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A portmanteau-type statistic based on sample covariance is proposed to test for the existence of the unit-root of an autoregressive model under a heavy-tailed linear noise, where the noise ɛ t = ∑ j = 0 ∞ d j η t − j and { η t } is a sequence of i.i.d. innovations belonging to the domain of attraction of an α -stable distribution for some α ∈ ( 0 , 2 ) . The proposed procedure is nonparametric and easy to implement. Under certain regular assumptions, the limit distribution of the statistics is shown to be a functional of a standard stable distribution. Further, the good finite sample studies show that the new test outperforms PP, DF and ADF tests in size and power. Applications to the daily world crude oil price and 3-month AA financial commercial paper rate are also given to illustrate the performance of the new test.

Because the ARMA–GARCH model can generate data with some important properties such as skewness, heavy tails, and volatility persistence, it has become a benchmark model in analyzing financial and economic data. The commonly employed quasi maximum likelihood estimation (QMLE) requires a finite fourth moment for both errors and the sequence itself to ensure a normal limit. The self-weighted quasi maximum exponential likelihood estimation (SWQMELE) reduces the moment constraints by assuming that the errors and their absolute values have median zero and mean one, respectively. Therefore, it is necessary to test zero median of errors before applying the SWQMELE, as changing zero mean to zero median destroys the ARMA–GARCH structure. This paper develops an efficient empirical likelihood test without estimating the GARCH model but using the GARCH structure to reduce the moment effect. A simulation study confirms the effectiveness of the proposed test. The data analysis shows that some financial returns do not have zero median of errors, which cautions the use of the SWQMELE.

The tail index is an important parameter in the whole of extreme value theory. In this article, we consider the estimation of the tail index in the presence of a random covariate, where the conditional distribution of the variable of interest is of Pareto-type. More precisely, we use a logarithmic function to link the tail index to the nonlinear predictor induced by covariates, which forms the nonparametric tail index regression models. To estimate the unknown function, we develop an estimation procedure via a local likelihood method. Consistency and asymptotic normality of the estimated functions are established. Subsequently, these theoretical results are illustrated through simulated and real datasets.

Physicochemical and gelation properties of myofibrillar proteins from silver carp surimi as affected by chopping under different vacuum degrees (0, 0.01, 0.02, 0.04, 0.06 and 0.08 MPa) were investigated. With the increase of vacuum degree, size and quantity of air bubbles in surimi paste decreased, disulfide bond content of myofibrillar proteins decreased significantly (p .05) and then slight increased (p .05), while surface hydrophobicity of myofibrillar proteins increased gradually (p .05). Gel mechanical properties, chemical interactions (nonspecific associations, hydrogen bond and hydrophobic interactions) and FAXL (cross-linking degree of free amino group) of heat-induced surimi gel increased significantly (p .05) with vacuum degree. Scanning electron microscopy (SEM) observation showed that three-dimensional network of surimi gel under higher vacuum degree was more compact and orderly. Results indicated that vacuum chopping imparted physicochemical and structural changes of fish myofibrillar protein, which might contribute to the improvement in gelling properties of myofibrillar proteins.

We propose empirical likelihood-based statistics to construct confidence regions for the regression coefficient of the parametric tail index regression model. Our limited simulation study shows the method is more accurate than the normal approximation in terms of coverage probability.

This paper deals with a new class of tail index varying coefficient models with the random covariate under Pareto-type distributions. To estimate the unknown coefficient functions, we develop an es...

Fisher’s Fiducial Inference for the parameters of a totality uniformly distributed on [α, β] is discussed. The corresponding fiducial distributions are derived. The maximum fiducial estimators, fiducial median estimators and fiducial expect estimators of α and β are got. The problems about the fiducial interval, fiducial region and hypothesis testing are discussed. An example which showed that Neyman-Pearson’s confidence interval has some place to be improved is illustrated. An idea about deriving fiducial distribution is proposed.