3.2. Test statisticsIn this section, we conduct Monte-Carlo experiments to examine the size and power properties of the test statistic for the existence of threshold, F1, and for threshold constancy, F2, proposed in Section 2.3. To examine the finite sample performance of the statistic F1 (the linear model against the time-varying threshold model), we set γ0 = 0, γ1 = γ2 = 1, β0 = 1, and β1 = 1. Thus, the rejection frequencies under the DGP given by (16) with β2 = 1 and β2 = {1.5, 2} are the size and power for the test statistic F1, respectively.