美元兑人民币汇率的时间序列模型

美元兑人民币汇率的时间序列模型 美元兑人民币汇率的时间序列模型 一、 背景意义 近年来，关于人民币升值问题的讨论非常激烈，尤其是美元兑人民币汇率呈现持续下跌的态势。而人民币被公认为与美元挂钩，人民币汇率再一次成为全球瞩目的焦点。世界上许多经济学家和政府决策者纷纷呼吁中国对人民币重估使其升值。然而，如果盲目的升值又会给我国经济带来严重的影响。比如1、会削弱中国商品在国际市场上的竞争力。中国商品以“物美价廉”打进世界市场，人民币升值必然会影响中国产品的出口以及在国际市场上的竞争力。2、外国企业来华投资数量将减少。中国的发展经验证明，缺少外资，或者是外资骤减对中国的持续发展非常不利。3、对发展中国的国内旅游业不利。4、导致购买力提高，从而导致严重的通货膨胀。故现阶段稳定人民币汇率具有重要意义。 人民币目前的状况与85年的日元很相像，国内长时期的高速发展的经济，同样的持续对美国的顺差，快速累积的高额美元储备，美国同样的双赤字恶化，美元持续走低的压力，甚至相似的低利率，最终我们也受到了同样的升值压力。 鉴于此，我们完全有必要采取一定的方法对美元兑人民币汇率进行准确的研究和预测，为相关部门提供一定的数据，最终能采取适当的措施稳定人民币汇率，从而有利于我国经济的发展。本文选择2004年以来的美元兑人民币汇率月度数据，先对数据进行一系列的分析和处理，选择合适的时间序列模型，然后借助模型对未来三个月的汇率进行预测。 二、 数据的预处理及模型识别 (一)数据来源:教材《应用时间序列分析》附录1.6 (二)数据预处理 下面通过对汇率序列xt及其差分序列Dxt的折线图、相关图和偏向关图分析判别其平稳性以及识别模型形式。 1、对于美元兑人民币汇率序列 (1)汇率序列的折线图 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national (2)汇率序列的相关图、偏相关图 2、汇率的一阶差分y=dxt序列 (1)差分序列折线图 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national (2)差分序列的相关图、偏相关图 由上图可知，汇率序列xt是非平稳序列。汇率差分序列Dxt是平稳序列。应该 用Dxt建立模型。再结合差分序列的相关图和偏相关图，偏自相关图一阶截尾， 应建立AR(1)模型。 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national 三、 研究方法介绍 这里采用的是时间序列分析方法中的时域分析法，它的基本思想是源于事件的发展通常都具有一定的惯性，这种惯性使用统计语言描述即为序列之间的相关关系，而这种相关关系具有一定的统计性质，时域分析的重点就是寻找这种统计规律，并且拟合适当的数学模型来描述这种规律，进而利用这个拟合模型来预测序列未来的走势。 四、 模型的建立与求解 由以上分析知汇率差分序列应建立AR(1)模型。运用Eviews 软件，估计结果如下: 由上图我们可以看出这一模型的自回归系数参数估计结果显著不为零，将估计参数代入AR(1)模型得 Yt = -0.028607 + 0.441605 (Yt-1+0.028607) + 即 Yt =-0.01597+ 0.441605 Yt-1 + 五、 模型的检验及优化 检验思想:时间序列模型的诊断检验有两类问题:一类是模型的显著性检验;另外一类是参数的显著性检验。模型的显著性检验即为检验模型的有效性，而有效diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national 性的是看它提取的信息是否充分，可通过检验其残差序列是否为白噪声序列得知。参数的显著性检验就是检验模型的每一个未知参数是否显著为零，其检验目的是为了使得模型更为精简。 1.、模型的显著性检验 Yt的残差序列的相关图及偏相关图如下: 比较上图中第五期和第六期的p值知:原假设发生的概率远大于5%，非小概率事件。故残差序列为白噪声序列，模型的残差中已不含有自回归和移动平均成分，说明模型拟合显著有效。 2.、参数的显著性检验 经计算知:均值的检验结果:t统计量:-3.535845 P值:0.0009<<0.05 系数的检验结果:t统计量:3.376150 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national P值:0.0014<<0.05 可得出结论:参数均显著 并且其他几个统计量，如R-squared、Adjusted R-squared等效果都还不错，而AR(1)模型的单位根0.44<1 再次验证了我们认为Yt平稳的判断。 通过以上模型检验和参数检验，我认为上式是一个满意的模型。然而，为确保所选用的模型是最优的，我还做了以下尝试:分别采用MA(3),ARMA(1,3),ARMA(1,2) 和ARMA(1,1)进行拟合分析，然后比较这些模型的AIC值和SBC值，最后得出所选择的AR(1)模型是最优的。 AR(1)模型的拟合效果及残差如下图所示: 由图形可看出拟合的效果还是不错的。从残差图可以看出，除个别数据外，其余数据的残差离零点均较近，这说明所选模型能较好的符合原始数据，而那个别数据可视为异常点。 六、 模型预测与评估 1、 修改workfile范围 2、 修改sample范围 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national 3、 进行预测 结果如下 YF SE 将2008年6月的汇率6.8591代入可得: 2008年7月的汇率预测值值为6.8591-0.033364=6.825736 置信度为95%的置信区间为(6.79026，6.861212) 2008年8月的汇率预测值值为6.825736-0.030708=6.795028 置信度为95%的置信区间为(6.758992，6.831064) 2008年9月的汇率预测值值为6.795028-0.029535=6.765493 置信度为95%的置信区间为(6.729349，6.801637) 参考真实数据 2008年7月 6.8388 2008年8月 6.8345 2008年9月 6.8183 预测误差为(6.825736-6.8388)/6.8388=-0.00191 (6.795028-6.8345)/ 6.8345=-0.00578 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national (6.765493-6.8183)/ 6.8183=-0.00774 七、结论 所选AR(1)模型能够较好的解释美元兑人民币的汇率，故可采用此模型对汇率进 行分析预测。 diagnosis treatment of functions. Medical laboratory specialist stages for a period of 1-3 years. A, training objectives (1) to supervise medical staff with the right choice testing and specimen collection. (2) able to properly interpret results of testing and counselling, participation in clinical diagnosis and treatment of disease consultation and discussion and a series of communication and Exchange and clinical tasks. (3) the limited inspection data can be translated into effective diagnosis and treatment of disease information. (4) take on scientific and technical research laboratory diagnosis-related tasks. Second, training requirements (1) the education requirements: Bachelor degree for clinical medicine and received a Bachelor of medicine degree above. (2) training years: Dr: research type 3 years (medical 12 months; test section 24 months) clinical type 2 years (test section 24 months) master: research type 3 years (medical 12 months; test section 24 months) clinical type 2.5 years (medical 6 months; test section 24 months) undergraduate: 3 years (medical 12 months; test section 24 months) three, and training method (1) First phase of the rotation order: test section 4-month rotations in clinical laboratory, clinical chemistry test inspection, examination in clinical Haematology, Clinical Immunology, clinical microbiology, initially familiar with the laboratory situation. Phase II: 12-month rotations in internal medicine, cardiovascular, renal, respiratory, digestive, Endocrinology, hematology, infectious diseases 7 Professional. Through the national