DYNAMIC QUANTILE MODELS

This paper introduces new dynamic quantile models called the Dynamic Additive Quantile (DAQ) model and Quantile Factor Model (QFM) for univariate time series and panel data, respectively. The Dynamic Additive Quantile (DAQ) model is suitable for applications to financial data such as univariate returns, and can be used for computation and updating of the Value-at-Risk. The Quantile Factor Mode (QFM) is a multivariate model that can represent the dynamics of cross-sectional distributions of returns, individual incomes, and corporate ratings. The estimation method proposed in the paper relies on an optimization criterion based on the inverse KLIC measure. Goodness of fit tests and diagnostic tools for fit assessment are also provided. For illustration, the models are estimated on stock return data form the Toronto Stock Exchange (TSX).Value-at-Risk, Factor Model, Information Criterion, Income Inequality, Panel Data, Loss-Given-Default

A term structure model with level factor cannot be realistic and arbitrage free

A large part of the term structure literature interprets the first underlying factors as a level factor, a slope factor, and a curvature factor. In this paper we consider factor models interpretable as a level factor model, a level and a slope factor model, respectively. We prove that such models are compatible with no-arbitrage restrictions and the positivity of rates either under rather unrealistic conditions on the dynamic of the short term interest rate, or at the cost of explosive long-term interest rates. This introduces some doubt on the relevance of the level and slope interpretations of factors in term structure models.Interest Rate, Term Structure, Affine Model, No Arbitrage, Level Factor, Slope Factor.

The Ordered Qualitative Model For Credit Rating Transitions

Information on the expected changes in credit quality of obligors is contained in credit migration matrices which trace out the movements of firms across ratings categories in a given period of time and in a given group of bond issuers. The rating matrices provided by Moody’s, Standard &Poor’s and Fitch became crucial inputs to many applications, including the assessment of risk on corporate credit portfolios (CreditVar) and credit derivatives pricing. We propose a factor probit model for modeling and prediction of credit rating matrices that are assumed to be stochastic and driven by a latent factor. The filtered latent factor path reveals the effect of the economic cycle on corporate credit ratings, and provides evidence in support of the PIT (point-in-time) rating philosophy. The factor probit model also yields the estimates of cross-sectional correlations in rating transitions that are documented empirically but not fully accounted for in the literature and in the regulatory rules established by the Basle Committee.Credit Rating, Migration, Migration Correlation, Credit Risk, Probit Model, Latent Factor, Business Cycle.

Coherency Conditions In Simultaneous Linear Equation Models With Endogenous Switching Regimes

In modeling disequilibrium macroeconomic systems which one would want to subject to econometric estimation one typically faces the problem of whether the structural model can determine a unique equilibrium. The problem inherits a special form because the regimes in which the equilibria can lie are each linear. By placing restrictions on the parameters that insure the uniqueness of such a solution for each value of the exogenous and random variables, we can improve the estimation procedure. This paper provides necessary and sufficient conditions for uniqueness -- or "coherency." These conditions are applied to a variety of models that have been prominent in the literature on econometrics with 'switching regimes' such as those of self-selectivity (Maddala), simultaneous equation tobit and probit (Amemiya, Schmidt) and multi-market macroeconomic disequilibrium (Gourieroux, Laffont and Nonfort).

The Wishart short rate model

We consider a short rate model, driven by a stochastic process on the cone of positive semidefinite matrices. We derive sufficient conditions ensuring that the model replicates normal, inverse or humped yield curves

