基于变系数回归模型的黄金价格预测研究
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摘要
长期以来,黄金作为价值尺度、流通手段、储藏手段、支付手段和世界货币等职能而备受关注,如何预测黄金价格成为理论和实证研究的重要课题。对于黄金价格预测的研究,目前较多的使用多元线性回归模型,由于多元线性回归模型假设变量对黄金价格的影响在整个时间上不变,这显然不符合实际的情况。针对该问题,本文选用变系数回归模型对黄金价格进行预测,能够动态的反应各个变量对黄金价格的影响力,极大的提高了预测精度。
影响黄金价格的因素众多而且纷杂,本文主要从美元指数、大宗商品价格、欧美股票市场、亚太股票市场和世界经济形势等方面对黄金价格的影响因素进行了相关性分析,并找出了其主要影响因素。最终选取美元指数、石油价格、白银价格、道琼斯指数、OECD领先指数和CRB指数为黄金价格的主要影响因素,把它们作为变系数模型的变量。
另外,本文采用加权最小二乘法对参数进行估计,更正了传统的最小二乘法假设样本数据对预测点的权重都相等这一缺陷,使得离预测点越近的样本的权重值越大。在权重函数的选择上,本文利用交叉互证法,以1990年1月至2009年12月的黄金价格数据为样本,选取不同的光滑参数,求出其对应的残差平方和值,计算最小残差平方和对应的光滑参数值,实现整个样本空间的最优。然后利用变系数回归模型和多元线性回归模型分别模拟预测了2000年1月至2009年12月的黄金价格,通过分析发现,变系数回归模型的残差平方和小于多元线性回归模型,并且后者的误差率常常明显高于前者。因此本文利用变系数回归模型预测了2010年1月至12月的黄金月价格,所得结论具有较重要的理论和实际应用价值。
For a long period, gold has attracted much attention as a measure of value, circulation means, storage means, payment, world monetary functions and so on, how to predict the gold price becomes an important academic and practical research topic. For the research of gold price forecast, the multiple linear regression model has been greatly studied at present, as it assumes that the impacts of variables on the price of gold remain invariability throughout time, which obviously does not accord with the actual situation. To avoid this problem, varying-coefficient regression model is applied to predict the gold price in this paper, the model has dynamic response to the various variables influence the price of gold, so it has greatly improved the prediction accuracy.
Many factors affect the price of gold and they are confused, the articles mainly explored correlation analysis in U.S. dollar index, commodity prices, European stock markets, the Asia-Pacific stock markets and world economic situation and other aspects of the factors affecting the gold price, and identify the main factors. Finally U.S. dollar index, oil prices, silver prices, DOW index, OECD leading index and the CRB index are chosen as main factors affecting the price of gold, and regard them as variable coefficient model parameters.
In addition, the weighted least squares is adopted as an estimation of the parameters, corrects the traditional least squares method defect which assumes the sample data weights equal points to the prediction, making sample weights larger closer with prediction points. In the choice of weighting function, the paper uses cross validation, chooses the gold price data from January 1990 to December 2009 as the sample, selects different smoothing parameters, and calculates the corresponding residual sum of squares values and the smoothing parameter value corresponding minimum residual sum of squares, to achieve the optimization for the entire sample space. Then predicts gold prices from January 2000 to December 2009 used the variable coefficient regression model and multiple linear regression model to simulate, the analysis found that the residual sum of squares of varying-coefficient regression model is less than multiple linear regression model, and the latter's error rate is often higher than the former. So this article predicts the 12 months gold prices from January 2010 December 2010 applies varying-coefficient regression model. The results have much theoretical and practical value.
