Introduction to m–m processes

In this paper, we introduce a new type of nonlinear model, called the min–max model, and analyze its properties for a pair of series. The stability conditions of this system are given for a nonlinearly integrated bivariate series. Under these stability conditions, the difference between the two series exhibits threshold-type nonlinearity. It is possible to construct a threshold error correction model from the min–max processes. Neglected nonlinearity tests are applied, both to the univariate series and to the bivariate system, in order to detect nonlinearity, and it turns out that the tests using the bivariate series have better power. We apply the min–max model to U.S. Treasury bills and commercial paper interest rates. The spread of these interest rates shows threshold-type nonlinearity, and this model outperforms a linear model in terms of its predictability for out-of-sample data.