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1.
We examine the asymptotic properties of the coefficient of determination, R2R2, in models with α-stableα-stable   random variables. If the regressor and error term share the same index of stability α<2α<2, we show that the R2R2  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 R2R2  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 R2R2  statistic should not, in itself, be used to reject the usefulness of a regression model.  相似文献   

2.
This paper develops a bootstrap theory for models including autoregressive time series with roots approaching to unity as the sample size increases. In particular, we consider the processes with roots converging to unity with rates slower than n-1n-1. We call such processes weakly   integrated processes. It is established that the bootstrap relying on the estimated autoregressive model is generally consistent for the weakly integrated processes. Both the sample and bootstrap statistics of the weakly integrated processes are shown to yield the same normal asymptotics. Moreover, for the asymptotically pivotal statistics of the weakly integrated processes, the bootstrap is expected to provide an asymptotic refinement and give better approximations for the finite sample distributions than the first order asymptotic theory. For the weakly integrated processes, the magnitudes of potential refinements by the bootstrap are shown to be proportional to the rate at which the root of the underlying process converges to unity. The order of boostrap refinement can be as large as o(n-1/2+?)o(n-1/2+?) for any ?>0?>0. Our theory helps to explain the actual improvements observed by many practitioners, which are made by the use of the bootstrap in analyzing the models with roots close to unity.  相似文献   

3.
A new test is proposed for the weak white noise null hypothesis. The test is based on a new automatic selection of the order for a Box–Pierce (1970) test statistic or the test statistic of Hong (1996). The heteroskedasticity and autocorrelation-consistent (HAC) critical values from Lee (2007) are used, allowing for estimation of the error term. The data-driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o(n−1/2)o(n1/2) provided there are sufficiently many of such coefficients. A simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative.  相似文献   

4.
We correct the limit theory presented in an earlier paper by Hu and Phillips [2004a. Nonstationary discrete choice. Journal of Econometrics 120, 103–138] for nonstationary time series discrete choice models with multiple choices and thresholds. The new limit theory shows that, in contrast to the binary choice model with nonstationary regressors and a zero threshold where there are dual rates of convergence (n1/4n1/4 and n3/4n3/4), all parameters including the thresholds converge at the rate n3/4n3/4. The presence of nonzero thresholds therefore materially affects rates of convergence. Dual rates of convergence reappear when stationary variables are present in the system. Some simulation evidence is provided, showing how the magnitude of the thresholds affects finite sample performance. A new finding is that predicted probabilities and marginal effect estimates have finite sample distributions that manifest a pile-up, or increasing density, towards the limits of the domain of definition.  相似文献   

5.
Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O(n−1)O(n1). This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O(n−3/2)O(n3/2). We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.  相似文献   

6.
7.
In this paper we show that the Quasi ML estimation method yields consistent Random and Fixed Effects estimators for the autoregression parameter ρρ in the panel AR(1) model with arbitrary initial conditions and possibly time-series heteroskedasticity even when the error components are drawn from heterogeneous distributions. We investigate both analytically and by means of Monte Carlo simulations the properties of the QML estimators for ρρ. The RE(Q)MLE for ρρ is asymptotically at least as robust to individual heterogeneity and, when the data are i.i.d. and normal, at least as efficient as the FE(Q)MLE for ρρ. Furthermore, the QML estimators for ρρ only suffer from a ‘weak moment conditions’ problem when ρρ is close to one if the cross-sectional average of the variances of the errors is (almost) constant over time, e.g. under time-series homoskedasticity. However, in this case the QML estimators for ρρ are still consistent when ρρ is local to or equal to one although they converge to a non-normal possibly asymmetric distribution at a rate that is lower than N1/2N1/2 but at least N1/4N1/4. Finally, we study the finite sample properties of two types of estimators for the standard errors of the QML estimators for ρρ, and the bounds of QML based confidence intervals for ρρ.  相似文献   

8.
An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d∈(−1/2,1/2)d(1/2,1/2). The class of spectral densities considered includes as a special case the stationary and invertible ARFIMA(p,d,qp,d,q) model. The leading term of the expansion is of the order O(1/k1−2d)O(1/k12d), where kk is the autocovariance order, consistent with the well known power law decay for such processes, and is shown to be accurate to an error of O(1/k3−2d)O(1/k32d). The derivation uses Erdélyi’s [Erdélyi, A., 1956. Asymptotic Expansions. Dover Publications, Inc, New York] expansion for Fourier-type integrals when there are critical points at the boundaries of the range of integration - here the frequencies {0,2π}{0,2π}. Numerical evaluations show that the expansion is accurate even for small kk in cases where the autocovariance sequence decays monotonically, and in other cases for moderate to large kk. The approximations are easy to compute across a variety of parameter values and models.  相似文献   

9.
No-arbitrage macro-finance models use variance decompositions to gauge the extent of association between the macro variables and yields. We show that results generated by this approach are sensitive to the order of variables in the recursive identification scheme. In a four-factor model, one may obtain 18 different sets of answers out of 24 possible. We propose an alternative measure that is based on levels of macro variables as opposed to shocks. We account for the correlation between the macro and latent factors via projection of the latter onto the former. As a result, the association between macro variables and yields can be computed uniquely via an R2R2. Macro variables explain 80% of the variation in the short rate and 50% of the slope, and 54% to 68% of the term premia.  相似文献   

