Weighted-indexed semi-Markov model: calibration and application to financial modeling

Financial Innovation

Table 4 RMSE of the autocorrelation of the squared returns for different combinations of returns/index discretization and number of states of the chain and of the index. Returns discretization is indicated by rows, index discretization by columns

	1-min interval			1-s interval
	Quantile	k-means	GMM	Quantile	k-means	GMM
Panel A: 3-state returns; 3-state index
Quantile	0.015	0.0194	0.0189	0.0385	0.0673	0.052
Sigma	0.0187	0.0279	0.0291	0.044	0.0454	0.0464
k-means	0.028	0.0269	0.0309	0.0637	0.0591	0.0465
GMM	–	–	–	0.01	0.0103	0.0103
Panel B: 5-state returns; 5-state index
Quantile	0.0065	0.0137	0.0185	–	–	–
Sigma	0.0554	0.0124	0.0312	0.0525	0.0488	0.0485
k-means	0.0332	0.0212	0.0271	0.0686	0.0461	0.0417
GMM	0.066	0.0271	0.0414	0.0725	0.0374	0.0468

Bold values indicate the combination of returns/index discretization with the lowest RMSE