Fonctions de production représentatives de fonctions à complémentarité stricte

In this paper, we analyse production function with complementary factors for the case of heterogenous firms. As an illustration, we restrict ourselves to the two factors case and we consider the functions: yi= Min (a1ix1i , a2ix2i), where the technical coefficients vary with the form. Then it is natural to introduce the representative function : y = g (x1, x2 ) = Min (a1x1, a2x2 ), where the average is taken with respect to the technical coefficients. We first characterize the functions which may be interpreted as representative and discuss the possibility to identify the heterogeneity distribution π from the representative production function g. These results are applied to the CES functions. Finally we discuss the notion of more or less heterogenous distribution, we examine how they are linked to heterogenity biases on the substitution coefficients and we use the obtained family of production technologies to introduce an ordering on the distributions of inputs in terms of technical efficiency. Dans cet article, nous analysons des fonctions de production à complémentarité stricte dans le cas d’entreprises hétérogènes. Nous restreignant pour simplifier au cas de deux facteurs, nous avons: yi= Min (a1ix1i , a2ix2i), où les coefficients techniques a1i a2i dépendent de l’entreprise i considérée. Il est alors naturel d’introduire la fonction de production moyenne (ou représentative) définie par : y = g (x1, x2 ) = Min (a1x1, a2x2 ), où la moyenne est prise sur les coefficients techniques.

The Wishart Autoregressive Process of Multivariate Stochastic Volatility

The Wishart Autoregressive (WAR) process is a multivariate process of stochastic positive definite matrices. The WAR is proposed in this paper as a dynamic model for stochastic volatility matrices. It yields simple nonlinear forecasts at any horizon and has factor representation, which separates white noise directions from those that contain all information about the past. For illustration, the WAR is applied to a sequence of intraday realized volatility covolatility matrices.Stochastic Volatility, Car Process, Factor Analysis, Reduced Rank, Realized Volatility

Minimum Distance Estimation of Search Costs using Price Distribution

Hong and Shum (2006) show equilibrium restrictions in a search model can be used to identify quantiles of the search cost distribution from observed prices alone. These quantiles can be difficult to estimate in practice. This paper uses a minimum distance approach to estimate them that is easy to compute. A version of our estimator is a solution to a nonlinear least squares problem that can be straightforwardly programmed on softwares such as STATA. We show our estimator is consistent and has an asymptotic normal distribution. Its distribution can be consistently estimated by a bootstrap. Our estimator can be used to estimate the cost distribution nonparametrically on a larger support when prices from heterogeneous markets are available. We propose a two-step sieve estimator for that case. The first step estimates quantiles from each market. They are used in the second step as generated variables to perform nonparametric sieve estimation. We derive the uniform rate of convergence of the sieve estimator that can be used to quantify the errors incurred from interpolating data across markets. To illustrate we use online bookmaking odds for English football leagues' matches (as prices) and find evidence that suggests search costs for consumers have fallen following a change in the British law that allows gambling operators to advertise more widely

Components of multifractality in the Central England Temperature anomaly series

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The series is analyzed as a complete data set and considering a sliding window of 11 years. In both cases, we quantify the broadness of the multifractal spectrum as well as its components defined by the deviations from the Gaussian distribution and the influence of the dependence between measurements. The results show that the chief contribution to the multifractal structure comes from the dynamical dependencies, mainly the weak ones, followed by a residual contribution of the deviations from Gaussianity. However, using the sliding window, we verify that the spikes in the non-Gaussian contribution occur at very close dates associated with climate changes determined in previous works by component analysis methods. Moreover, the strong non-Gaussian contribution found in the multifractal measures from the 1960s onwards is in agreement with global results very recently proposed in the literature.Comment: 21 pages, 10 figure

Recentered importance sampling with applications to Bayesian model validation

Since its introduction in the early 1990s, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This article examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on Bayesian model validation. We demonstrate that, in certain applications, the curse of dimensionality can be reduced by a simple modification of IS. In addition to providing new theoretical insight into the behavior of the IS approximation in a wide class of models, our result facilitates the implementation of computationally intensive Bayesian model checks. We illustrate the simplicity, computational savings, and potential inferential advantages of the proposed approach through two substantive case studies, notably computation of Bayesian p-values for linear regression models and simulation-based model checking. Supplementary materials including the Appendix and the R code for Section 3.1.2 are available online