Statistics and Its Interface
Volume 16 (2023)
Network vector autoregressive moving average model
Pages: 593 – 615
Modeling a continuous response of a large-scale network is an important task and it has become prevailing in practice at present. This paper proposes a novel network vector autoregressive moving average (NARMA) model which considers the responses from both an ultra-high dimension vector and the network structure effects. Compared with the network vector autoregressive (NAR, ) model, we take into account the lagged innovations and corresponding network effect in our proposed model. With more parameters considered and a moving average term incorporated, the proposed NARMA model can fit the data more closely and accurately, thus has a better performance than the NAR model. A modified least square estimation for the NARMA model is introduced, and the consistency properties are fully investigated. Finally, we demonstrate the superiority of the proposed NARMA model by investigating the financial contagions of S&P500 index constituents.
network data, modified least square estimator, vector autoregressive moving average, high dimensional time series
This paper was partially supported by NSFC (12101585, 71771203) and Natural Science Foundation of Anhui.
Received 8 April 2022
Accepted 26 June 2022
Published 14 April 2023