JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (1): 115-123.doi: 10.6040/j.issn.1671-9352.4.2022.205

Previous Articles     Next Articles

Interval time series models-based vessel price index forecasting

Yuanyuan XU1(),Hongyue GUO1,*(),Lidong WANG2   

  1. 1. Collabrative Innovation Center for Transport Studies, Dalian Maritime University, Dalian 116026, Liaoning, China
    2. School of Science, Dalian Maritime University, Dalian 116026, Liaoning, China
  • Received:2022-08-02 Online:2024-01-20 Published:2024-01-19
  • Contact: Hongyue GUO E-mail:yyxu_dmu@163.com;hyguo@dlmu.edu.cn

RichHTML

1

PDF (PC)

180

Abstract:

This study considers the forward freight agreement (FFA) as an exogenous variable to analyze its specific impact on the vessel price index. With the center and range method, an interval autoregression model, an interval error correction model considering the co-integration between the upper and lower bounds of the interval time series, and interval error correction model with an additional incorporation of the exogenous variable FFA are established, respectively. The constructed models are employed to perform the interval prediction of the bulk carrier newship price index and bulk carrier secondhand price index. Based on the criteria MAE and RMSE, the prediction accuracy is higher after adding the co-integration term and FFA into the models.

Key words: interval time series, vessel price index, forward freight agreements

CLC Number: 

  • F551

Table 1

Examples on interval-valued prices of bulk carrier index"

月份新造干散货船月份二手干散货船
YtL YtU YtL YtU
2000-01 107.43 107.87 2010-07 214.67 215.25
2000-02 108.10 108.60 2010-08 214.77 214.77
2000-03 108.73 108.85 2010-09 216.31 218.94
2000-04 108.80 109.42 2010-10 216.18 219.08
… … … … … …

Fig.1

Interval-valued prices of bulk carrier"

Fig.2

Bulk carrier newship price index difference of (a) center series and (b) range series"

Fig.3

Bulk Carrier Secondhand Price Index difference of (a) center series and (b) range series"

Table 2

Descriptive statistics for interval prices of bulk barrier"

船类 变量 均值 中值 最大值 最小值 标准差 偏度 峰度 JB统计量 P值
新造船 YtL 136.55 130.94 191.21 105.23 20.71 0.80 0.03 28.68 0.00
YtU 137.19 131.40 191.58 105.36 20.90 0.78 -0.02 26.97 0.00
YCt 136.87 131.19 191.40 105.35 20.80 0.79 0.00 27.80 0.00
YRt 0.33 0.19 5.73 0.01 0.57 5.71 43.26 22 374.49 0.00
Δln YCt 0.14 0.08 4.42 -6.13 1.25 -0.36 4.91 276.86 0.00
Δln YRt 0.00 0.00 4.05 -3.29 1.26 0.10 0.07 0.53 0.76
二手船 YtL 126.18 118.35 216.31 70.64 34.93 0.75 0.05 13.10 0.00
YtU 129.15 119.15 219.08 71.15 35.89 0.71 -0.09 12.03 0.00
YCt 127.67 118.66 217.63 70.90 35.38 0.73 -0.02 12.54 0.00
YRt 1.68 1.25 9.02 0.05 1.64 1.60 2.94 112.55 0.00
Δln YCt -0.18 -0.26 10.91 -10.03 3.54 0.03 0.48 1.66 0.44
Δln YRt 0.02 0.10 3.10 -3.49 1.37 -0.08 -0.17 0.25 0.88

Table 3

Results of the co-integration test on interval-valued price series"

船类 变量 lag ADF P值 结论 船类 变量 lag ADF P值 结论
新造船 ln YtU 0 1.76 0.980 不平稳 二手船 lnYtU 0 -0.63 0.46 不平稳
1 0.77 0.865 不平稳 1 -0.48 0.51 不平稳
lnYtL 0 1.48 0.964 不平稳 lnYtL 0 -0.63 0.45 不平稳
1 1.05 0.921 不平稳 1 -0.41 0.53 不平稳
ΔlnYtU 0 -7.70 ≤0.01 平稳 Δln YtU 0 -6.85 ≤0.01 平稳
1 -5.30 ≤0.01 平稳 1 -4.34 ≤0.01 平稳
lnYtL 0 -11.78 ≤0.01 平稳 ln YtL 0 -6.63 ≤0.01 平稳
1 -6.53 ≤0.01 平稳 1 -4.63 ≤0.01 平稳
ut 0 -12.54 ≤0.01 平稳 ut 0 -8.99 ≤0.01 平稳
1 -8.53 ≤0.01 平稳 1 -6.39 ≤0.01 平稳

Fig.4

Interval-valued prices of FFA"

Fig.5

The FFA price (a) center series and (b) range series"

Table 4

Interval-valued time series models estimation results of bulk carrier newship price index"

