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修订与勘误：ARMA过程样本逆自相关的渐近分布
J. R. M. Hosking, Amendments and Corrections: The Asymptotic Distribution of the Sample Inverse Autocorrelations of an Autoregressive Moving-Average Process, Biometrika, Vol. 69, No. 2 (Aug., 1982), p. 491
多元时间序列模型的拉格朗日乘子检验
SUMMARY Generalizing Hosking (1980a), the Lagrange-multiplier test procedure is applied to hypotheses concerning multivariate autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of-fit tests for multivariate processes are derived in this manner and three other tests are obtained for multivariate moving-average models.
分数阶差分
The family of autoregressive integrated moving-average processes, widely used in time series analysis, is generalized by permitting the degree of differencing to take fractional values. The fractional differencing operator is defined as an infinite binomial series expansion in powers of the backward-shift operator. Fractionally differenced processes exhibit long-term persistence and antipersistence; the dependence between observations a long time span apart decays much more…
多变量 Portmanteau 综合检验统计量
Box and Pierce have derived a goodness-of-fit test, the portmanteau test, for univariate autoregressive moving-average (ARMA) time series models. This test is here extended to multivariate ARMA models; the test statistic may be conveniently expressed as a function of the covariances between the residuals of the fitted model. A modified form of the statistic designed to have superior properties in small samples is derived, and the two forms of the statistic are compared via…
ARMA 过程样本逆自相关的渐近分布
The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.
时间序列模型的拉格朗日乘子检验
Summary The Lagrange-multiplier test procedure is applied to hypotheses concerning autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of fit tests are derived in this manner against specific alternative hypotheses and two other tests are obtained which have the nature of pure significance tests.
ARMA 过程样本逆自相关的渐近分布
The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.
参数估计后 ARMA 时间序列模型中 R² 的渐近分布
The properties of the estimator of the squared multiple correlation coefficient, R2, for an autoregressive-moving average process are considered. It is shown that the estimator has an asymptotic distribution which is normal with mean .R2 and variance obtainable from the autocorrelations of the process.
自回归时间序列拟合优度统计量渐近分布的统一推导
Summary The portmanteau and Quenouille goodness-of-fit tests for an ar(p) model are derived as likelihood-ratio tests against particular alternative hypotheses, and their asymptotic distributions are thereby obtained.