A likelihood ratio test for stationarity of rating transitions

We study the time-stationarity of rating transitions, modelled by a time-continuous discrete-state Markov process and derive a likelihood ratio test. For multiple Markov processes from a multiplicative intensity model, maximum likelihood parameter estimates can be written as martingale transform of the processes, counting transitions between the rating states, so that the profile partial likelihood ratio is asymptotically χ²${\chi }^2$-distributed. An application to an internal rating data set reveals highly significant instationarity.     

A score-test on measurement errors in rating transition times

We model credit rating histories as continuous-time discrete-state Markov processes. Infrequent monitoring of the debtors’ solvency will result in erroneous observations of the rating transition times, and consequently in biased parameter estimates. We develop a score test against such measurement errors in the transition data that is independent of the error distribution. We derive the asymptotic χ²${\chi }^2$-distribution for the test statistic under the null by stochastic limit theory. The test is applied to an international corporate portfolio, while accounting for economic and debtor-specific covariates. The test indicates that measurement errors in the transition times are a real problem in practice.     

Knowledge spillovers in US patents: A dynamic patent intensity model with secret common innovation factors

During the past two decades, innovations protected by patents have played a key role in business strategies. This fact enhanced studies of the determinants of patents and the impact of patents on innovation and competitive advantage. Sustaining competitive advantages is as important as creating them. Patents help sustaining competitive advantages by increasing the production cost of competitors, by signaling a better quality of products and by serving as barriers to entry. If patents are rewards for innovation, more R&D should be reflected in more patent applications but this is not the end of the story. There is empirical evidence showing that patents through time are becoming easier to get and more valuable to the firm due to increasing damage awards from infringers. These facts question the constant and static nature of the relationship between R&D and patents. Furthermore, innovation creates important knowledge spillovers due to its imperfect appropriability. Our paper investigates these dynamic effects using US patent data from 1979 to 2000 with alternative model specifications for patent counts. We introduce a general dynamic count panel data model with dynamic observable and unobservable spillovers, which encompasses previous models, is able to control for the endogeneity of R&D and therefore can be consistently estimated by maximum likelihood. Apart from allowing for firm specific fixed and random effects, we introduce a common unobserved component, or secret stock of knowledge, that affects differently the propensity to patent of each firm across sectors due to their different absorptive capacity.     

A semiparametric stochastic volatility model

In this paper the correlation structure in the classical leverage stochastic volatility (SV) model is generalized based on a linear spline. In the new model the correlation between the return and volatility innovations is time varying and depends nonparametrically on the type of news arrived to the market. Theoretical properties of the proposed model are examined. The model estimation and comparison are conducted by Bayesian methods. The performance of the estimates are examined in simulations. The new model is fitted to daily and weekly US data and compared with the classical SV and GARCH models in terms of their in-sample and out-of-sample performances. Empirical results suggest evidence in favor of the proposed model. In particular, the new model finds strong evidence of time varying leverage effect in individual stocks when the classical model fails to identify the leverage effect.     

Reinforced urn processes for credit risk models

We propose a Bayesian nonparametric model to estimate rating migration matrices and default probabilities using the reinforced urn processes (RUP) introduced in Muliere et al. (2000). The estimated default probability becomes our prior information in a parametric model for the prediction of the number of bankruptcies, with the only assumption of exchangeability within rating classes. The Polya urn construction of the transition matrix justifies a Beta distributed de Finetti measure. Dependence among the processes is introduced through the dependence among the default probabilities, with the Bivariate Beta Distribution proposed in Olkin and Liu (2003) and its multivariate generalization.     

Bayesian estimation and model selection for spatial Durbin error model with finite distributed lags

In this paper we investigate a spatial Durbin error model with finite distributed lags and consider the Bayesian MCMC estimation of the model with a smoothness prior. We study also the corresponding Bayesian model selection procedure for the spatial Durbin error model, the spatial autoregressive model and the matrix exponential spatial specification model. We derive expressions of the marginal likelihood of the three models, which greatly simplify the model selection procedure. Simulation results suggest that the Bayesian estimates of high order spatial distributed lag coefficients are more precise than the maximum likelihood estimates. When the data is generated with a general declining pattern or a unimodal pattern for lag coefficients, the spatial Durbin error model can better capture the pattern than the SAR and the MESS models in most cases. We apply the procedure to study the effect of right to work (RTW) laws on manufacturing employment.     

A spatial model for multivariate lattice data

In this article, we develop Markov random field models for multivariate lattice data. Specific attention is given to building models that incorporate general forms of the spatial correlations and cross-correlations between variables at different sites. The methodology is applied to a problem in environmental equity. Using a Bayesian hierarchical model that is multivariate in form, we examine the racial distribution of residents of southern Louisiana in relation to the location of sites listed with the U.S. Environmental Protection Agency's Toxic Release Inventory.     

Bayesian hypothesis testing in latent variable models

Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on the decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function. In addition, it is easy to interpret. The method is illustrated using a one-factor asset pricing model and a stochastic volatility model with jumps.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

A Gaussian approximation scheme for computation of option prices in stochastic volatility models

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from daily data on the Swiss Franc to Euro and Japanese Yen to Euro over the period 1999–2002.     

