Statistics and Its Interface

Volume 16 (2023)

Number 4

Network vector autoregressive moving average model

Pages: 593 – 615

DOI: https://dx.doi.org/10.4310/22-SII747

Authors

Xiao Chen (Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anui, China)

Yu Chen (Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anui, China)

Xixu Hu (School of Data Science, City University of Hong Kong)

Abstract

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, [26]) 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.

Keywords

network data, modified least square estimator, vector autoregressive moving average, high dimensional time series

Received 8 April 2022

Accepted 26 June 2022

Published 14 April 2023