Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

Algorithm 2

Computation of empirical size.

Step  1. Obtain 𝑇^∗ using Algorithm 1, for each of the 𝐵 bootstrap samples,

reject null model if 𝑇^∗≥𝑇, otherwise accept it.

Step  2. Determine the proportion of 𝐵 bootstrap samples, say 𝑝_𝑐, for which

the null hypothesis is rejected.

Step  3. Repeat Step  1-2 for each of the 𝑁 Monte Carlo runs.

Step  4. Empirical size, 𝛼, is determined as the proportion of Monte Carlo

runs for which the 𝑝_𝑐≤𝛼, where 𝛼 is the level of significance,

          𝑝𝛼=#(_𝑐≤𝛼)𝑁.