different complexity and examine
their consistency and asymptotic normality when n and T tend to infinity. The
performance of these estimators at finite T is examined and compared with a
granularity-based approach in a simulation study. The use of the MCL estimator
is also illustrated in an empirical application