The spatio-temporal autoregressive moving average (STARMA) model is frequently used in several studies of multivariate time series data, where the assumption of stationarity is important, but it is not always guaranteed in practice. One way to proceed is to consider locally stationary processes. In this paper we propose a time-varying spatio-temporal autoregressive and moving average (tvSTARMA) modelling based on the locally stationarity assumption. The time-varying parameters are expanded as linear combinations of wavelet bases and procedures are proposed to estimate the coefficients. Some simulations and an application to historical daily precipitation records of Midwestern states of the USA are illustrated.

翻译：时空自回归移动平均( STARMA)模型在多元时间序列数据研究中应用广泛，该模型对平稳性假设要求较高，但实际应用中该假设并不总能得到满足。一种可行的解决思路是采用局部平稳过程。本文基于局部平稳性假设，提出了一种时变时空自回归移动平均(tvSTARMA)建模方法。通过将时变参数展开为小波基函数的线性组合，我们提出了相应的系数估计方法。最后通过数值模拟和针对美国中西部地区历史日降水数据的实例分析验证了该方法。