Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

Mildly explosive autoregression with mixing innovations

In this paper, the limit distribution of the least squares estimator for mildly explosive autoregressive models with strong mixing innovations is established, which is shown to be Cauchy as in the iid case. The result is applied to identify the onset and the end of an explosive period of an econometric time series. Simulations and data analysis are also conducted to demonstrate the usefulness of the result.     

Inference for a simultaneous linear partially explosive model with polynomial regression components of different degrees

This paper is concerned with the estimation of the coefficients of simultaneous partially explosive model with polynomial regression components of different degrees in its equations. Since the least squares method breaks down in this case, a three stage estimation procedure is suggested for obtaining CAN estimates of the coefficients.     

On the estimation of coefficients of a simultaneous linear explosive model of higher orders with moving average errors generating a pair of time series

In this paper, estimation of coefficients of simultaneous linear partially explosive model of higher orders with moving average errors is considered. It has been shown that the above model can be decomposed into a purely explosive model and an autoregressive model. A two stage estimation, procedure is carried out towards proposing estimators for the partially explosive model. The asymptotic properties of these estimators are also studied.     

Least squares estimation of the coefficients of a partially explosive model,with polynomial regressions of same degree,generating a pair of related time series

This paper is concerned with a partially explosive linear model with polynomial regression components generating a pair of related time series. The least squares estimates of the coefficients are shown to be √N-consistent and asymptotically singular normal, when the degrees of polynomial regression components are same, thus generalising a result due to Venkataraman (1974).     

Asymptotic theory of estimation of parameters in autoregressive models under general set-up of the roots

In this paper the asymptotic distribution of the least square estimator of the oarameters of a pth order autoreqressive process with stationary φ -mixing error variables having uniformly bounded fourth order moments has been considered. (That the error variables are also Gaussian has been assumed for the explosive case). A comoo-nent-wise break up of the process with respect to the roots has been made and the limiting distribution of each comoonent obtained by using the invariance principle of φ-mixing processes. The main aim of this paper is to reflect on the explosive case where a refinement of Anderson's technique (1959) has been made.     

Estimation in a semiparametric panel data model with nonstationarity

In this paper, we consider a partially linear panel data model with nonstationarity and certain cross-sectional dependence. Accounting for the explosive feature of the nonstationary time series, we particularly employ Hermite orthogonal functions in this study. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the unknown functions for the cases where N and T go jointly to infinity. Rates of convergence and asymptotic normalities are established for the proposed estimators. Both the finite sample performance and the empirical applications show that the proposed estimation methods work well.     

Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression

This paper provides a means of accurately simulating explosive autoregressive processes and uses this method to analyze the distribution of the likelihood ratio test statistic for an explosive second-order autoregressive process of a unit root. While the standard Dickey–Fuller distribution is known to apply in this case, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies. This has previously constituted a bar on supporting asymptotic results by means of simulation, and analyzing the finite sample properties of tests in the explosive region.     

Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression

This paper provides a means of accurately simulating explosive autoregressive processes and uses this method to analyze the distribution of the likelihood ratio test statistic for an explosive second-order autoregressive process of a unit root. While the standard Dickey-Fuller distribution is known to apply in this case, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies. This has previously constituted a bar on supporting asymptotic results by means of simulation, and analyzing the finite sample properties of tests in the explosive region.     

Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates

This article empirically compares the Markov-switching and stochastic volatility diffusion models of the short rate. The evidence supports the Markov-switching diffusion model. Estimates of the elasticity of volatility parameter for single-regime models unanimously indicate an explosive volatility process, whereas the Markov-switching models estimates are reasonable. Itis found that either Markov switching or stochastic volatility, but not both, is needed to adequately fit the data. A robust conclusion is that volatility depends on the level of the short rate. Finally, the Markov-switching model is the best for forecasting. A technical contribution of this article is a presentation of quasi-maximum likelihood estimation techniques for the Markov-switching stochastic-volatility model.     

Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

Admissibility of estimators in the non-regular family under entropy loss function

In this paper we have considered the problem of finding admissible estimates for a fairly general class of parametric functions in the so called “non-regular” type of densities. The admissibility of generalized Bayes and Pitman estimates of functions of parameters have been established under entropy loss function.     

