Simulation Analysis of Threshold Autoregressive Unit Root Tests

Table 5

TAR symmetry testing in the presence of GARCH.

		(𝜙1,𝜙2)
		(0.01, 0.98)	(0.05, 0.94)	(0.10, 0.89)	(0.15, 0.84)	(0.25, 0.70)
	Φ𝜇	0.09	0.17	0.36	0.63	0.99
	Φ𝜇,𝑤	0.13	0.16	0.18	0.20	0.20
𝑇=200	Φ𝜇,𝑛	0.28	0.26	0.37	0.44	0.42
	Φ^𝑐𝜇	34.01	35.87	39.03	41.37	44.73
	Φ^𝑐𝜇,𝑤	35.52	35.39	35.05	34.37	34.90
	Φ^𝑐𝜇,𝑛	36.59	37.04	37.84	38.27	39.25
	Φ𝜇	0.14	0.25	0.90	1.86	2.61
	Φ𝜇,𝑤	0.15	0.15	0.21	0.24	0.34
𝑇=400	Φ𝜇,𝑛	0.22	0.26	0.34	0.45	0.57
	Φ^𝑐𝜇	29.37	31.84	35.54	38.72	41.60
	Φ^𝑐𝜇,𝑤	29.82	29.41	28.71	28.05	28.82
	Φ^𝑐𝜇,𝑛	30.85	31.14	31.46	31.90	33.18
	Φ𝜇	0.11	0.39	2.09	4.76	5.38
	Φ𝜇,𝑤	0.09	0.13	0.22	0.39	0.44
𝑇=800	Φ𝜇,𝑛	0.11	0.15	0.37	0.63	0.67
	Φ^𝑐𝜇	26.83	29.26	33.95	38.42	41.23
	Φ^𝑐𝜇,𝑤	26.52	25.20	23.73	23.01	24.20
	Φ^𝑐𝜇,𝑛	27.51	26.93	26.56	27.21	28.85

The reported results represent empirical sizes of the test of the symmetry hypothesis at the 5% level of significance for the TAR model under deterministic and consistent threshold estimation using alternative covariance matrix estimators. The results were derived over 20,000 simulations.