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**Testing and modeling multivariate threshold models.**
*(English)*
Zbl 1063.62578

Summary: Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this article I use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The finite-sample performance of the proposed test is studied by simulation. The modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost of carrying the contracts. In this particular application, thresholds are determined in part by the transaction costs. I also apply the proposed procedure to U.S. monthly interest rates and two river flow series of Iceland.

### MSC:

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |