Simulation Analysis of Threshold Autoregressive Unit Root Tests

Table 4

MTAR unit root 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	4.99	5.99	7.61	9.09	8.78
	Φ^∗𝜇,𝑤	4.98	5.07	4.92	4.90	4.74
𝑇=200	Φ^∗𝜇,𝑛	5.06	5.23	5.22	5.01	4.50
	Φ^𝜇∗,𝑐	5.30	6.33	7.83	9.13	9.66
	Φ^∗,𝑐𝜇,𝑤	4.94	4.97	4.59	4.26	3.95
	Φ^∗,𝑐𝜇,𝑛	4.94	5.07	4.81	4.41	3.83
	Φ^∗𝜇	5.21	6.21	8.31	9.84	8.59
	Φ^∗𝜇,𝑤	5.06	4.92	4.78	4.63	4.28
𝑇=400	Φ^∗𝜇,𝑛	4.96	4.92	4.82	4.68	4.05
	Φ^𝜇∗,𝑐	4.96	6.54	8.42	10.12	9.74
	Φ^∗,𝑐𝜇,𝑤	5.00	4.63	4.21	3.80	3.43
	Φ^∗,𝑐𝜇,𝑛	4.95	4.52	4.09	3.68	3.14
	Φ^∗𝜇	5.09	6.29	8.15	10.04	8.04
	Φ^∗𝜇,𝑤	5.03	4.76	4.61	4.41	4.48
𝑇=800	Φ^∗𝜇,𝑛	5.25	5.02	4.82	4.59	4.43
	Φ^𝜇∗,𝑐	5.21	6.63	8.94	10.56	10.05
	Φ^∗,𝑐𝜇,𝑤	5.21	4.88	4.27	3.60	3.26
	Φ^∗,𝑐𝜇,𝑛	5.04	4.72	4.09	3.59	3.24

The reported results represent empirical sizes of the test of the unit root 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.