方程 变量ARECMECM-X
系数 P值 系数 P值 系数 P值
中点方程 β0c 0.032 8 0.313 8 0.033 7 0.307 8 0.034 1 0.304 5
β1c 0.549 1*** 0.000 0 0.541 8*** 0.000 0 0.533 8*** 0.000 0
γc -0.194 0*** 0.013 4 -0.215 8*** 0.007 1
δ1c 0.649 8* 0.024 6
β0r -0.014 7 0.416 8 -0.014 9 0.413 4 -0.014 9 0.413 6
极差方程 β1r -0.510 6*** 0.000 0 -0.578 8*** 0.000 0 -0.578 8*** 0.000 0
γr -0.343 2*** 0.000 2 -0.343 1*** 0.000 1
δ1r -0.000 4 0.498 4

Table 5

Interval-valued time series models estimation results of bulk carrier secondhand price index"

方程 变量ARECMECM-X
系数 P值 系数 P值 系数 P值
中点方程 β0c -0.234 2 0.181 1 -0.217 5 0.198 7 -0.216 4 0.186 7
β1c 0.613 6*** 0.000 6 0.643 1*** 0.000 1 0.607 6*** 0.000 1
γc 0.128 6 0.132 2 0.159 1 0.073 2
δ1c 4.472 8*** 0.000 1
极差方程 β0r 0.028 9 0.405 2 0.032 3 0.386 9 0.032 8 0.385 6
β1r -0.461 4*** 0.000 1 -0.659 7*** 0.000 0 -0.660 3*** 0.000 0
γr -0.238 8*** 0.000 1 -0.238 9*** 0.000 1
δ1r 0.099 6 0.259 4

Table 6

Comparison results on the data of bulk carrier newship price index"

评价指标训练集测试集
AR ECM ECM-X AR ECM ECM-X
MAEL 0.906 9 0.901 7 0.897 2 0.770 2 0.762 6 0.720 6
MAEU 0.831 1 0.810 0 0.802 7 0.909 9 1.164 2 1.157 6
RMSEL 1.701 8 1.694 5 1.666 8 0.981 1 0.948 0 0.939 7
RMSEU 1.360 3 1.317 6 1.303 5 1.303 7 1.554 1 1.541 0

Table 7

Comparison results on the data of Bulk Carrier Secondhand Price Index"

