Paramsothy Silvapulle

Comparison of semiparametric and parametric methods for estimating copulas

Copulas have attracted significant attention in the recent literature for modeling multivariate observations. An important feature of copulas is that they enable us to specify the univariate marginal distributions and their joint behavior separately. The copula parameter captures the intrinsic dependence between the marginal variables and it can be estimated by parametric or semiparametric methods. For practical applications, the so called inference function for margins (IFM) method has emerged as the preferred fully parametric method because it is close to maximum likelihood (ML) in approach and is easier to implement. The purpose of this paper is to compare the ML and IFM methods with a semiparametric (SP) method that treats the univariate marginal distributions as unknown functions. In this paper, we consider the SP method proposed by Genest et al. [1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82(3), 543-552], which has attracted considerable interest in the literature. The results of an extensive simulation study reported here show that the ML/IFM methods are nonrobust against misspecification of the marginal distributions, and that the SP method performs better than the ML and IFM methods, overall. A data example on household expenditure is used to illustrate the application of various data analytic methods for applying the SP method, and to compare and contrast the ML, IFM and SP methods. The main conclusion is that, in terms of statistical computations and data analysis, the SP method is better than ML and IFM methods when the marginal distributions are unknown which is almost always the case in practice.

A Score Test against One-Sided Alternatives

Abstract A score-type statistic, T s , is introduced for testing H: ψ = 0 against K: ψ ≥ 0 and more general one-sided hypotheses when nuisance parameters may be present; ψ is a vector parameter. The main advantages of T s , are that it requires estimation of the model only under the null hypothesis and that, it is asymptotically equivalent to the likelihood ratio statistic; these are precisely the reasons for the popularity of the score tests for testing against two-sided alternatives. In this sense, T s preserves the main attractive features of the classical two-sided score test. The theoretical results are presented in a general framework where the likelihood-based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown. Computation of T s , is simplified by the fact that it can be computed easily once the corresponding two-sided statistic has been computed. The relevance and simplicity of T s are illustrated by discussing ...

Australian mutual fund performance appraisal using data envelopment analysis

Outlines previous research on measuring the performance of investment funds, suggesting that data envelopment analysis (DEA) techniques can overcome some of the problems of the capital asset pricing model and give pointers for improvement. Uses DEA to assess the relative performance of 257 Australian mutual funds 1995‐1999 and logistic regression to investigate the characteristics which affect it. Describes the methodology and presents the results, which suggest that scale efficiency is the main source of overall technical efficiency and that both are higher for risk‐averse funds with high positive net asset flows. Explains the ASSIRT rating system for managed funds and finds the ratings strongly associated with DEA relative efficiency scores. Believes the findings are useful to analysts, investors and managers.

Experimental evidence on robustness of data envelopment analysis

There is an on-going debate about variable selection in data envelopment analysis (DEA) as there are no diagnostic checks for model misspecification. This paper contributes to this debate by investigating the sensitivity of DEA efficiency estimates to including inappropriate and/or omitting several important variables in a large-sample DEA model. Data are simulated from constant, increasing and decreasing returns-to-scale (RS) Cobb–Douglas production processes. For constant and decreasing RS processes with irrelevant inputs, DEA tends to overestimate efficiency in almost all production units. When relevant variables are omitted, variable RS appears to be a safer option. The correct RS specification is vital when the DEA model includes irrelevant variables. The effect of omission of relevant inputs on individual production unit efficiency is more adverse compared to the inclusion of irrelevant ones.

Structural VAR models for Malaysian monetary policy analysis during the pre- and post-1997 Asian crisis periods

This article conducts an in-depth investigation into building a Structural Vector Autoregression (SVAR) model and analysing the Malaysian monetary policy. Considerable attention is paid to: (i) the selection of foreign, policy and target variables; (ii) establish identifying restrictions and improve the estimates of impulse response functions; (iii) assess the importance of intermediate channels in transmitting monetary policy mechanism; and (iv) the way in which the 1997 Asian financial crisis affected the working of monetary policy. Malaysia is an interesting small open economy to study because, following this crisis, the government imposed capital and exchange rate control measures. The overall results suggest that the crisis and the subsequent major shift in the exchange rate regime have significantly affected the Malaysian ‘Black Box’. In the pre-crisis period, domestic variables appear to be more vulnerable to foreign monetary shocks. Further, the exchange rate played a significant role in transmitting the interest rate shocks, whereas credit and asset prices helped to propagate the money shock. In the post-crisis period however, asset prices play a more domineering role in intensifying the effects of both interest rate and money shocks on output, and the economy was insulated from foreign shocks.

