Abstract

In applications of the fitting and forecasting of Seasonal Vector AutoRegressive Moving Average (SVARMA) models, it is important to quickly and accurately compute the autocovariances. Recursive time domain approaches rely on expressing the seasonal AutoRegressive matrix polynomials as a high order non-seasonal AutoRegressive matrix polynomial; initialization of the recursions is therefore costly, because a large-dimensional matrix must be inverted. However, the resulting high-order polynomial has many zeroes that are not intelligently exploited, indicating that this time domain approach is not optimal. It is proposed to compute the autocovariances via integrating the spectral density, taking advantage of analytical expressions for the inverse AutoRegressive matrix polynomials in terms of determinant and adjoint. The R and RCPP code can be hundreds of times faster than the time domain methods when the dimension and seasonal period are large.

摘要

在季节向量自回归移动平均（SVARMA）模型的拟合和预测应用中，快速准确地计算自协方差非常重要。递归时域方法依赖于将季节性自回归矩阵多项式表示为高阶非季节性自回归矩阵多项式；因此，递归的初始化成本很高，因为必须反转大维矩阵。然而，得到的高阶多项式有许多没有被智能利用的零，表明这种时域方法不是最优的。建议通过积分谱密度来计算自协方差，利用逆自回归矩阵多项式在行列式和伴随方面的解析表达式。