评价指标训练集测试集
AR ECM ECM-X AR ECM ECM-X
MAEL 2.343 6 2.120 1 2.165 8 2.896 4 2.800 2 2.766 6
MAEU 2.997 3 3.102 3 2.640 8 2.452 1 2.398 8 2.355 6
RMSEL 3.373 1 2.898 8 2.907 7 4.403 2 4.417 4 4.270 2
RMSEU 4.199 5 4.385 4 3.836 2 3.540 3 3.569 0 3.371 9
1 陈继红, 刘雯. 基于协整和VEC模型的VLCC新造船舶价格波动性[J]. 数学的实践与认识, 2016, 46 (24): 69- 78.
CHEN Jihong , LIU Wen . Fluctuation of the price of newbuilding VLCC ships based on cointegration and VEC model[J]. Mathematics in Practice and Theory, 2016, 46 (24): 69- 78.
2 HER M T , CHUNG C C . Ship price predictions of panamax second-hand bulk carriers using grey models[J]. Journal of Marine Science and Technology, 2019, 27 (3): 229- 234.
3 TGEODORE S , MICHAEL T . Support vector machine algorithms: an application to ship price forecasting[J]. Computational Economics, 2021, 57, 55- 87.
doi: 10.1007/s10614-020-10032-2
4 SYRIOPOULOS T , TSATSARONIS M , KARAMANOS I . Support vector machine algorithms: an application to ship price forecasting[J]. Computational Economics, 2021, 57, 55- 87.
doi: 10.1007/s10614-020-10032-2
5 GAO R , LIU J H , BAI X W , et al. Annual dilated convolution neural network for newbuilding ship prices forecasting[J]. Neural Computing and Applications, 2022, 34, 11853- 11863.
doi: 10.1007/s00521-022-07075-x
6 GAO R B , LIU J H , DU L , et al. Shipping market forecasting by forecast combination mechanism[J]. Maritime Policy and Management, 2022, 49 (8): 1059- 1074.
doi: 10.1080/03088839.2021.1945698
7 WANG X , ZHANG Z , LI S . Set-valued and interval-valued stationary time series[J]. Journal of Multivariate Analysis, 2016, 145, 208- 223.
doi: 10.1016/j.jmva.2015.12.010
8 SUN Y Y , HAN A , HONG Y M , et al. Threshold autoregressive models for interval valued time series data[J]. Journal of Econometrics, 2018, 206 (2): 414- 446.
doi: 10.1016/j.jeconom.2018.06.009
9 MOORE R E. Interval analysis[D]. Englewood Cliffs: Prentice-Hall, 1966.
10 LIMA N , DE CARVALHO F A . An exponential-type kernel robust regression model for interval-valued variables[J]. Information Sciences, 2018, 2018 (454/455): 419- 442.
11 BILLARD L, DIDAY E. Regression analysis for interval-valued data & data analysis, classification and related methods[C]//Proceedings of the Seventh Conference of the International Federation of Classification Societies. Belgium: Springer, 2000: 369-374.
12 BILLARD L , DIDAY E . From the statistics of data to the statistics of knowledge: symbolic data analysis[J]. Journal of the American Statistical Association, 2003, 98 (462): 470- 487.
doi: 10.1198/016214503000242
13 NETO L E A , CARVALHO F A T . Center and range method for fitting a linear regression model to symbolic interval data[J]. Computational Statistics and Data Analysis, 2008, 52 (3): 1500- 1515.
doi: 10.1016/j.csda.2007.04.014
14 NETO L E A , CARVALHO F A T . Constrained linear regression models for symbolic interval-valued variables[J]. Computational Statistics and Data Analysis, 2010, 54 (2): 333- 347.
doi: 10.1016/j.csda.2009.08.010
15 HAN A , HONG Y M , WANG S Y , et al. A vector autoregressive moving average model for interval-valued time series data[J]. Advances in Econometrics, 2016, 36, 417- 460.
16 YANG W , HAN A , WANG S Y . Analysis of crisis impact on crude oil prices: a new approach with interval time series modelling[J]. Quantitative Finance, 2016, 16 (12): 1917- 1928.
doi: 10.1080/14697688.2016.1211795
17 杨威, 韩艾, 汪寿阳. 基于区间型数据的金融时间序列预测研究[J]. 系统工程学报, 2016, 31 (6): 817- 831.
YANG Wei , HAN Ai , WANG Shouyang . Research on financial time Series prediction based on interval data[J]. Journal of Systems Engineering, 2016, 31 (6): 817- 831.
18 陈炜, 徐慧琳, 汪寿阳, 等. 基于误差修正与分解的区间值股价时间序列预测研究[J]. 系统工程理论与实践, 2023, 43 (2): 383- 397.
CHEN Wei , XU Huilin , WANG Shouyang , et al. Error correction and decomposition method for forecast of interval-valued stock price time series[J]. Systems Engineering-Theory and Practice, 2023, 43 (2): 383- 397.
19 闵德权, 张鑫, 崔琪. 远期运费协议与新造船市场的波动溢出效应研究[J]. 中国水运, 2019, 19 (12): 37- 39.
MIN Dequan , ZHANG Xin , CUI Qi . A study on volatility spillover effects of forward freight agreements and new shipbuilding market[J]. China Water Transport, 2019, 19 (12): 37- 39.
20 杨芊, 林国龙, 丁一. FFA市场与二手船市场的波动溢出效应[J]. 武汉理工大学学报(交通科学与工程版), 2015, 39 (5): 1001- 1004.
doi: 10.3963/j.issn.2095-3844.2015.05.022
YANG Qian , LIN Guolong , DING Yi . Volatility spillover effects between forward freight market and second-hand ship maket[J]. Journal of Wuhan University of Technology (Transportation Science and Engineering), 2015, 39 (5): 1001- 1004.
doi: 10.3963/j.issn.2095-3844.2015.05.022
21 陶志富, 刘金培, 朱家明, 等. 区间值时间序列预测效果测度研究[J]. 模糊系统与数学, 2018, 32 (4): 135- 144.
TAO Zhifu , LIU Jinpei , ZHU Jiaming , et al. Study on measurement of interval-value time series prediction effect[J]. Fuzzy Systems and Mathematics, 2018, 32 (4): 135- 144.
No related articles found!
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] GUO Qiao-jin, DING Yi, LI Ning. A context based method for ROI detection in digitized mammograms[J]. J4, 2010, 45(7): 70 -75 .
[2] FU Hai-yan,LU Chang-jing,SHI Kai-quan . (F,F-)-law inference and law mining[J]. J4, 2007, 42(7): 54 -57 .
[3] TANG Xiao-hong1, HU Wen-xiao2*, WEI Yan-feng2, JIANG Xi-long2, ZHANG Jing-ying2, SHAO Xue-dong3. Screening and biological characteristics studies of wide wine-making yeasts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 12 -17 .
[4] YUAN Rui-qiang,LIU Guan-qun,ZHANG Xian-liang,GAO Hui-wang . Features of hydrogen and oxygen isotopes in groundwater ofthe shallow part of Yellow River Delta[J]. J4, 2006, 41(5): 138 -143 .
[5] GUO Wen-juan, YANG Gong-ping*, DONG Jin-li. A review of fingerprint image segmentation methods[J]. J4, 2010, 45(7): 94 -101 .
[6] ZHANG Wen, ZHANG Hua-xiang*, LI Ming-fang, JI Hua. A decision tree construction approach: two-step forward is better than one[J]. J4, 2010, 45(7): 114 -118 .
[7] SONG Ying,ZHANG Xing-fang ,WANG Qing-ping . α-reverse triple I method in the parametric Kleene's system[J]. J4, 2007, 42(7): 45 -48 .
[8] HE Hai-lun， CHEN Xiu-lan* . Circular dichroism detection of the effects of denaturants and buffers on the conformation of cold-adapted protease MCP-01 and  mesophilic protease BP01[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 23 -29 .
[9] WANG Bi-yu, CAO Xiao-hong*. The perturbation for the Browder’s theorem of operator matrix#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 90 -95 .
[10] HU Xuan-zi1, XIE Cun-xi2. A robot local path plan based on artificial immune network[J]. J4, 2010, 45(7): 122 -126 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd