Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

Table 2

Empirical size at 1% nominal size for an AR(1) process: 𝑦_𝑡=𝜙𝑦_𝑡−1+𝜀_𝑡.

𝑚	𝑇	𝜙
		0.1	0.4	0.7	0.8	0.9
5	𝑄^∗𝑚(𝑟)̂	0.021	0.020	0.027	0.024	0.027
	𝑄^∗𝑚(𝜔)	0.012	0.011	0.010	0.005	0.015
	𝑄^∗𝑚(𝑟,̂𝜔)	0.014	0.015	0.016	0.007	0.020
10	𝑄^∗𝑚(𝑟)̂	0.008	0.015	0.016	0.017	0.022
	𝑄^∗𝑚(𝜔)	0.007	0.012	0.006	0.009	0.018
	𝑄^∗𝑚(𝑟,̂𝜔)	0.006	0.011	0.008	0.010	0.017
15	𝑄^∗𝑚(𝑟)̂	0.013	0.025	0.020	0.018	0.025
	𝑄^∗𝑚(𝜔)	0.006	0.010	0.007	0.010	0.015
	𝑄^∗𝑚(𝑟,̂𝜔)	0.007	0.013	0.010	0.010	0.015
20	𝑄^∗𝑚(𝑟)̂	0.024	0.022	0.022	0.022	0.034
	𝑄^∗𝑚(𝜔)	0.011	0.011	0.011	0.012	0.009
	𝑄^∗𝑚(𝑟,̂𝜔)	0.011	0.015	0.018	0.014	0.019
25	𝑄^∗𝑚(𝑟)̂	0.021	0.020	0.027	0.024	0.027
	𝑄^∗𝑚(𝜔)	0.012	0.011	0.010	0.005	0.015
	𝑄^∗𝑚(𝑟,̂𝜔)	0.014	0.015	0.016	0.007	0.018