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Samadi, S.Y., Hajebi, M. and Farnoosh, R. (2019), A semiparametric approach for modelling multivariate nonlinear time series. Can J Statistics, 47: 668-687. doi:10.1002/cjs.11518
Multivariate time series data are becoming ubiquitous in many real world applications. The vector autoregressive (VAR) model, which is linear in both the model parameters and lagged variables, is one of the most common, successful, and easy to implement models for multivariate time series analysis. However, there are situations in which the use of a linear VAR model is inappropriate. For example, transportation costs associated with international trade may prevent a complete international arbitrage between the prices of the same goods in different locations. The existence of such price critical points or thresholds indicates that there will not be a response to price shocks for small values of the price difference, whereas there will be an asymmetric adjustment for higher values, that would invalidate the assumption of linearity. This paper considers a combination of parametric and nonparametric estimation approaches to estimate the nonlinear vector autoregressive function for both independent and weakly dependent stationary vector time series errors. First, the multivariate Taylor series expansion is used to parametrically approximate the vector autoregressive function. Then, the initial approximation of the nonlinear autoregressive function is adjusted and improved by multiplying it by a diagonal adjustment factor matrix which is estimated nonparametrically. Both the theoretical and the numerical results show that the proposed algorithms are effective and feasible.