10.
This article proposes a nonparametric test of monotonicity for conditional distributions and its moments. Unlike previous proposals, our method does not require smooth estimation of the derivatives of nonparametric curves. Distinguishing features of our approach are that critical values are pivotal under the null in finite samples and that the test is invariant to any monotonic continuous transformation of the explanatory variable. The test statistic is the sup-norm of the difference between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate. The resulting test is able to detect local alternatives converging to the null at the parametric rate n−1/2n1/2, with nn the sample size. The finite sample performance of the test is examined by means of a Monte Carlo experiment and an application to testing intergenerational income mobility.  相似文献   

11.
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 χ2χ2-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.  相似文献   

12.
In this paper we derive an asymptotic theory for linear panel regression augmented with estimated common factors. We give conditions under which the estimated factors can be used in place of the latent factors in the regression equation. For the principal components estimate of the factor space it is shown that these conditions are satisfied when T/N→0T/N0 and N/T3→0N/T30 under regularity. Monte Carlo studies verify the asymptotic theory.  相似文献   

13.
This paper is concerned with the discrete time stochastic volatility model Yi=exp(Xi/2)ηiYi=exp(Xi/2)ηi, Xi+1=b(Xi)+σ(Xi)ξi+1Xi+1=b(Xi)+σ(Xi)ξi+1, where only (Yi)(Yi) is observed. The model is rewritten as a particular hidden model: Zi=Xi+εiZi=Xi+εi, Xi+1=b(Xi)+σ(Xi)ξi+1Xi+1=b(Xi)+σ(Xi)ξi+1, where (ξi)(ξi) and (εi)(εi) are independent sequences of i.i.d. noise. Moreover, the sequences (Xi)(Xi) and (εi)(εi) are independent and the distribution of εε is known. Then, our aim is to estimate the functions bb and σ2σ2 when only observations Z1,…,ZnZ1,,Zn are available. We propose to estimate bfbf and (b22)f(b2+σ2)f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces. By ratio strategy, estimators of bb and σ2σ2 are then deduced. The mean square risk of the resulting estimators are studied and their rates are discussed. Lastly, simulation experiments are provided: constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples.  相似文献   

14.
15.
This paper extends the cross-sectionally augmented panel unit root test (CIPSCIPS) proposed by Pesaran (2007) to the case of a multifactor error structure, and proposes a new panel unit root test based on a simple average of cross-sectionally augmented Sargan–Bhargava statistics (CSBCSB). The basic idea is to exploit information regarding the mm unobserved factors that are shared by kk observed time series in addition to the series under consideration. Initially, we develop the tests assuming that m0m0, the true number of factors, is known and show that the limit distribution of the tests does not depend on any nuisance parameters, so long as k≥m0−1km01. Small sample properties of the tests are investigated by Monte Carlo experiments and are shown to be satisfactory. Particularly, the proposed CIPSCIPS and CSBCSB tests have the correct size for all   combinations of the cross section (NN) and time series (TT) dimensions considered. The power of both tests rises with NN and TT, although the CSBCSB test performs better than the CIPSCIPS test for smaller sample sizes. The various testing procedures are illustrated with empirical applications to real interest rates and real equity prices across countries.  相似文献   

16.
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 χ2χ2-distributed. An application to an internal rating data set reveals highly significant instationarity.  相似文献   

17.
18.
We consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable ΔΔ is influenced by a set of covariates that can be partitioned as (X,Z)(X,Z) where ZZ (real valued) is the covariate of primary interest and XX (vector valued) denotes a set of control variables. For any fixed XX, the conditional probability of the event of interest (Δ=1Δ=1) is assumed to be a non-decreasing function of ZZ. The effect of the control variables is captured by a regression parameter ββ. We show that the baseline conditional probability function (corresponding to X=0X=0) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing asymptotic confidence intervals for the conditional probability function (the regression function) that avoids the need to estimate nuisance parameters. Interestingly enough, the calibration of the likelihood ratio based confidence sets for the regression function no longer involves the usual χ2χ2 quantiles, but those of the distribution of a new random variable that can be characterized as a functional of convex minorants of Brownian motion with quadratic drift. Confidence sets for the regression parameter ββ can however be constructed using asymptotically χ2χ2 likelihood ratio statistics. The finite sample performance of the methods are assessed via a simulation study. The techniques of the paper are applied to data sets on primary school attendance among children belonging to different socio-economic groups in rural India.  相似文献   

19.
In this paper, we make five contributions to the literature on information and entropy in generalized method of moments (GMM) estimation. First, we introduce the concept of the long run canonical correlations (LRCCs) between the true score vector and the moment function f(vt,θ0)f(vt,θ0) and show that they provide a metric for the information contained in the population moment condition E[f(vt,θ0)]=0E[f(vt,θ0)]=0. Second, we show that the entropy of the limiting distribution of the GMM estimator can be written in terms of these LRCCs. Third, motivated by the above results, we introduce an information criterion based on this entropy that can be used as a basis for moment selection. Fourth, we introduce the concept of nearly redundant moment conditions and use it to explore the connection between redundancy and weak identification. Fifth, we analyse the behaviour of the aforementioned entropy-based moment selection method in two scenarios of interest; these scenarios are: (i) nonlinear dynamic models where the parameter vector is identified by all the combinations of moment conditions considered; (ii) linear static models where the parameter vector may be weakly identified for some of the combinations considered. The first of these contributions rests on a generalized information equality that is proved in the paper, and may be of interest in its own right.  相似文献   

20.
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