基于贝叶斯理论MCMC优化参数的负荷预测模型
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摘要
电力负荷预测是电力技术经济分析的重要组成部分,在电力规划、运行、调度中发挥着重要的作用。电力负荷预测对于电力系统经济安全可靠地运行具有重要的意义。本文提出了基于贝叶斯理论马尔可夫链蒙特卡洛(MCMC)算法优化参数的负荷预测模型。利用MCMC学习优化模型的参数时,模型的参数被看作随机变量。首先,利用样本数据和先验分布,根据贝叶斯定理计算参数的后验概率分布。然后,利用参数的后验概率分布来确定模型参数的估计值。计算参数的后验概率分布常常需要在高维的参数空间中进行积分计算。由于很难求出多重积分的解析值,数值计算方法常常用来计算多重积分。本文利用MCMC算法对高维积分进行近似计算。本文的主要研究工作如下：
1)分析了气象因素和短期负荷之间的关系,通过散点图和拟合曲线来确定气象因素和短期负荷是否存在联系。由分析结果可知温度和相对湿度是两个对负荷有着明显影响的气象因素。
2)建立了基于贝叶斯神经网络日负荷曲线预测模型。气象因素变量和时间变量作为贝叶斯神经网络的输入变量,负荷作为输出变量。隐层神经元的数目手动给定的。贝叶斯神经网络的权参数是一个高维随机变量。本文提出了一种新的混合马尔可夫链蒙特卡洛算法来学习贝叶斯神经网络的权向量参数。这是将Leapfrog迭代算法和Metropolis-Hasting抽样方法相结合的混合算法。在学习贝叶斯神经网络的参数时贝叶斯神经网络看作是一个Hamilton动力系统,权向量参数看作是动力系统的位置变量。混合MCMC算法用来构造一个权向量参数的马尔可夫链,使得权向量参数的后验概率分布就是这个马尔可夫链的平稳分布。叶斯神经网络作为预测模型对整日负荷曲线进行预测。实验结果表明由混合马尔可夫链蒙特卡洛算法确定参数的贝叶斯神经网络较高的预测精度和较强的泛化能力。很好地克服了过拟合现象。
3)提出了基于具有解释变量状态空间模型的月度典型负荷预测方法。本文考虑月度的最大负荷和最小负荷典型负荷的预测。由于气象因素温度和相对湿度与负荷之间存在着正相关的关系,加热指数、制冷指数和相对湿度作为状态空间模型中回归项的解释变量。这个状态空间模型中有两种参数,一是解释变量的回归系数,另外一种是扰动项的方差参数。回归系数参数的估计值可以由Kalman滤波算法计算得到。学习方差参数时,根据共轭分布原则方差参数的先验分布选定为逆伽马分布。首先利用Gibbs抽样方法和Metropolis-Hasting抽样方法对方差参数进行抽样,得到一个马尔可夫链,然后利用蒙特卡洛方法估计出参数的取值。利用状态空间模型分别对月度的最大负荷和最小负荷进行了平滑拟合,并利用这个模型对未来6个月的最大负荷和最小负荷进行预测。实验结果表明该模型能够很好地平滑拟合已知的的样本数据,平滑拟合的平均绝对百分比误差和均方根误差都比较小。预测结果表明由MCMC算法确定参数的状态空间模型能够比较精确地预测3个月的典型负荷,而后3个月的预测误差就比较大了。
4)建立了一种新的超短期负荷预测模型—贝叶斯ARIMA-GARCH预测模型。分析超短期负荷数据,发现扰动项具有明显的异方差特性。假设超短期负荷数据是由均值部分和方差部分组成。为了既要考虑负荷数据均值部分的变化情况,也要考虑扰动项的异方差特性,提出了利用ARIMA-GARCH模型对超短期负荷数据进行建模。其中ARIMA(p,d,q)模型用来描述超短期负荷数据均值部分变化情况,GARCH(1,1)模型用来刻画方差部分的异方差特性。ARIMA(p,d,q)模型的阶数p,d和q由负荷时间序列数据的自相关函数和偏自相关函数的截尾性和拖尾性确定。拟极大似然估计法通常用来估计GARCH(1,1)模型的参数。本文给出了一种新的组合MCMC算法估计GARCH(1,1)模型参数方法,这种方法是把Gibbs抽样方法和Metropolis准则相结合在一起来构造参数的马尔可夫链。其中Gibbs算法对GARCH(1,1)模型的方差参数和自由度参数进行抽样,得到一个候选样本。然后根据Metropolis准则判断是否接受这个样本做为马尔可夫链得元素。本文把由QMLE算法和组合MCMC算法估计参数的ARIMA-GARCH模型对未来一个小时内的12个5分钟时刻的负荷值进行预测。以3月份和7月份的数据为例,预测了15日12点到13点12个5分钟时刻的负荷。预测结果表明由组合MCMC算法确定参数的ARIMA-GARCH模型的预测精度要高于由拟极大似然估计法估计参数的模型的预测精度,而且ARIMA-GARCH模型的预测误差要远远小于单一的ARIMA模型的预测误差。
Electric load forecasting is one important component of electricity technical economy. It is a very important work for electricity network programming, electricity power system satisfyingly running and load distribution. This paper presents a new type of load forecasting model. Based on the Bayesian theory, the model parameters were optimized by the Markov chain Monte Carlo algorithms. During the learning process, given the sample data and prior distribution, The posterior distribution was used to estimate the model's parameters. The posterior calculation is an integration over the high dimensional parameter space. Usually numerical integration algorithms were used to compute the posterior. In this paper, the high dimensional integration was approximate calculated by two MCMC algorithms Gibbs sam-pling algorithm and Metropolis-Hasting sampling algorithm respectively. The main contents discussed in this thesis are:
