Robustness of a semiparametric estimator of a copula

Copulas offer a convenient way of modelling multivariate observations and capturing the intrinsic dependence between the components of a multivariate random variable. A semiparametric method for estimating the dependence parameters of copulas was proposed by Genest, Ghoudi and Rivest (1995), in which the marginal distributions are estimated nonparameterically by empirical distribution functions. Thus, this method does not require any marginal distribution to have a known parametric form. However, a standard concern about semiparametric methods is the possibility that it may be substantially less efficient than the parametric method when the model is completely parametric and correctly specified. In this paper we investigate the efficiency-robustness properties of the foregoing semiparametric method by simulation; in particular, we evaluate the performance of this method when the marginal distributions are specified correctly and when they are specified incorrectly. The results show that the semiparametric method is better than the parametric methods. An example involving the household expenditure data for Australia is used to compare and contrast the methodsCopulas; multivariate joint distribution; inference function method;maximum likelihood mathod;semiparametric method

Semiparametric estimation of the dependence parameter of the error terms in multivariate regression

A semiparametric method is developed for estimating the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonparametric part of the method treats the marginal distributions of the error term as unknown, and estimates them by suitable empirical distribution functions. Then a pseudolikelihood is maximized to estimate the dependence parameter. It is shown that this estimator is asymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric estimator is better than the parametric methods available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic efficiency due to the estimation of the regression parameters. An empirical example on portfolio management is used to illustrate the method. This is an extension of earlier work by Oakes (1994) and Genest et al. (1995) for the case when the observations are independent and identically distributed, and Oakes and Ritz (2000) for the multivariate regression model.Copula; Pseudo-likelihood; Robustness.

Role of Exchange Rate Volatility in Exchange Rate Pass-Through to Import Prices: Some Evidence from Japan

This paper investigates the effect of exchange rate volatility on the degree of exchange rate pass-through in Japan for the period January 1975 to June 1997. Although several studies put forward theoretical arguments for the volatility-domestic import price relationship, only a very few studies produced empirical evidence. The volatility of contractual currency based exchange rate index returns was modelled using GARCH-type processes with skewed student t-distribution, capturing the typical nature of exchange rate returns. Using a three-state regime switching threshold model, we examine the response of import prices, the degree of pass-through in particular, to different volatility regimes, low, medium and high. The results show that the exchange rate pass- through coefficient is significantly different across all three volatility regimes only during recession.

Exchange Rate Pass-Through to Manufactured Import Prices: The Case of Japan

This paper examines the exchange rate pass-through to yen based manufactured import prices of Japan using asymmetric unit root and cointegration tests and asymmetric models. Due to sticky prices, for example, there are reasons to believe that the degree of pass-through depends on whether the exchange rate appreciates or depreciates. The sample used in this study covers the period January 1975 to June 1997. Using two state regime switching models, the estimated pass-through coefficients corresponding to appreciation and depreciation of the currency are found to be 98 percent and 83 percent respectively; these coefficients are shown to be significantly different, particularly in the post recession period. Moreover, we have shown that the recession in Japan in the 1990s has significantly affected the exchange rate passthrough relationship particularly when the yen depreciates and that the proposition that exchange rate depreciation and appreciation have systematic asymmetric effects on exchange rate pass-through coefficient. Forcing appreciations and depreciations to have the same effects on the import prices does not appear to uncover the true underlying exchange rate pass through relationship.Exchange rate pass-through, Japan, threshold autoregression.

Assessing Dependence Changes in the Asian Financial Market Returns Using Plots Based on Nonparametric Measures

