Modeling the price side of econometric models: An analysis of the underlying hypotheses

Using a non-linear vector autoregression, this paper investigates the dynamic interactions between a set of disaggregated price series. A hypothesis, positing that all sectoral prices are a function of a ‘major price index’, is tested and the way this hypothesis is used in econometric models is discussed. The model is based upon the theory of covariance stationary time series. Non-linear estimation procedures are used.     

The analysis of unbalanced linear models with variance components

Statistical inference for fixed effects, random effects and components of variance in an unbalanced linear model with variance components will be discussed. Variance components will be estimated by Restricted Maximum Likelihood. Iterative procedures for computing the estimates, such as Fisher scoring and the EM-algorithm, are described.     

Testing the specification of multivariate models in the presence of alternative hypotheses

In this paper we propose a non-nested hypothesis test for testing the specification of a multivariate econometric model in the presence of an alternative model which purports to explain the same phenomenon. We demonstrate that the new test statistic tends to minus the same random variable as the CPD test statistic introduced by Pesaran and Deaton (1978), provided that the truth is ‘close’ to the null hypothesis. Since the new test is simpler to compute than the multivariate CPD test, it would seem to be the procedure of choice.     

A two-stage test for one-way analysis of variance

A two-stage analogue of the Ftest for one-way analysis of variance is proposed. Critical values are given for selected cases and the method of obtaining critical values is described. Comparisons of the one-stage and two-stage tests are made in terms of the expected sample size required to achieve a given power.     

Exact and asymptotic tests for possibly non-regular hypotheses on stochastic volatility models

We study the problem of testing hypotheses on the parameters of one- and two-factor stochastic volatility models (SV), allowing for the possible presence of non-regularities such as singular moment conditions and unidentified parameters, which can lead to non-standard asymptotic distributions. We focus on the development of simulation-based exact procedures–whose level can be controlled in finite samples–as well as on large-sample procedures which remain valid under non-regular conditions. We consider Wald-type, score-type and likelihood-ratio-type tests based on a simple moment estimator, which can be easily simulated. We also propose a C(α)-type test which is very easy to implement and exhibits relatively good size and power properties. Besides usual linear restrictions on the SV model coefficients, the problems studied include testing homoskedasticity against a SV alternative (which involves singular moment conditions under the null hypothesis) and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors (which raises identification difficulties). Three ways of implementing the tests based on alternative statistics are compared: asymptotic critical values (when available), a local Monte Carlo (or parametric bootstrap) test procedure, and a maximized Monte Carlo (MMC) procedure. The size and power properties of the proposed tests are examined in a simulation experiment. The results indicate that the C(α)-based tests (built upon the simple moment estimator available in closed form) have good size and power properties for regular hypotheses, while Monte Carlo tests are much more reliable than those based on asymptotic critical values. Further, in cases where the parametric bootstrap appears to fail (for example, in the presence of identification problems), the MMC procedure easily controls the level of the tests. Moreover, MMC-based tests exhibit relatively good power performance despite the conservative feature of the procedure. Finally, we present an application to a time series of returns on the Standard and Poor’s Composite Price Index.     

Joint and marginal specification tests for conditional mean and variance models

This article proposes a class of joint and marginal spectral diagnostic tests for parametric conditional means and variances of linear and nonlinear time series models. The use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified. The new tests are based on a generalized spectral approach and do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, the proposed tests are robust to higher order dependence of unknown form, in particular to conditional skewness and kurtosis. It turns out that the asymptotic null distributions of the new tests depend on the data generating process. Hence, we implement the tests with the assistance of a wild bootstrap procedure. A simulation study compares the finite sample performance of the proposed and competing tests, and shows that our tests can play a valuable role in time series modeling. Finally, an application to the S&P 500 highlights the merits of our approach.     

Canonical forms and tests of hypotheses Part II: Multivariate mixed linear models

Abstract  In the literature on multivariate analysis of variance, exact test procedures are restricted to linear models with fixed effects only. In this paper tests are presented for multivarite linear hypotheses with respect to mixed models, which constitude a generalization of (univariate) regular models described by R oebruck (1982). Furthermore it is shown, that the matrices, which are used to compute the test statistics, can be derived from the univariate "sums of squares" in the same manner as in the case of fixed models. The applicability of this theory is demonstrated by two examples.     

Efficiencies for optimum designs when transforming the response in nonlinear models with nonconstant variance

Often the responses from mechanistic models have to be transformed to achieve error distributions that are symmetric and have constant variance. Because of the nature of the relationship between the response and the mechanistic model, it is necessary to transform both sides of the model. Expressions are given for the parameter sensitivities in the transformed model and examples given of optimum designs for particular values of λ, together with the efficiency of these designs as λ varies. Approaches to finding designs robust to variations in λ are indicated and exemplified.     

Charity brands: A qualitative study of current practice

A number of fundraising managers and directors of UK charities were interviewed with the objective of understanding to what extent branding was used in the sector, what development possibilities exist for commercial techniques in charities, and what the constraints may be on such practices. It was found that many charities already use day-to-day brand techniques, (without describing them as ‘branding’), but brand development work was scarce. Charities have a number of objectives competing with fundraising when considering their brand content. They must also satisfy the need to respect issues about how the cause itself is communicated, and possible needs to re-educate the donor community or the public. One commercial practice in particular could be developed further in charity branding: this is the idea of using the personality of the charity itself as something with which donors could associate positively.     