美国R&D资本存量测算及对我国的启示

 内容提要：有关R&;D资本存量的测算理论与方法问题，国内研究尚处于起步阶段，国外一些学者则进行了较深入研究。美国BEA通过R&;D卫星账户的构建在R&;D资本存量方面积累了大量经验。本文首先分析了R&;D资本存量测算中存在的困难，并基于2007年美国R&;D卫星账户，对BEA关于R&;D资本存量的测算方法进行介绍与分析，最后指出了我国R&;D资本存量测算需要进一步做的工作。     

Bayesian and maximum likelihood estimations of the inverted exponentiated half logistic distribution under progressive Type II censoring

In this paper, the estimation of parameters, reliability and hazard functions of a inverted exponentiated half logistic distribution (IEHLD) from progressive Type II censored data has been considered. The Bayes estimates for progressive Type II censored IEHLD under asymmetric and symmetric loss functions such as squared error, general entropy and linex loss function are provided. The Bayes estimates for progressive Type II censored IEHLD parameters, reliability and hazard functions are also obtained under the balanced loss functions. However, the Bayes estimates cannot be obtained explicitly, Lindley approximation method and importance sampling procedure are considered to obtain the Bayes estimates. Furthermore, the asymptotic normality of the maximum likelihood estimates is used to obtain the approximate confidence intervals. The highest posterior density credible intervals of the parameters based on importance sampling procedure are computed. Simulations are performed to see the performance of the proposed estimates. For illustrative purposes, two data sets have been analyzed.     

Estimation for the parameters of the generalized half-normal distribution

As an applicable and flexible lifetime model, the two-parameter generalized half-normal (GHN) distribution has been received wide attention in the field of reliability analysis and lifetime study. In this paper maximum likelihood estimates of the model parameters are discussed and we also proposed corresponding bias-corrected estimates. Unweighted and weighted least squares estimates for the parameters of the GHN distribution are also presented for comparison purpose. Moreover, the likelihood ratio test is provided as complementary. Simulation study and illustrative examples are provided to compare the performance of the proposed methods.     

A NOTE ON ASYMPTOTIC POSTERIOR NORMALITY FOR STOCHASTIC PROCESSES

In a recent paper, Sweeting & Adekola (1987) presented a fairly general set of conditions for asymptotic posterior normality which covers a wide class of problems. In this paper we present an example of an explosive autoregressive model where our condition A4 does not hold.     

On the calculations of the maximum likelihood estimates for the polynomial spline regression model with unknown knots and AR(1) errors

Asymptotic distributions of the maximum likelihood estimators of the regression coefficients and knot points for the polynomial spline regression models with unknown knots and AR(1) errors have been derived by Chan (1989). Chan showed that under some mild conditions the maximum likelihood estimators, after suitable standardization, asymptotically follow normal distributions as n diverges to infinity. For the calculations of the maximum likelihood estimators, iterative methods must be applied. But this is not easy to implement for the model considered. In this paper, we suggested an alternative method to compute the estimates of the regression parameters and knots. It is shown that the estimates obtained by this method are asymptotically equivalent to the maximum likelihood estimates considered by Chan.     

When bubbles burst: econometric tests based on structural breaks

Speculative bubbles have played an important role ever since in financial economics. During an ongoing bubble it is relevant for investors and policy-makers to know whether the bubble continues to grow or whether it is already collapsing. Prices are typically well approximated by a random walk in absence of bubbles, while periods of bubbles are characterised by explosive price paths. In this paper we first propose a conventional Chow-type testing procedure for a structural break from an explosive to a random walk regime. It is shown that under the null hypothesis of a mildly explosive process a suitably modified Chow-type statistic possesses a standard normal limiting distribution. Second, a monitoring procedure based on the CUSUM statistic is suggested. It timely indicates such a structural change. Asymptotic results are derived and small-sample properties are studied via Monte Carlo simulations. Finally, two empirical applications illustrate the merits and limitations of our suggested procedures.     

Bayesian inference of the inverse Weibull mixture distribution using type-I censoring

A large number of models have been derived from the two-parameter Weibull distribution including the inverse Weibull (IW) model which is found suitable for modeling the complex failure data set. In this paper, we present the Bayesian inference for the mixture of two IW models. For this purpose, the Bayes estimates of the parameters of the mixture model along with their posterior risks using informative as well as the non-informative prior are obtained. These estimates have been attained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. For the former case, Bayes estimates are obtained under three loss functions while for the latter case only the squared error loss function is used. Simulation study is carried out in order to explore numerical aspects of the proposed Bayes estimators. A real-life data set is also presented for both cases, and parameters obtained under case when shape parameter is known are tested through testing of hypothesis procedure.     

RECURSIVE RESIDUALS FOR MULTIVARIATE REGRESSION MODELS

Recursive residuals and their relationship to the recursive estimation of regression parameters have been developed for unvaried regression mod els. Such residuals and estimates have been used to test the constancy of regression over time. The current paper extends this work to multivariate regression modal.