A flexible prior distribution for Markov switching autoregressions with Student-t errors

This paper proposes an empirical Bayes approach for Markov switching autoregressions that can constrain some of the state-dependent parameters (regression coefficients and error variances) to be approximately equal across regimes. By flexibly reducing the dimension of the parameter space, this can help to ensure regime separation and to detect the Markov switching nature of the data. The permutation sampler with a hierarchical prior is used for choosing the prior moments, the identification constraint, and the parameters governing prior state dependence. The empirical relevance of the methodology is illustrated with an application to quarterly and monthly real interest rate data.     

A test of cross section dependence for a linear dynamic panel model with regressors

This paper proposes a new testing procedure for detecting error cross section dependence after estimating a linear dynamic panel data model with regressors using the generalised method of moments (GMM). The test is valid when the cross-sectional dimension of the panel is large relative to the time series dimension. Importantly, our approach allows one to examine whether any error cross section dependence remains after including time dummies (or after transforming the data in terms of deviations from time-specific averages), which will be the case under heterogeneous error cross section dependence. Finite sample simulation-based results suggest that our tests perform well, particularly the version based on the [Blundell, R., Bond, S., 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115–143] system GMM estimator. In addition, it is shown that the system GMM estimator, based only on partial instruments consisting of the regressors, can be a reliable alternative to the standard GMM estimators under heterogeneous error cross section dependence. The proposed tests are applied to employment equations using UK firm data and the results show little evidence of heterogeneous error cross section dependence.     

Maximum likelihood estimation of partially observed diffusion models

This paper develops a maximum likelihood (ML) method to estimate partially observed diffusion models based on data sampled at discrete times. The method combines two techniques recently proposed in the literature in two separate steps. In the first step, the closed form approach of Aït-Sahalia (2008) is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states. In the second step, the efficient importance sampling technique of Richard and Zhang (2007) is used to integrate out the latent states, thereby yielding the likelihood function. Using both simulated and real data, we show that the proposed ML method works better than alternative methods. The new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations. Therefore, the method has a wide range of applicability and its computational cost is moderate.     

Estimation of stable distributions by indirect inference

This article deals with the estimation of the parameters of an α-stable distribution with indirect inference, using the skewed-t distribution as an auxiliary model. The latter distribution appears as a good candidate since it has the same number of parameters as the α-stable distribution, with each parameter playing a similar role. To improve the properties of the estimator in finite sample, we use constrained indirect inference. In a Monte Carlo study we show that this method delivers estimators with good properties in finite sample. We provide an empirical application to the distribution of jumps in the S&P 500 index returns.     

Information measures for generalized gamma family

The objective of this paper is to integrate the generalized gamma (GG)$(\mathit{GG})$ distribution into the information theoretic literature. We study information properties of the GG$\mathit{GG}$ distribution and provide an assortment of information measures for the GG$\mathit{GG}$ family, which includes the exponential, gamma, Weibull, and generalized normal distributions as its subfamilies. The measures include entropy representations of the log-likelihood ratio, AIC, and BIC, discriminating information between GG$\mathit{GG}$ and its subfamilies, a minimum discriminating information function, power transformation information, and a maximum entropy index of fit to histogram. We provide the full parametric Bayesian inference for the discrimination information measures. We also provide Bayesian inference for the fit of GG$\mathit{GG}$ model to histogram, using a semi-parametric Bayesian procedure, referred to as the maximum entropy Dirichlet (MED). The GG$\mathit{GG}$ information measures are computed for duration of unemployment and duration of CEO tenure.     

Improved inference in the evaluation of mutual fund performance using panel bootstrap methods

Two new methodologies are introduced to improve inference in the evaluation of mutual fund performance against benchmarks. First, the benchmark models are estimated using panel methods with both fund and time effects. Second, the non-normality of individual mutual fund returns is accounted for by using panel bootstrap methods. We also augment the standard benchmark factors with fund-specific characteristics, such as fund size. Using a dataset of UK equity mutual fund returns, we find that fund size has a negative effect on the average fund manager’s benchmark-adjusted performance. Further, when we allow for time effects and the non-normality of fund returns, we find that there is no evidence that even the best performing fund managers can significantly out-perform the augmented benchmarks after fund management charges are taken into account.     

On Bayesian analysis and computation for functions with monotonicity and curvature restrictions

Our goal is inference for shape-restricted functions. Our functional form consists of finite linear combinations of basis functions. Prior elicitation is difficult due to the irregular shape of the parameter space. We show how to elicit priors that are flexible, theoretically consistent, and proper. We demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non-uniform prior that addresses this issue. We introduce simulation methods that meet challenges posed by the shape of the parameter space. We analyze data from a consumer demand experiment.     

Spurious regressions in technical trading

This paper investigates the spurious effect in forecasting asset returns when signals from technical trading rules are used as predictors. Against economic intuition, the simulation result shows that, even if past information has no predictive power, buy or sell signals based on the difference between the short-period and long-period moving averages of past asset prices can be statistically significant when the forecast horizon is relatively long. The theoretical analysis reveals that both ‘momentum’ and ‘contrarian’ strategies can be falsely supported, while the probability of obtaining each result depends on the type of the test statistics employed.     

Extreme-quantile tracking for financial time series

Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the stationarity assumption may be violated by erratic changes of regime, say. As a result, we provide a method for estimating conditional risk measures applicable to both stationary and nonstationary series. A backtesting study for the UBS share price over the subprime crisis exemplifies our approach.