影响黄金价格的因素众多而且纷杂,本文主要从美元指数、大宗商品价格、欧美股票市场、亚太股票市场和世界经济形势等方面对黄金价格的影响因素进行了相关性分析,并找出了其主要影响因素。最终选取美元指数、石油价格、白银价格、道琼斯指数、OECD领先指数和CRB指数为黄金价格的主要影响因素,把它们作为变系数模型的变量。
另外,本文采用加权最小二乘法对参数进行估计,更正了传统的最小二乘法假设样本数据对预测点的权重都相等这一缺陷,使得离预测点越近的样本的权重值越大。在权重函数的选择上,本文利用交叉互证法,以1990年1月至2009年12月的黄金价格数据为样本,选取不同的光滑参数,求出其对应的残差平方和值,计算最小残差平方和对应的光滑参数值,实现整个样本空间的最优。然后利用变系数回归模型和多元线性回归模型分别模拟预测了2000年1月至2009年12月的黄金价格,通过分析发现,变系数回归模型的残差平方和小于多元线性回归模型,并且后者的误差率常常明显高于前者。因此本文利用变系数回归模型预测了2010年1月至12月的黄金月价格,所得结论具有较重要的理论和实际应用价值。
For a long period, gold has attracted much attention as a measure of value, circulation means, storage means, payment, world monetary functions and so on, how to predict the gold price becomes an important academic and practical research topic. For the research of gold price forecast, the multiple linear regression model has been greatly studied at present, as it assumes that the impacts of variables on the price of gold remain invariability throughout time, which obviously does not accord with the actual situation. To avoid this problem, varying-coefficient regression model is applied to predict the gold price in this paper, the model has dynamic response to the various variables influence the price of gold, so it has greatly improved the prediction accuracy.
Many factors affect the price of gold and they are confused, the articles mainly explored correlation analysis in U.S. dollar index, commodity prices, European stock markets, the Asia-Pacific stock markets and world economic situation and other aspects of the factors affecting the gold price, and identify the main factors. Finally U.S. dollar index, oil prices, silver prices, DOW index, OECD leading index and the CRB index are chosen as main factors affecting the price of gold, and regard them as variable coefficient model parameters.
In addition, the weighted least squares is adopted as an estimation of the parameters, corrects the traditional least squares method defect which assumes the sample data weights equal points to the prediction, making sample weights larger closer with prediction points. In the choice of weighting function, the paper uses cross validation, chooses the gold price data from January 1990 to December 2009 as the sample, selects different smoothing parameters, and calculates the corresponding residual sum of squares values and the smoothing parameter value corresponding minimum residual sum of squares, to achieve the optimization for the entire sample space. Then predicts gold prices from January 2000 to December 2009 used the variable coefficient regression model and multiple linear regression model to simulate, the analysis found that the residual sum of squares of varying-coefficient regression model is less than multiple linear regression model, and the latter's error rate is often higher than the former. So this article predicts the 12 months gold prices from January 2010 December 2010 applies varying-coefficient regression model. The results have much theoretical and practical value.
引文
[1] Pedrudee Ongsritrakul, Nuanwan Soonthornphisaj, Apply Decision Tree and Support Vector Regression to Predict the Gold Price[C], Proceedings of the International Joint Conference on Neural Networks, Portland, OR, United states, 2003:2488-2492
