Adaptive Heterogeneous Autoregressive Models of Realized Volatility Based on a Genetic Algorithm

Table 3

Moving window out-of-sample forecast performance comparison results.

Windows		AHAR-RV	HAR-RV	AHAR-RV-J	HAR-RV-J	AHAR-RV-CJ	HAR-RV-CJ
1–700; 701–800		(1,4,109)	(1,5,22)	(1,4,109)	(1,5,22)	(1,4,106)	(1,5,22)
	MAE	0.37826	0.37225	0.37826	0.37225	0.38011	0.37374
	MAPE	0.05156	0.05076	0.05156	0.05076	0.05185	0.05105
	RMSE	0.46385	0.46438	0.46386	0.46442	0.46653	0.46875
	Theil	0.03058	0.03063	0.03058	0.03064	0.03074	0.03090
101–800; 801–900		(1,3,16)	(1,5,22)	(1,3,16)	(1,5,22)	(1,3,18)	(1,5,22)
	MAE	0.41608	0.41853	0.41540	0.41782	0.44916	0.45973
	MAPE	0.05511	0.05541	0.05501	0.05531	0.05938	0.06083
	RMSE	0.62675	0.62882	0.62596	0.62823	0.66261	0.66838
	Theil	0.04049	0.04063	0.04044	0.04059	0.04295	0.04331
201–900; 901–1000		(1,3,18)	(1,5,22)	(1,3,18)	(1,5,22)	(1,4,18)	(1,5,22)
	MAE	0.31402	0.31845	0.31421	0.31874	0.32064	0.32252
	MAPE	0.03936	0.03985	0.03937	0.03987	0.04011	0.04031
	RMSE	0.40048	0.39764	0.40052	0.39761	0.40216	0.40251
	Theil	0.02464	0.02446	0.02464	0.02447	0.02475	0.02477
301–1000; 1001–1100		(1,3,18)	(1,5,22)	(1,3,18)	(1,5,22)	(1,4,18)	(1,5,22)
	MAE	0.41896	0.41987	0.41931	0.42000	0.42379	0.42471
	MAPE	0.05152	0.05161	0.05154	0.05160	0.05195	0.05209
	RMSE	0.52583	0.52826	0.52590	0.52831	0.52727	0.52907
	Theil	0.03145	0.03159	0.03146	0.03160	0.03157	0.03167
401–1100; 1101–1200		(1,3,16)	(1,5,22)	(1,3,16)	(1,5,22)	(1,3,16)	(1,5,22)
	MAE	0.44809	0.45146	0.44837	0.45172	0.45576	0.45750
	MAPE	0.05052	0.05087	0.05055	0.05090	0.05131	0.05147
	RMSE	0.55241	0.55648	0.55276	0.55678	0.55940	0.56262
	Theil	0.03145	0.03170	0.03147	0.03172	0.03189	0.03209

Note: bold number indicates that the AHAR model’s forecast performance is worse than that of the corresponding HAR model in terms of the loss function in its row.