Algorithm 1: Multi-stage Bandwidth Detection.

Input Samples $\mathit{y}$ and significance level $\alpha$;

Output Detected bandwidth K or None;

1: for $k=1,2,\cdots ,M-1$ do

2:  Calculate test statistic according to (13);

3:  Calculate the p-value of the test according to (15);

4:  if $p>\alpha$ then

5:   Let bandwidth $K=k$ and stop;

6:  else

7:   $k=k+1$;

8:  end if

9: end for