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同期相关的双变量时间序列AI 解读

Bivariate autoregressive-moving average time series with diagonal parameter matrices for the autoregressive and moving average components exhibit only contemporaneous or instantaneous correlation. In practice, different lengths of each series may be available. An efficient maximum likelihood algorithm for parameter estimation is derived. The statistical efficiency of this new procedure is compared with that of the standard multivariate and univariate procedures which utilize…

分数差分时间序列建模AI 解读

Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy.

分数差分时间序列建模AI 解读

Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy.

乘法季节 ARMA 模型的对偶性及其他性质AI 解读

Model duality is defined between four models referred to as the primal, the dual, the autoregressive adjoint and the moving average adjoint. A duality theorem which generalizes the results of Box & Pierce (1970) and Pierce (1970) is presented. Applications of this duality theorem to autoregressive-moving average models and multiplicative seasonal autoregressive-moving average models are discussed. These applications include: (i) a convenient method for calculating the…

多变量ARMA时间序列模型中残差自相关的分布AI 解读

SUMMARY The large-sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.

Box–Jenkins模型残差自相关的分布AI 解读

Summary The large sample distribution of the residual autocorrelations in the arma model is derived. The main advantage of this derivation over that of Box and Pierce (1970) is that it extends directly to more general situations. Generalizations of the derived distribution are presented for the residual autocorrelations in the multiplicative seasonal arma model and for the autocorrelations of a subseries of the residuals.