This paper investigates whether or not there are significant changes in the dependence between the Thai equity market and six Asian markets - namely, Singaporean, Malaysian, Hong Kong, Korean, Indonesian and Taiwanese markets - due to 1997-July financial crisis. If so, this may be an indication that the underlying bivariate joint distributions capturing the dependence between the Thai market and these six markets have changed. We employ the chi-plot proposed by Fisher and Switzer (2001) and the Kendall plot proposed by Genest and Boies (2003) to examine the dependence in these six markets for the pre- and post-1997 financial crisis periods. We find that marginal distributions of all seven markets have notably changed due to this financial crisis, and that the functional forms of the underlying joint distributions generating the dependence in the Korean, Indonesian and Taiwan markets have also changed for the post-crisis period. It appears that the same parametric copula can capture the dependence in the Singapore, Malaysia and Hong Kong markets for both pre- and post-crisis periods, and that only the tail indices of bivariate distributions between the Thai and these three markets have changed. It is interesting to observe that the same conclusions can be drawn using both chi- and Kendall plots.chi-plot, copula, dependence, Kendall-plot

Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown

This paper proposes a semiparametric method for estimating duration models when there are inequality constraints on some parameters and the error distribution may be unknown. Thus, the setting considered here is particularly suitable for practical applications. The parameters in duration models are usually estimated by a quasi-MLE. Recent advances show that a semiparametrically efficient estimator [SPE] has better asymptotic optimality properties than the QMLE provided that the parameter space is unrestricted. However, in several important duration models, the parameter space is restricted, for example in the commonly used linear duration model some parameters are non-negative. In such cases, the SPE may turn out to be outside the allowed parameter space and hence are unsuitable for use. To overcome this difficulty, we propose a new constrained semiparametric estimator. In a simulation study involving duration models with inequality constraints on parameters, the new estimator proposed in this paper performed better than its competitors. An empirical example is provided to illustrate the application of the new constrained semiparametric estimator and to show how it overcomes difficulties encountered when the unconstrained estimator of nonnegative parameters turn out to be negative.Adaptive inference; Conditional duration model; Constrained inference; Efficient semiparametric estimation; Order restricted inference; Semiparametric efficiency bound.

Pranab Kumar Sen: Life and works

In this article, we describe briefly the highlights and various accomplishments in the personal as well as the academic life of Professor Pranab Kumar Sen.Comment: Published in at http://dx.doi.org/10.1214/193940307000000013 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Half-Life Estimation based on the Bias-Corrected Bootstrap: A Highest Density Region Approach

The half-life is defined as the number of periods required for the impulse response to a unit shock to a time series to dissipate by half. It is widely used as a measure of persistence, especially in international economics to quantify the degree of mean reversion of the deviation from an international parity condition. Several studies have proposed bias-corrected point and interval estimation methods. However, they have found that the confidence intervals are rather uninformative with their upper bound being either extremely large or infinite. This is largely due to the distribution of the half-life estimator being heavily skewed and multi-modal. In this paper, we propose a bias-corrected bootstrap procedure for the estimation of half-life, adopting the highest density region (HDR) approach to point and interval estimation. Our Monte Carlo simulation results reveal that the bias-corrected bootstrap HDR method provides an accurate point estimator, as well as tight confidence intervals with superior coverage properties to those of its alternatives. As an application, the proposed method is employed for half-life estimation of the real exchange rates of seventeen industrialized countries. The results indicate much faster rates of mean-reversion than those reported in previous studies.Autoregressive Model, Bias-correction, Bootstrapping, Confidence interval, Half-life, Highest density region.

Nonlinear Modelling of Purchasing Power Parity in Indonesia

This paper models the dynamics of the adjustment process of Indonesian purchasing power parity (PPP) relative to US, Japan and Singapore by employing a nonlinear framework, which is recently shown to be appropriate in the presence of transaction costs associated with international trade. Using monthly observations from January 1979 to June 2003 (post-Bretton Woods period), covering the managed- and free-floating regimes in Indonesia, the real exchange rates were tested for their mean-reverting properties. A large number of studies found the real exchange series to be mean-averting and persistent, creating PPP puzzles. Using the linear framework many attempted to resolve these puzzles unsuccesfully. Motivated by the success of recent studies on PPP, applying a non-linear ESTAR to model the adjustment process, we tested for mean-reverting properties of all three real exchange rates for small and large deviations from the long-run equilibrium. We find that the small deviations are non-stationary, persistent and they can be explosive, while the large deviations are stationary with the adjustment process being very fast, making the overall adjustment process mean-revertingPurchasing Power Parity, ESTAR model, Mean-reversion