Simulation Analysis of Threshold Autoregressive Unit Root Tests

Table 6

MTAR 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)
	Φ^∗𝜇	4.35	5.41	7.43	9.80	11.62
	Φ^∗𝜇,𝑤	4.98	4.94	5.29	5.42	5.46
𝑇=200	Φ^∗𝜇,𝑛	6.11	6.22	6.71	7.23	7.43
	Φ^𝜇∗,𝑐	26.71	30.73	35.95	40.28	43.13
	Φ^∗,𝑐𝜇,𝑤	29.73	30.09	29.37	28.93	27.49
	Φ^∗,𝑐𝜇,𝑛	33.15	33.93	33.98	34.06	33.42
	Φ^∗𝜇	4.50	6.12	9.35	12.64	14.41
	Φ^∗𝜇,𝑤	4.68	4.82	4.90	5.09	5.10
𝑇=400	Φ^∗𝜇,𝑛	5.68	5.87	6.18	6.55	6.56
	Φ^𝜇∗,𝑐	25.11	30.24	37.19	43.18	44.91
	Φ^∗,𝑐𝜇,𝑤	25.72	26.05	25.66	24.81	23.72
	Φ^∗,𝑐𝜇,𝑛	28.06	28.62	29.15	29.14	28.95
	Φ^∗𝜇	4.73	7.14	12.12	17.05	18.63
	Φ^∗𝜇,𝑤	4.68	4.94	5.04	5.16	4.94
𝑇=800	Φ^∗𝜇,𝑛	5.20	5.40	5.84	6.30	6.29
	Φ^𝜇∗,𝑐	21.68	27.70	37.28	44.45	44.76
	Φ^∗,𝑐𝜇,𝑤	21.49	21.27	21.02	20.70	20.04
	Φ^∗,𝑐𝜇,𝑛	22.60	23.19	24.03	24.32	24.09

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