Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

Algorithm 1

Bootstrap sampling procedure.

Step  1. Generate bootstrap sample 𝑦^∗_𝑡 using resamples of residuals, 𝜀_𝑡̂,

obtained by fitting the model under null hypothesis to the simulated time

series. We denoted these resampled residuals as 𝜀^∗_𝑡.

Step  2. Fit the null model to the bootstrap sample 𝑦^∗_𝑡 and obtain residuals

as 𝜀^∗_𝑡̂=𝑦^∗_𝑡−𝑦^∗_𝑡, where 𝑦^∗_𝑡 is the fitted series.

Step  3. Using the residuals, 𝜀^∗_𝑡̂, obtained in Step  2 above, calculate

test-statistic 𝑇. We denote it as 𝑇^∗.

Step  4. Repeat Step  1–3 for each of the 𝐵 bootstrap samples.