Testing Moving Average Against Autoregressive Disturbances in the Linear-Regression Model

This article considers testing for first-order moving average against first-order autoregressive disturbances in the linear-regression model. Tests investigated include approximate point-optimal invariant (POI) tests, an asymptotic test of the second-order residual autocorrelation coefficient, and a Lagrange multiplier. (LM) test. A Monte Carlo experiment compares their small-sample performances. Of the asymptotic tests, the LM test has the most satisfactory sizes, but its rival has the better overall power. We find that the approximate POI tests have superior size and power properties in comparison to the asymptotic tests. An approximate POI test is applied to a random-walk model for Australian real interest rates.

Tests Against Inequality Constraints When Some Nuisance Parameters Are Present Only under the Alternative: Test of ARCH in ARCH-M Models

In this article we develop improved statistical tests for situations satisfying the following two nonstandard conditions simultaneously: (a) Some nuisance parameters become unidentified under the null hypothesis, and (b) the alternative hypothesis is restricted in the sense that it has inequality constraints/multiparameter one-sided hypotheses. In the statistical and econometric literature, inference problems under these two nonstandard conditions have been studied separately but not simultaneously. For example, procedures to deal with the nonstandard condition (a) only have been studied by Bera and Ra and by Andrews and Ploberger; surveys of test procedures to deal with (b) only may be found in the work of Robertson, Wright, and Dykstra. A main contribution of this article is that, by pooling the ideas and insights from both these areas of literature, we develop new tests to deal with (a) and (b) simultaneously. Based on the approach that we take, we would conjecture that our tests should perform better than other tests that are available for tests under the nonstandard conditions (a) and (b). As an example, we consider the problem of testing whether or not the error variance is constant over time, in an ARCH-in-Mean (ARCH-M) model. We use this example to motivate and explain our ideas. A data example illustrates the application of the test in a simple situation. In a simulation study, we observed that the new test procedures proposed here performed better than the other available ones for this problem.

A Score Test For Seasonal Fractional Integration And Cointegration

This paper develops a time domain score statistic for testing fractional integration at zero and seasonal frequencies in quarterly time series models. Further, it introduces the notion of fractional cointegration at different frequencies between two seasonally integrated, I(1) series. In testing problems involving seasonal fractional cointegration, it is argued that the alternative hypothesis is one-sided for which the usual score test may not be appropriate. Therefore, based on ideas in Silvapulle and Silvapulle (1995), a one-sided score statistic is constructed. A simulation study finds that the score statistic generally has desirable size and power properties in moderately sized samples. The score test is applied to the quarterly Australian consumption function. The income and consumption series are found to be I(1) at zero and seasonal frequencies and these two series are not cointegrated at any frequency.

Nonnested testing for autocorrelation in the linear regression model

This paper investigates the construction and application of point-optimal invariant (POI) tests of joint AR(1)−AR(4) disturbances against jointMA(1)−MA(4) disturbances in the linear regression model. A Monte Carlo experiment is conducted to assess and compare the small sample performances of two asymptotic tests and two POI tests. Of the asymptotic tests, the Lagrange multiplier test is found to have distinctly better small sample properties than the prediction test. We also find that the extra computation required to perform a POI test is rewarded by a clear improvement in size and power properties in comparison to the asymptotic tests. The use of a POI test is illustrated with an application to a quarterly model of price inflation in the United Kingdom during 1947–1970. The paper concludes with some discussion of the problem of testing general AR(p) disturbances against MA(q) disturbances.

Tests against inequality constraints in semiparametric models

We consider the problem of testing that a subvector of a finite dimensional parameter is zero against that it satisfies some inequality constraints in a semiparametric model. To our knowledge, this problem has not been studied in the literature in a general context. Huang (Ann. Statist. 24 (1996) 540) developed maximum likelihood estimation in a class of semiparametric models, and Choi et al. (Ann. Statist. 24 (1996) 84) developed efficient tests against unrestricted alternatives in a large class of semiparametric models which includes the adaptable ones. In this paper, we introduce local tests as a general approach to developing tests against inequality constraints, and apply them in different semiparametric models. In particular, we apply our local tests to develop adaptive tests and efficient tests in the classes of semiparametric models studied by Huang (1996) and Choi et al. (1996), thus extending their results to inequality constrained framework.