1)The relationship between the weather factors and electricity load was discussed. An-alyzing the sample data, the scatter figures and fitting curves were used to determine the relationship. The conclusion is that temperature and relative humidity are two important weather influence factors.
2) The load curve forecasting model is established based on Bayesian Neural network learned by hybrid Monte Carlo Markov chain algorithm. The weather factors and time vari-able are the input variables, and electricity load is the output variable. The hidden neural units were given artificially. In Bayesian Neural network, the weight vector parameters were learned by a new hybrid Monte Carlo Markov chain algorithm. Bayesian neural network is considered as a Hamilton dynamic system, the weight vector parameters are the position variable in the Hamilton dynamic system. The Leapforg iterative algorithm and Metropolis-Hasting algorithm combines to construct an Markov chain of weight vector parameters, such that the in variant distribution of Markov chain is the desired posterior distribution. Then, using the Markov chain, we can get the estimation value of the weight vector parameter. The hourly loads ahead seven days were forecasted by the Bayesian neural network. The experi-ment result shows that the Bayesian neural network learned by hybrid Monte Carlo Markov chain algorithm has higher forecasting accuracy and good generalization performance than artificial neural network learned by BP algorithm. It can welly overcome the over-fitting phenomena.
3) A monthly special load forecasting method is proposed. The forecasting model is the state space model with explanatory variables. Because there exists some positive correlation between special load and weather factors temperature and relative humidity, the cooling degree and heating degree and relative humidity are the three explanatory variables. Our state space model has two types parameters, the regress coefficients of the explanatory variables and the variance of the fluctuation term. The regress coefficients are estimated by the Kalman filter. Gibbs sampling and Metropolis-Hasting sampling algorithms are used to construct a Markov chain of Variance parameters. Using Monte Carlo approximation calculating method, the conditional posterior expectation is obtained from the Markov chain. The estimation of variance parameters are conditional posterior expectation. The state space model can welly smooth the sample data. The root mean square error(RMSE) and Mean absolute percentage error(MAPE) are small. The State space model with weather factor explanatory variables forecasts the maximum load and minimum load ahead6months. The forecasting result shows that this model has higher forecasting accurity for the first three months, but for the second three months, the forecasting error is relatively large.
