A similarity-based approach to time-varying coefficient non-stationary autoregression

We suggest in this article a similarity-based approach to time-varying coefficient non-stationary autoregression. In a given sample, the model can display characteristics consistent with stationary, unit root and explosive behaviour, depending on the similarity between the dependent variable and its past values. We establish consistency of the quasi-maximum likelihood estimator of the model, with a general norming factor. Asymptotic score-based hypothesis tests are derived. The model is applied to a data set comprised of dual stocks traded in NASDAQ and the Tokyo Stock Exchange.