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二重维纳积分的独立性AI 解读

In this paper a necessary and sufficient condition is obtained for two double Wiener integrals to be statistically independent, first in the case of symmetric and continuous kernels. It is also shown that, for more than two double Wiener integrals, pairwise independence implies mutual independence. After that, the continuity condition on the kernels is somewhat relaxed, and it is shown that Craig's (1943, Annals of Mathematical Statistics 14, 195–197) theorem on the…

季节单位根检验中 t 与 F 统计量极限分布的近似AI 解读

Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), Ghysels, Lee, and Noh (1994, Journal of Econometrics 62, 415–442), Smith and Taylor (1998, Journal of Econometrics 85, 269–288; 1999, Journal of Time Series Analysis 20, 453–476; 1999, Discussion paper 99-15 in economics, University of Birmingham), and Taylor (1998, Journal of Time Series Analysis 19, 349–368) have developed a method…

含高阶多项式趋势的单位根季节自回归模型AI 解读

Seasonal autoregressive models with a polynomial trend of higher degee are treated. In the unit root case, the limiting distribution of the normalized least squares estimator for the autoregressive parameter and that of the corresponding t -statistic are discussed as the length of the sample period tends to infinity. In the case where the polynomial trend has the second or third degree, the joint moment generating functions associated with these limiting distributions are…

近积分季节自回归模型中单位根检验统计量的渐近分布AI 解读

Seasonal autoregressive models with an intercept or linear trend are discussed. The main focus of this paper is on the models in which the intercept or trend parameters do not depend on the season. One of the most important results from this study is the asymptotic distribution for the ordinary least squares estimator of the autoregressive parameter obtained under nearly integrated condition, and another is the approximation to the limiting distribution of the t -statistic…

单位根原假设下若干检验统计量的渐近矩AI 解读

For three models of linear autoregression the moments of the asymptotic distributions of the test statistics for testing the unit root are obtained in the null case, when the true drift or trend is lacking.

含非零初值、局部漂移与趋势的近单位根模型：最小二乘估计与检验的渐近分布AI 解读

This paper considers the distribution of the Dickey-Fuller test in a model with non-zero initial value and drift and trend. We show how stochastic integral representations for the limiting distribution can be derived either from the local to unity approach with local drift and trend or from the continuous record asymptotic results of Sørensen [29]. We also show how the stochastic integral representations can be utilized as the basis for finding the corresponding…

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非稳定自回归误差下时间序列回归估计量极限分布的一般方法AI 解读

The authors consider the time series regression model where the error term follows a nonstable autoregressive process and present a general approach for delivering the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads them to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. The authors' methodology is illustrated and percent…

回归系数恒定性对随机游走备择检验的渐近理论AI 解读

The LBI (locally best invariant) test is suggested under normality for the constancy of regression coefficients against the alternative hypothesis that one component of the coefficients follows a random walk process. We discuss the limiting null behavior of the test statistic without assuming normality under two situations, where the initial value of the random walk process is known or unknown. The limiting distribution is that of a quadratic functional of Brownian motion…

正态性下周期图及相关统计量的近似分布AI 解读

Under normality, we obtain higher-order approximations to the distributions of the periodogram and related statistics. Our approach is based on the theorem which decomposes the periodogram into the sum of two independent random variables. It is seen that this decomposition enables us to study fairly closely the higher-order properties of not only the periodogram, but also periodogram-based statistics such as the estimators of the spectrum and prediction error variance. Some…