4)This paper presents a new ultra short term load forecasting model-Bayesian ARIMA-GARCH model. The fluctuation of ultra short load data has the heteroscedasticity property. The ARIMA(p,d,q)-GARCH(1,1) model can simultaneously consider the change ruler of the mean item and the heteroscedasticity of the variance item. ARIMA(p,d,q) model describes the attribution of mean item and GARCH(1,1) describes the variance item. It's parameters p, d, q are determined by the autocorrelation function(ACF) and partial autocorrelation func-tion(PACF). The coefficients parameters of GARCG(1,1)model usually are estimated by the pseudo-maximum likelihood. This paper propose a new combinational sample estimation method. Given the prior distribution and the sample observation data, An candidate sam-ple of variance parameters and free degree parameters is drew by the Gibbs algorithm form the conditional probability distribution, and the Metropolis criterion determines that if reject this candidate sample. Thus, the combinational sampling method can get a Markov chain of these parameters. After the parameter estimation work, the ARIMA(p,d,q)-GARCH(1,1) model which parameters are estimated by MCMC algorithm and PMLE algorithm respec-tively forecasts the twelve load value at every5minture time point of next hour. From experiment result, the ARIMA (p,d,q)-GARCH(1,1) Estimated by MCMC algorithm have higher forecasting accuracy than that estimated by QMLE algorithm. The forecasting errors RMSE and MAPE are far smaller than that of the single ARIMA model.
1)分析了气象因素和短期负荷之间的关系,通过散点图和拟合曲线来确定气象因素和短期负荷是否存在联系。由分析结果可知温度和相对湿度是两个对负荷有着明显影响的气象因素。
2)建立了基于贝叶斯神经网络日负荷曲线预测模型。气象因素变量和时间变量作为贝叶斯神经网络的输入变量,负荷作为输出变量。隐层神经元的数目手动给定的。贝叶斯神经网络的权参数是一个高维随机变量。本文提出了一种新的混合马尔可夫链蒙特卡洛算法来学习贝叶斯神经网络的权向量参数。这是将Leapfrog迭代算法和Metropolis-Hasting抽样方法相结合的混合算法。在学习贝叶斯神经网络的参数时贝叶斯神经网络看作是一个Hamilton动力系统,权向量参数看作是动力系统的位置变量。混合MCMC算法用来构造一个权向量参数的马尔可夫链,使得权向量参数的后验概率分布就是这个马尔可夫链的平稳分布。叶斯神经网络作为预测模型对整日负荷曲线进行预测。实验结果表明由混合马尔可夫链蒙特卡洛算法确定参数的贝叶斯神经网络较高的预测精度和较强的泛化能力。很好地克服了过拟合现象。
3)提出了基于具有解释变量状态空间模型的月度典型负荷预测方法。本文考虑月度的最大负荷和最小负荷典型负荷的预测。由于气象因素温度和相对湿度与负荷之间存在着正相关的关系,加热指数、制冷指数和相对湿度作为状态空间模型中回归项的解释变量。这个状态空间模型中有两种参数,一是解释变量的回归系数,另外一种是扰动项的方差参数。回归系数参数的估计值可以由Kalman滤波算法计算得到。学习方差参数时,根据共轭分布原则方差参数的先验分布选定为逆伽马分布。首先利用Gibbs抽样方法和Metropolis-Hasting抽样方法对方差参数进行抽样,得到一个马尔可夫链,然后利用蒙特卡洛方法估计出参数的取值。利用状态空间模型分别对月度的最大负荷和最小负荷进行了平滑拟合,并利用这个模型对未来6个月的最大负荷和最小负荷进行预测。实验结果表明该模型能够很好地平滑拟合已知的的样本数据,平滑拟合的平均绝对百分比误差和均方根误差都比较小。预测结果表明由MCMC算法确定参数的状态空间模型能够比较精确地预测3个月的典型负荷,而后3个月的预测误差就比较大了。
4)建立了一种新的超短期负荷预测模型—贝叶斯ARIMA-GARCH预测模型。分析超短期负荷数据,发现扰动项具有明显的异方差特性。假设超短期负荷数据是由均值部分和方差部分组成。为了既要考虑负荷数据均值部分的变化情况,也要考虑扰动项的异方差特性,提出了利用ARIMA-GARCH模型对超短期负荷数据进行建模。其中ARIMA(p,d,q)模型用来描述超短期负荷数据均值部分变化情况,GARCH(1,1)模型用来刻画方差部分的异方差特性。ARIMA(p,d,q)模型的阶数p,d和q由负荷时间序列数据的自相关函数和偏自相关函数的截尾性和拖尾性确定。拟极大似然估计法通常用来估计GARCH(1,1)模型的参数。本文给出了一种新的组合MCMC算法估计GARCH(1,1)模型参数方法,这种方法是把Gibbs抽样方法和Metropolis准则相结合在一起来构造参数的马尔可夫链。其中Gibbs算法对GARCH(1,1)模型的方差参数和自由度参数进行抽样,得到一个候选样本。然后根据Metropolis准则判断是否接受这个样本做为马尔可夫链得元素。本文把由QMLE算法和组合MCMC算法估计参数的ARIMA-GARCH模型对未来一个小时内的12个5分钟时刻的负荷值进行预测。以3月份和7月份的数据为例,预测了15日12点到13点12个5分钟时刻的负荷。预测结果表明由组合MCMC算法确定参数的ARIMA-GARCH模型的预测精度要高于由拟极大似然估计法估计参数的模型的预测精度,而且ARIMA-GARCH模型的预测误差要远远小于单一的ARIMA模型的预测误差。
Electric load forecasting is one important component of electricity technical economy. It is a very important work for electricity network programming, electricity power system satisfyingly running and load distribution. This paper presents a new type of load forecasting model. Based on the Bayesian theory, the model parameters were optimized by the Markov chain Monte Carlo algorithms. During the learning process, given the sample data and prior distribution, The posterior distribution was used to estimate the model's parameters. The posterior calculation is an integration over the high dimensional parameter space. Usually numerical integration algorithms were used to compute the posterior. In this paper, the high dimensional integration was approximate calculated by two MCMC algorithms Gibbs sam-pling algorithm and Metropolis-Hasting sampling algorithm respectively. The main contents discussed in this thesis are:
