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1.
In this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data, is robust to strong serial correlation, and has a standard normal limiting null distribution under either I(0)I(0) or I(1)I(1) shocks. In contrast to other available robust linear trend tests, our proposed test achieves the Gaussian asymptotic local power envelope in both the I(0)I(0) and I(1)I(1) cases. For near-I(1)I(1) errors our proposed procedure is conservative and a modification for this situation is suggested. An estimator of the trend parameter, together with an associated confidence interval, which is asymptotically efficient, again regardless of whether the shocks are I(0)I(0) or I(1)I(1), is also provided.  相似文献   

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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   

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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   

5.
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   

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This paper is about how to estimate the integrated covariance X,YTX,YT of two assets over a fixed time horizon [0,T][0,T], when the observations of XX and YY are “contaminated” and when such noisy observations are at discrete, but not synchronized, times. We show that the usual previous-tick covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. This is an analytic characterization of the Epps effect. We also provide the optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization. Finally, a two scales covariance estimator is provided which simultaneously cancels (to first order) the Epps effect and the effect of microstructure noise. The gain is demonstrated in data.  相似文献   

11.
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   

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In a sample-selection model with the ‘selection’ variable QQ and the ‘outcome’ variable YY, YY is observed only when Q=1Q=1. For a treatment DD affecting both QQ and YY, three effects are of interest: ‘participation  ’ (i.e., the selection) effect of DD on QQ, ‘visible performance  ’ (i.e., the observed outcome) effect of DD on Y≡QYYQY, and ‘invisible performance  ’ (i.e., the latent outcome) effect of DD on YY. This paper shows the conditions under which the three effects are identified, respectively, by the three corresponding mean differences of QQ, YY, and Y|Q=1Y|Q=1 (i.e., Y|Q=1Y|Q=1) across the control (D=0D=0) and treatment (D=1D=1) groups. Our nonparametric estimators for those effects adopt a two-sample framework and have several advantages over the usual matching methods. First, there is no need to select the number of matched observations. Second, the asymptotic distribution is easily obtained. Third, over-sampling the control/treatment group is allowed. Fourth, there is a built-in mechanism that takes into account the ‘non-overlapping support problem’, which the usual matching deals with by choosing a ‘caliper’. Fifth, a sensitivity analysis to gauge the presence of unobserved confounders is available. A simulation study is conducted to compare the proposed methods with matching methods, and a real data illustration is provided.  相似文献   

14.
We propose a test for the slope of a trend function when it is a priori unknown whether the series is trend-stationary or contains an autoregressive unit root. The procedure is based on a Feasible Quasi Generalized Least Squares method from an AR(1) specification with parameter αα, the sum of the autoregressive coefficients. The estimate of αα is the OLS estimate obtained from an autoregression applied to detrended data and is truncated to take a value 1 whenever the estimate is in a T−δTδ neighborhood of 1. This makes the estimate “super-efficient” when α=1α=1 and implies that inference on the slope parameter can be performed using the standard Normal distribution whether α=1α=1 or |α|<1|α|<1. Theoretical arguments and simulation evidence show that δ=1/2δ=1/2 is the appropriate choice. Simulations show that our procedure has better size and power properties than the tests proposed by [Bunzel, H., Vogelsang, T.J., 2005. Powerful trend function tests that are robust to strong serial correlation with an application to the Prebish–Singer hypothesis. Journal of Business and Economic Statistics 23, 381–394] and [Harvey, D.I., Leybourne, S.J., Taylor, A.M.R., 2007. A simple, robust and powerful test of the trend hypothesis. Journal of Econometrics 141, 1302–1330].  相似文献   

15.
We consider a stochastic frontier model with error ε=v−uε=vu, where vv is normal and uu is half normal. We derive the distribution of the usual estimate of u,E(u|ε)u,E(u|ε). We show that as the variance of vv approaches zero, E(u|ε)−uE(u|ε)u converges to zero, while as the variance of vv approaches infinity, E(u|ε)E(u|ε) converges to E(u)E(u). We graph the density of E(u|ε)E(u|ε) for intermediate cases. To show that E(u|ε)E(u|ε) is a shrinkage of u towards its mean, we derive and graph the distribution of E(u|ε)E(u|ε) conditional on uu. We also consider the distribution of estimated inefficiency in the fixed-effects panel data setting.  相似文献   

16.
Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under αα-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators remain root-nn consistent (the optimal rate) under the whole family of stable distributions, irrespective of their asymmetry and tail index. While parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0)(α0,b0) of the tail index αα and skewness parameter bb, while preserving root-nn consistency under any (α,b)(α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.  相似文献   

17.
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   

18.
In this article we study coherent risk measures in general economic models where the set of financial positions is an ordered Banach space EE and the safe asset an order unit x0x0 of EE. First we study some properties of risk measures. We show that the set of normalized (with respect to x0x0) price systems is weak star compact and by using this result we prove a maximum attainment representation theorem which improves the one of Jaschke and Küchler (2001). Also we study how a risk measure changes under different safe assets and we show a kind of equivalence between these risk measures. In the sequel we study subspaces of EE consisting of financial positions of risk greater or equal to zero and we call these subspaces unsure. We find some criteria and we give examples of these subspaces. In the last section, we combine the unsure subspaces with the theory of price-bubbles of Gilles and LeRoy (1992).  相似文献   

19.
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   

20.
Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of nn individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we suggest and demonstrate how to use the false discovery rate (FDR)(FDR) in evaluating I(1)/I(0)I(1)/I(0) classifications.  相似文献   

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