[2] Wang Chengbiao, Chen Yanhui, Li Lihong, The forecast of gold price based on the GM(1,1) and Markov chain[C], Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, 2007, Nanjing, China, VOLS 1 AND 2:739-743
[3] Edel Tully, Brian M.Lucey, A power GARCH examination of the gold market[J], Research in International Business and Finance, 2007,21(2):316-325
[4] Larry A. Sjaastad, The price of gold and the exchange rates: Once again[J], Resources Policy, 2008, 33(2):118-124
[5] A.G. Malliaris, Mary Malliaris, Time Series and Neural Networks Comparison on Gold, Oil and the Euro[C], Proceedings of International Joint Conference on Neural Networks, Atlanta, Georgia, USA, June 14-19, 2009:1961-1967
[6] Stephen Hamston, .Gold as a Store of value[J/OL], The World Gold Council, 1998
[7] Ugur Soytas, RamazanSari, Shawkat Hammoudeh, Erk Hacihasanoglu, world oil prices, precious metal prices and macroeconomy in Turkey[J], Energy Policy, 2009,37(12):5557-5566
[8] Zhang Jinliang, Tang Mingming, Tao Mingxin, Effects Simulation of International Gold Prices on Crude Oil Prices based on WBNNK Model[C], 2009 ISECS International Colloquium on Computing, Communication, Control, and Management, 2009:459-464
[9] John Baffes, Oil spills on other commodities[J], Resources Policy, 2007,32(3):126-134
[10] Alvaro Escribano, Clive W.J. GRANGER, Investigating the Relationship between Gold and Silver Prices[J], Journal of Forecasting, 1998, 17(2):81-107
[11] Shawkat Hammoudeh, Yuan Yuan, Metal volatility in presence of oil and interest rate shocks[J], Energy Economics,2008, 30(2):606–620
[12] C. Ciner, On the long run relationship between gold and silver prices A note[J], Global Finance Journal, 2001,12(2):299-303
[13] Thomas J. Urich, Modes of fluctuation in metal futures prices[J], Journal of Futures Markets, 2000, 20(3):219-241
[14] K. Ivanova, M. Ausloos, Low q-moment multifractal analysis of Gold price, Dow Jones Industrial Average and BGL-USD exchange rate[J], The European Physical Journal B, 1999, 8(4):665-669
[15] Graham Smith, The price of Gold and Stoek Priee Indices for the United States[J/OL]. The World Gold Council. 2001
[16] Xu Li, Song Shaowen, Wang Beibei, Study on the gold price and yield based on GARCH models[C], Proceedings of 2008 International Conference on Risk and Reliability Management, 2008, Beijin China, Vols I And II: 222-226
[17] Antonino Parisi, Franco Parisi, David Diaz, Forecasting gold price changes: Rolling and recursive neural network models[J], Journal of Multinational financial management, 2008,18(5):477-487
[18] Chunmei Liu, Price forecast for gold futures based on GA-BP neural network[C], Proceedings - International Conference on Management and Service Science, September 20-22, 2009, Wuhan, China
[19] Terence C. Mills, Statistical analysis of daily gold price data[J], Physica A: Statistical Mechanics and its Applications, 2004, 338(3-4):559—566
[20] Xu Guo-Xiang, Shia Ben-Chang, Hsu Yen-Bin, Shen Po-Chih,Chu Kuo-Hao, To Integrate Text Mining and Artificial Neural Network to Forecast Gold Futures Price[C], 2009 International Conference on New Trends in Information and Service Science, 2009:1014-1020
[21]胡恩同,黄金的双重属性与其价格决定机制[J],黄金科学技术, 2005, 13(9):1-7
[22]李楠,黄金价格决定因素研究[J], 2009, 36:79-80
[23]李家林,长期黄金价格影响因素实证分析[J],生产力研究, 2009, 14:48-50
