# Nonlinear network vector autoregression

Student thesis: Doctoral Thesis

### Abstract

As we all know, the time series model is one of the most important aspects of modern econometric analysis. The autoregressive model is the theoretical basis of time series. The classic autoregressive model has two features that can be improved, linear, and one-dimensional. Economic theory shows that many important macroeconomic time series exhibit nonlinear characteristics. If this non-linear feature is ignored, the conclusion is likely to be wrong by only using linear analysis. Therefore, it is necessary to expand the linear model and propose nonlinear methods. Economic theory also shows that there is a mutual influence between individuals, and it is also necessary to consider it as a network.In this dissertation, we consider three nonlinear autoregressive models for timeseries with network structure: The Threshold Network autoregressive (TNAR) model, the Threshold Network quantile autoregressive (TNQAR) model and the Markov Switching Network autoregressive (MS-NAR) model. For the TNAR model, we provide the parameter conditions for the stationary of the time series. Under this parameter condition, the TNAR process can be approximated by the geometrically ergodic process. Under these conditions, we discuss the statistical inference (estimation and test) of the TNAR model and give the asymptotic theory on the inference. The test for nonlinearity is applied. Simulation results and modeling for Twitter data were applied to support our methodology for TNAR models.For the TNQAR model, we also provide the parameter conditions for the stationary of the time series. Under these parameter conditions, the TNQAR process can be approximated by the geometric traversal process. Under these condition, we discuss the statistical inference (estimation and test) of the TNQAR model and give the asymptotic theory on the inference. A normality test is applied on the data and a Hill estimator is provided to check whether the conditional distribution of the historical information is a thick tail or not. Simulation results and modeling of hedge fund data were used to support our methodology for TNQAR models. The Markovian Switching model is provided and its maximum likelihood estimation method is discussed. Finally, the techniques and the process in collecting Twitter data are presented.
Date of Award 19 Oct 2020 English University Of Strathclyde University of Strathclyde Jiazhu Pan (Supervisor) & Xuerong Mao (Supervisor)

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