Table 4 MASE predictive accuracy of...

Table 4

MASE predictive accuracy of cyclical model comparing to ARIMA, regARIMA, TBATS, H-W Model and ANN methods

Models	Training/Estimation (Sample period)		Test (Out of sample period)
Models	Period	MASE	Period	MASE
BDI
ARIMA(0,1,1)	2000–2016	0.147	2017	0.116
Reg with ARMA	2000–2016	0.149	2017	0.122
TBATS	2000–2016	0.142	2017	0.110
HW additive	2000–2016	0.161	2017	0.109
HW multiplicative	2000–2016	0.150	2017	0.074
ANN(lag 2, c(10,11))	2000–2016	0.182	2017	0.076
System dynamics	2000–2016	0.138*	2017	0.067*
Handysize
ARIMA(1,1,4) (1,0,0)[12]	2000–2016	0.096	2017	0.141
Reg with ARMA	2000–2016	0.094	2017	0.094
TBATS	2000–2016	0.091*	2017	1.000
HW additive	2000–2016	0.103	2017	0.086
HW multiplicative	2000–2016	0.105	2017	0.160
ANN(lag 2, c(9,9))	2000–2016	0.096	2017	0.053
System dynamics	2000–2016	0.098	2017	0.047*
Panamax
ARIMA(2,1,1) (0,0,1)[12]	2000–2016	0.101	2017	0.183
Reg with ARMA	2000–2016	0.101	2017	0.174
TBATS	2000–2016	1.00	2017	0.161
HW additive	2000–2016	0.114	2017	0.068
HW multiplicative	2000–2016	0.112	2017	0.042
ANN(lag 2, c(9,9))	2000–2016	0.100	2017	0.064
System dynamics	2000–2016	0.096*	2017	0.036*
Capesize
ARIMA(2,1,1) (0,0,1)[12]	2000–2016	0.117	2017	0.151
Reg with ARMA	2000–2016	0.118	2017	0.110
TBATS	2000–2016	0.116	2017	0.140
HW additive	2000–2016	0.127	2017	0.098
HW multiplicative	2000–2016	0.119	2017	0.122
ANN(lag 2, c(9,9))	2000–2016	0.125	2017	0.036
System dynamics	2000–2016	0.113*	2017	0.034*
Supramax
ARIMA(2,1,1) (0,0,1)[12]	2000–2016	0.099	2017	0.125
Reg with ARMA	2000–2016	0.099	2017	0.094
TBATS	2000–2016	0.096*	2017	0.083
HW additive	2000–2016	0.110	2017	0.059
HW multiplicative	2000–2016	0.103	2017	0.066
ANN(lag 2, c(9,9))	2000–2016	0.097	2017	0.050*
System dynamics	2000–2016	0.100	2017	0.053

Models	Training/Estimation (Sample period)		Test (Out of sample period)
Models	Period	MASE	Period	MASE
BDI
ARIMA(0,1,1)	2000–2016	0.147	2017	0.116
Reg with ARMA	2000–2016	0.149	2017	0.122
TBATS	2000–2016	0.142	2017	0.110
HW additive	2000–2016	0.161	2017	0.109
HW multiplicative	2000–2016	0.150	2017	0.074
ANN(lag 2, c(10,11))	2000–2016	0.182	2017	0.076
System dynamics	2000–2016	0.138*	2017	0.067*
Handysize
ARIMA(1,1,4) (1,0,0)[12]	2000–2016	0.096	2017	0.141
Reg with ARMA	2000–2016	0.094	2017	0.094
TBATS	2000–2016	0.091*	2017	1.000
HW additive	2000–2016	0.103	2017	0.086
HW multiplicative	2000–2016	0.105	2017	0.160
ANN(lag 2, c(9,9))	2000–2016	0.096	2017	0.053
System dynamics	2000–2016	0.098	2017	0.047*
Panamax
ARIMA(2,1,1) (0,0,1)[12]	2000–2016	0.101	2017	0.183
Reg with ARMA	2000–2016	0.101	2017	0.174
TBATS	2000–2016	1.00	2017	0.161
HW additive	2000–2016	0.114	2017	0.068
HW multiplicative	2000–2016	0.112	2017	0.042
ANN(lag 2, c(9,9))	2000–2016	0.100	2017	0.064
System dynamics	2000–2016	0.096*	2017	0.036*
Capesize
ARIMA(2,1,1) (0,0,1)[12]	2000–2016	0.117	2017	0.151
Reg with ARMA	2000–2016	0.118	2017	0.110
TBATS	2000–2016	0.116	2017	0.140
HW additive	2000–2016	0.127	2017	0.098
HW multiplicative	2000–2016	0.119	2017	0.122
ANN(lag 2, c(9,9))	2000–2016	0.125	2017	0.036
System dynamics	2000–2016	0.113*	2017	0.034*
Supramax
ARIMA(2,1,1) (0,0,1)[12]	2000–2016	0.099	2017	0.125
Reg with ARMA	2000–2016	0.099	2017	0.094
TBATS	2000–2016	0.096*	2017	0.083
HW additive	2000–2016	0.110	2017	0.059
HW multiplicative	2000–2016	0.103	2017	0.066
ANN(lag 2, c(9,9))	2000–2016	0.097	2017	0.050*
System dynamics	2000–2016	0.100	2017	0.053

Note(s): *Italic figures indicate the minimum error rate in given column

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