[24]梁维全,黄金价格波动的影响因素的实证研究[J],中国证券期货, 2009,5:48-51
[25]杨柳勇,史震涛,黄金价格的长期决定因素分析[J],统计研究, 2004, 6:21-24
[26]刘曙光,胡再勇,黄金价格的长期决定因素稳定性分析[J],世界经济研究, 2008, 2:35-42
[27]周华林,黄金价格影响因素的实证分析[J],重庆交通大学学报(社科版), 2008, 8(6):42-46
[28]付丹,梅雪,张晖,黄金价格与通货膨胀相关性的实证分析[J],黄金, 2009, 30(1):4-7
[29]傅瑜,近期黄金价格波动的实证研究[J],产业经济研究, 2004, 1:30-40
[30]刘洪君,浅谈黄金价格[J],黄金科学技术, 2009, 17(1):60-63
[31]张宏颖,马艳华,于萍,世界黄金价格变化趋势及影响因素[J],工业技术经济, 1999, 18(3):63-65
[32]邱红,李肖钰,影响黄金价格的因素分析[J],东方企业文化, 2010, 2:86
[33]范思琦,孙黎,白岩,影响黄金价格因素及应对策略[J],黄金, 2006, 27(12):8-11
[34]刘澄,张均东,国际黄金、白银价格变动的实证分析[J],特区经济, 2007, 12:93-94
[35]杨叶,黄金价格和石油价格的联动分析[J],黄金, 2007, 28(2):4-7
[36]张次兰,郇红艳,石油价格与黄金价格的实证分析[J],黄金市场, 2009, 3:50-51
[37]张莹,胥莉,陈宏民,石油与黄金产业价格联动关系研究[J],财经问题研究, 2007, 7:35-39
[38]钱冰冰, Type-2模糊系统在黄金价格预测中的应用[J],佳木斯大学学报(自然科学版), 2007, 25(3):387-389
[39]黄师娟,张德生,常振海,张华,国际黄金价格的小波变换FAR预测模型[J],西安工业大学学报[J], 2009, 29(1):84-88
[40]方超逸,国际黄金价格走势分析与预测方法[J],黄金, 2009, 30(11):4-7
[41]谢明铎,吴加荣,何穗,黄金交易市场的预测分析[J],湖北师范学院学报(自然科学版), 2009, 29(3):60-65
[42]顾孟钧,张志和,陈友,基于BP神经网络的国际黄金价格预测模型[J],商业研究, 2008, 9(下旬刊):26
[43]李京, GA-BP算法在黄金价格预测中的应用[J],金融经济, 2010,(2):73-74
[44]张均东,刘澄,孙彬,基于人工神经网络算法的黄金价格预测问题研究[J],经济问题, 2010, 1:110-114
[45]王中香,王凤,何穗,基于神经网络的黄金期货价格的预测[J],湖北师范学院学报(自然科学版), 2009, 29(3):85-88
[46]胡乃联,宋鑫,自适应过滤模型在黄金价格预测中的应用[J],黄金, 1999, 20(5):53-54
[47]郑秀田,基于GARCH-M模型的黄金市场风险与收益关系研究[J], 2008, 29(5):4-7
[48]潘贵豪,胡乃联,刘焕中,李国清,基于ARMA-GARCH模型的黄金价格实证分析[J],黄金, 2010, 31(1):5-8
[49]林雨,孔刘柳,刘培,基于ARFIMA模型的黄金价格预测[J],南华大学学报(社会科学版), 2010, 11(1):36-38
[50]舒通,基于变系数回归模型的石油价格预测[J],数理统计与管理, 2008, 27(5):815-820
[51]何晓群,刘文卿,浅谈加权最小二乘法及其残差图--兼答孙小素副教授[J],统计研究, 2006, (4):53-57
[52]欧阳光,变系数回归模型的参数估计[J],湘南学院学报, 2005, 26(2):15-19+22
[53] Mei Changlin, zhang Wenxiu, Statistical Inferences for Varying-Coefficint Models Based on Locally Weighted Regression Technique[J], Acta Mathematicae Applicatae Sinica, 2001, 17(3):407-417
[54]覃文忠,王建梅,刘妙龙,地理加权回归分析空间数据的空间非平稳性[J],辽宁师范大学学报(自然科学版), 2005, 28(4):476-479
[2] Wang Chengbiao, Chen Yanhui, Li Lihong, The forecast of gold price based on the GM(1,1) and Markov chain[C], Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, 2007, Nanjing, China, VOLS 1 AND 2:739-743
[3] Edel Tully, Brian M.Lucey, A power GARCH examination of the gold market[J], Research in International Business and Finance, 2007,21(2):316-325
[4] Larry A. Sjaastad, The price of gold and the exchange rates: Once again[J], Resources Policy, 2008, 33(2):118-124
[5] A.G. Malliaris, Mary Malliaris, Time Series and Neural Networks Comparison on Gold, Oil and the Euro[C], Proceedings of International Joint Conference on Neural Networks, Atlanta, Georgia, USA, June 14-19, 2009:1961-1967
[6] Stephen Hamston, .Gold as a Store of value[J/OL], The World Gold Council, 1998
[7] Ugur Soytas, RamazanSari, Shawkat Hammoudeh, Erk Hacihasanoglu, world oil prices, precious metal prices and macroeconomy in Turkey[J], Energy Policy, 2009,37(12):5557-5566
[8] Zhang Jinliang, Tang Mingming, Tao Mingxin, Effects Simulation of International Gold Prices on Crude Oil Prices based on WBNNK Model[C], 2009 ISECS International Colloquium on Computing, Communication, Control, and Management, 2009:459-464
[9] John Baffes, Oil spills on other commodities[J], Resources Policy, 2007,32(3):126-134
[10] Alvaro Escribano, Clive W.J. GRANGER, Investigating the Relationship between Gold and Silver Prices[J], Journal of Forecasting, 1998, 17(2):81-107
