Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

Table 5

Empirical power by fitting an AR(1) process against an ARMA(1,1) process: 𝑦_𝑡=0.8𝑦_𝑡−1+𝜀_𝑡+𝜃𝜀_𝑡−1 using 1000 Monte Carlo runs.

𝑚	𝑇	𝜃
		0.1	0.4	0.7	0.8	0.9
5	𝑄^∗𝑚(𝑟)̂	0.103	0.703	1	1	1
	𝑄^∗𝑚(𝜔)	0.081	0.771	1	1	1
	𝑄^∗𝑚(𝑟,̂𝜔)	0.208	0.846	1	1	1
10	𝑄^∗𝑚(𝑟)̂	0.092	0.520	0.917	1	0.978
	𝑄^∗𝑚(𝜔)	0.115	0.601	1	1	1
	𝑄^∗𝑚(𝑟,̂𝜔)	0.228	0.784	1	1	1
15	𝑄^∗𝑚(𝑟)̂	0.063	0.554	0.941	0.963	0.955
	𝑄^∗𝑚(𝜔)	0.051	0.552	1	1	1
	𝑄^∗𝑚(𝑟,̂𝜔)	0.196	0.747	1	1	1
20	𝑄^∗𝑚(𝑟)̂	0.094	0.441	0.832	0.964	0.907
	𝑄^∗𝑚(𝜔)	0.063	0.491	1	1	1
	𝑄^∗𝑚(𝑟,̂𝜔)	0.187	0.698	1	1	1
25	𝑄^∗𝑚(𝑟)̂	0.020	0.475	0.801	0.896	0.858
	𝑄^∗𝑚(𝜔)	0.053	0.571	0.982	1	1
	𝑄^∗𝑚(𝑟,̂𝜔)	0.176	0.669	0.994	1	1