A structural VAR and VECM modeling method for open-high-low-close data contained in candlestick chart

Financial Innovation

Table 5 Results of the VAR and VECM for OHLC data of 50 ETF

Criterion	q = 30			q = 50			q = 70
Criterion	Naive	Yes	No	Naive	Yes	No	Naive	Yes	No
MAPE
\(x^{(o)}_t\)	1.259%	0.773%	0.647%	1.261%	0.670%	0.539%	1.263%	0.645%	0.496%
\(x^{(h)}_t\)	1.051%	1.072%	1.066%	1.053%	1.004%	0.984%	1.054%	0.975%	0.943%
\(x^{(l)}_t\)	1.117%	1.090%	1.054%	1.120%	0.980%	0.952%	1.120%	0.952%	0.911%
\(x^{(c)}_t\)	1.208%	1.482%	1.496%	1.210%	1.376%	1.349%	1.211%	1.357%	1.306%
\(\bar{x}_{t}\)	1.159%	1.104%	1.066%	1.161%	1.015%	0.956%	1.162%	0.982%	0.914%
RMSE
\(x^{(o)}_t\)	0.048	0.035	0.031	0.048	0.031	0.025	0.048	0.028	0.024
\(x^{(h)}_t\)	0.040	0.044	0.041	0.040	0.039	0.037	0.040	0.037	0.035
\(x^{(l)}_t\)	0.044	0.045	0.044	0.044	0.039	0.038	0.044	0.038	0.037
\(x^{(c)}_t\)	0.047	0.058	0.058	0.047	0.053	0.052	0.047	0.052	0.051
\(\bar{x}_{t}\)	0.045	0.045	0.043	0.045	0.040	0.038	0.045	0.039	0.037
RMSEH	0.052	0.055	0.053	0.052	0.049	0.047	0.053	0.047	0.045
AR	0.387	0.403	0.399	0.387	0.427	0.429	0.387	0.440	0.449
VAR Ratio	-	6.56%	6.51%	-	6.31%	3.59%	-	1.56%	2.62%
VECM Ratio	-	93.44%	93.49%	-	93.69%	96.41%	-	98.44%	97.38%
Failure 1	0	0	0	0	0	0	0	0	0
Failure 2	0	0	9	0	0	2	0	0	0
Failure 3	0	0	380	0	0	271	0	0	123