Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement

Table 3

ARMSE for under different models for and .

Sample size (n)	Without noncrossing constraint			With noncrossing restriction
	RRQ	ECQ	AECQ	RRQ	ECQ	AECQ
250	0.58236	0.64552	0.73307	0.58200	0.64230	0.72728
500	0.56989	0.61336	0.60766	0.56816	0.61083	0.60341
1000	0.53386	0.58654	0.53386	0.55780	0.58529	0.53186
2000	0.56051	0.58204	0.49562	0.55800	0.57880	0.49360
3000	0.55478	0.57663	0.48235	0.55235	0.57369	0.48073
4000	0.55271	0.57619	0.47032	0.55013	0.57295	0.46832

RRQ, restricted regression quantiles in [11]. ECQ, extreme conditional quantiles in [25]. AECQ, proposed adjusted extreme conditional quantiles.