[11] Shawkat Hammoudeh, Yuan Yuan, Metal volatility in presence of oil and interest rate shocks[J], Energy Economics,2008, 30(2):606–620
[12] C. Ciner, On the long run relationship between gold and silver prices A note[J], Global Finance Journal, 2001,12(2):299-303
[13] Thomas J. Urich, Modes of fluctuation in metal futures prices[J], Journal of Futures Markets, 2000, 20(3):219-241
[14] K. Ivanova, M. Ausloos, Low q-moment multifractal analysis of Gold price, Dow Jones Industrial Average and BGL-USD exchange rate[J], The European Physical Journal B, 1999, 8(4):665-669
[15] Graham Smith, The price of Gold and Stoek Priee Indices for the United States[J/OL]. The World Gold Council. 2001
[16] Xu Li, Song Shaowen, Wang Beibei, Study on the gold price and yield based on GARCH models[C], Proceedings of 2008 International Conference on Risk and Reliability Management, 2008, Beijin China, Vols I And II: 222-226
[17] Antonino Parisi, Franco Parisi, David Diaz, Forecasting gold price changes: Rolling and recursive neural network models[J], Journal of Multinational financial management, 2008,18(5):477-487
[18] Chunmei Liu, Price forecast for gold futures based on GA-BP neural network[C], Proceedings - International Conference on Management and Service Science, September 20-22, 2009, Wuhan, China
[19] Terence C. Mills, Statistical analysis of daily gold price data[J], Physica A: Statistical Mechanics and its Applications, 2004, 338(3-4):559—566
[20] Xu Guo-Xiang, Shia Ben-Chang, Hsu Yen-Bin, Shen Po-Chih,Chu Kuo-Hao, To Integrate Text Mining and Artificial Neural Network to Forecast Gold Futures Price[C], 2009 International Conference on New Trends in Information and Service Science, 2009:1014-1020
[21]胡恩同,黄金的双重属性与其价格决定机制[J],黄金科学技术, 2005, 13(9):1-7
[22]李楠,黄金价格决定因素研究[J], 2009, 36:79-80
[23]李家林,长期黄金价格影响因素实证分析[J],生产力研究, 2009, 14:48-50
[24]梁维全,黄金价格波动的影响因素的实证研究[J],中国证券期货, 2009,5:48-51
[25]杨柳勇,史震涛,黄金价格的长期决定因素分析[J],统计研究, 2004, 6:21-24
[26]刘曙光,胡再勇,黄金价格的长期决定因素稳定性分析[J],世界经济研究, 2008, 2:35-42
[27]周华林,黄金价格影响因素的实证分析[J],重庆交通大学学报(社科版), 2008, 8(6):42-46
[28]付丹,梅雪,张晖,黄金价格与通货膨胀相关性的实证分析[J],黄金, 2009, 30(1):4-7
[29]傅瑜,近期黄金价格波动的实证研究[J],产业经济研究, 2004, 1:30-40
[30]刘洪君,浅谈黄金价格[J],黄金科学技术, 2009, 17(1):60-63
[31]张宏颖,马艳华,于萍,世界黄金价格变化趋势及影响因素[J],工业技术经济, 1999, 18(3):63-65
[32]邱红,李肖钰,影响黄金价格的因素分析[J],东方企业文化, 2010, 2:86
[33]范思琦,孙黎,白岩,影响黄金价格因素及应对策略[J],黄金, 2006, 27(12):8-11
[34]刘澄,张均东,国际黄金、白银价格变动的实证分析[J],特区经济, 2007, 12:93-94
[35]杨叶,黄金价格和石油价格的联动分析[J],黄金, 2007, 28(2):4-7
[36]张次兰,郇红艳,石油价格与黄金价格的实证分析[J],黄金市场, 2009, 3:50-51
[37]张莹,胥莉,陈宏民,石油与黄金产业价格联动关系研究[J],财经问题研究, 2007, 7:35-39
[38]钱冰冰, Type-2模糊系统在黄金价格预测中的应用[J],佳木斯大学学报(自然科学版), 2007, 25(3):387-389
[39]黄师娟,张德生,常振海,张华,国际黄金价格的小波变换FAR预测模型[J],西安工业大学学报[J], 2009, 29(1):84-88
[40]方超逸,国际黄金价格走势分析与预测方法[J],黄金, 2009, 30(11):4-7
[41]谢明铎,吴加荣,何穗,黄金交易市场的预测分析[J],湖北师范学院学报(自然科学版), 2009, 29(3):60-65
[42]顾孟钧,张志和,陈友,基于BP神经网络的国际黄金价格预测模型[J],商业研究, 2008, 9(下旬刊):26
[43]李京, GA-BP算法在黄金价格预测中的应用[J],金融经济, 2010,(2):73-74
[44]张均东,刘澄,孙彬,基于人工神经网络算法的黄金价格预测问题研究[J],经济问题, 2010, 1:110-114
[45]王中香,王凤,何穗,基于神经网络的黄金期货价格的预测[J],湖北师范学院学报(自然科学版), 2009, 29(3):85-88
[46]胡乃联,宋鑫,自适应过滤模型在黄金价格预测中的应用[J],黄金, 1999, 20(5):53-54
[47]郑秀田,基于GARCH-M模型的黄金市场风险与收益关系研究[J], 2008, 29(5):4-7
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