Conditional feature screening for mean and variance functions in models with multiple-index structure

The existing methods for feature screening focus mainly on the mean function of regression models. The variance function, however, plays an important role in statistical theory and application. We thus investigate feature screening for mean and variance functions with multiple-index framework in high dimensional regression models. Notice that some information about predictors can be known in advance from previous investigations and experience, for example, a certain set of predictors is related to the response. Based on the conditional information, together with empirical likelihood, we propose conditional feature screening procedures. Our methods can consistently estimate the sets of active predictors in the mean and variance functions. It is interesting that the proposed screening procedures can avoid estimating the unknown link functions in the mean and variance functions, and moreover, can work well in the case of high correlation among the predictors without iterative algorithm. Therefore, our proposal is of computational simplicity. Furthermore, as a conditional method, our method is robust to the choice of the conditional set. The theoretical results reveal that the proposed procedures have sure screening properties. The attractive finite sample performance of our method is illustrated in simulations and a real data application.     

Two kinds of variance/covariance estimates in linear mixed models

For longitudinal data, the within-subject covariance matrix plays an important role in statistical inference and it is of great interest to investigate this. In the paper, two kinds of estimators are investigated for the random effect covariance matrix D ₁ and the error variance σ ² in linear mixed models. One is to estimate D ₁ first and then to estimate σ ²; the other kind is to estimate σ ² first and then for D ₁. Both kinds of estimators are consistent. The covariance matrices of these covariance estimators and the variances of these two error variance estimators are calculated. In particular, the mean square errors of these estimators are also derived for one dimensional random effects. Besides, a simulation study is conducted to investigate the performances of these estimators.     

The locally MIMSQE of nonnormal error variance in quadratically balanced models

Without normality assumption, an explicit form of the locally minimum mean square error translation-invariant quadratic estimator for the error variance in a quadratically balanced design is obtained. The estimator depends on the kurtosis of the random error. Under the normality the estimator becomes globally optimal.     

On the properties of the coefficient of determination in regression models with infinite variance variables

We examine the asymptotic properties of the coefficient of determination, R²$R^2$, in models with α-stable$\alpha \text{-stable}$   random variables. If the regressor and error term share the same index of stability α<2$\alpha <2$, we show that the R²$R^2$  statistic does not converge to a constant but has a nondegenerate distribution on the entire [0,1]$[0,1]$ interval. We provide closed-form expressions for the cumulative distribution function and probability density function of this limit random variable, and we show that the density function is unbounded at 0 and 1. If the indices of stability of the regressor and error term are unequal, we show that the coefficient of determination converges in probability to either 0 or 1, depending on which variable has the smaller index of stability, irrespective of the value of the slope coefficient. In an empirical application, we revisit the Fama and MacBeth (1973) two-stage regression and demonstrate that in the infinite-variance case the R²$R^2$  statistic of the second-stage regression converges to 0 in probability even if the slope coefficient is nonzero. We deduce that a small value of the R²$R^2$  statistic should not, in itself, be used to reject the usefulness of a regression model.     

Specification testing in discretized diffusion models: Theory and practice

We propose two new tests for the specification of both the drift and the diffusion functions in a discretized version of a semiparametric continuous-time financial econometric model. Theoretically, we establish some asymptotic consistency results for the proposed tests. Practically, a simple selection procedure for the bandwidth parameter involved in each of the proposed tests is established based on the assessment of the power function of the test under study. To the best of our knowledge, this is the first approach of this kind in specification of continuous-time financial econometrics. The proposed theory is supported by good small and medium-sample studies.     

The best quadratic estimator of the residual variance in regression analysis

De beste kwadratische schattingsfunctie van de storingsvariantie in regressie-analyse.
Dit artikel handelt over de schatting van de variantie σ² van de storingen in de regressieanalyse onder klassieke veronderstellingen: niet-stochastische waarden aangenomen door de verklarende variabelen en normaliteit, onafhankelijkheid en homoskedasticiteit van de storingen. Bekend is dat de schatting volgens maximale aannemelijkheid neerkomt op net bepalen van de kwadratensom van de volgens kleinste-kwadraten geschatte storingen en deling door T (het aantal waarne-mingen); voorts, dat de schatting die minimale variantie heeft binnen de klasse van schattingsfuncties die zuiver zijn en kwadratisch in de afhankelijke variabele (de beste zuivere kwadratische schattingsfunctie) gevonden wordt door genoemde kwadratensom te delen door T–A, waarbij λ het aantal te schatten coëfficiënten is [d.w.z. het aantal verklarende variabelen (+ 1 indien een constante term aanwezig is)]. Hier wordt aangetoond, dat de schattingsfunctie van σ² die een minimaal tweede moment heeft binnen de klasse van schattingsfuncties die kwadratisch zijn in de afhankelijke variabele (de beste kwadratische schattingsfunctie) gevonden wordt door de kwadratensom van de volgens kleinste kwadraten geschatte storingen te delen door T–Λ+ 2.     

Repeated substitution method: The ratio estimator for the population variance

This paper proposes a new unbiased estimator for the population variance in finite population sample surveys using auxiliary information. This estimator has a smaller mean squared error than the conventional unbiased estimator, the ratio estimator established by Isaki (1983) and it has the same precision than the regression estimator. Furthermore, it is a much more interesting estimator from the computation viewpoint.     

上市公司资本结构行业差异分析

本文基于我国10个行业上市公司连续5年的面板数据分行业建立的动态调整模型.研究发现:我国上市公司的资本结构存在显著的行业差异;资本结构影响因素对不同行业的影响力的大小和方向也存在很大差异;同时各行业受宏观经济因素的影响,资本结构的调整成本和资本结构的适宜度也各不相同.