1)The relationship between the weather factors and electricity load was discussed. An-alyzing the sample data, the scatter figures and fitting curves were used to determine the relationship. The conclusion is that temperature and relative humidity are two important weather influence factors.
2) The load curve forecasting model is established based on Bayesian Neural network learned by hybrid Monte Carlo Markov chain algorithm. The weather factors and time vari-able are the input variables, and electricity load is the output variable. The hidden neural units were given artificially. In Bayesian Neural network, the weight vector parameters were learned by a new hybrid Monte Carlo Markov chain algorithm. Bayesian neural network is considered as a Hamilton dynamic system, the weight vector parameters are the position variable in the Hamilton dynamic system. The Leapforg iterative algorithm and Metropolis-Hasting algorithm combines to construct an Markov chain of weight vector parameters, such that the in variant distribution of Markov chain is the desired posterior distribution. Then, using the Markov chain, we can get the estimation value of the weight vector parameter. The hourly loads ahead seven days were forecasted by the Bayesian neural network. The experi-ment result shows that the Bayesian neural network learned by hybrid Monte Carlo Markov chain algorithm has higher forecasting accuracy and good generalization performance than artificial neural network learned by BP algorithm. It can welly overcome the over-fitting phenomena.
3) A monthly special load forecasting method is proposed. The forecasting model is the state space model with explanatory variables. Because there exists some positive correlation between special load and weather factors temperature and relative humidity, the cooling degree and heating degree and relative humidity are the three explanatory variables. Our state space model has two types parameters, the regress coefficients of the explanatory variables and the variance of the fluctuation term. The regress coefficients are estimated by the Kalman filter. Gibbs sampling and Metropolis-Hasting sampling algorithms are used to construct a Markov chain of Variance parameters. Using Monte Carlo approximation calculating method, the conditional posterior expectation is obtained from the Markov chain. The estimation of variance parameters are conditional posterior expectation. The state space model can welly smooth the sample data. The root mean square error(RMSE) and Mean absolute percentage error(MAPE) are small. The State space model with weather factor explanatory variables forecasts the maximum load and minimum load ahead6months. The forecasting result shows that this model has higher forecasting accurity for the first three months, but for the second three months, the forecasting error is relatively large.
4)This paper presents a new ultra short term load forecasting model-Bayesian ARIMA-GARCH model. The fluctuation of ultra short load data has the heteroscedasticity property. The ARIMA(p,d,q)-GARCH(1,1) model can simultaneously consider the change ruler of the mean item and the heteroscedasticity of the variance item. ARIMA(p,d,q) model describes the attribution of mean item and GARCH(1,1) describes the variance item. It's parameters p, d, q are determined by the autocorrelation function(ACF) and partial autocorrelation func-tion(PACF). The coefficients parameters of GARCG(1,1)model usually are estimated by the pseudo-maximum likelihood. This paper propose a new combinational sample estimation method. Given the prior distribution and the sample observation data, An candidate sam-ple of variance parameters and free degree parameters is drew by the Gibbs algorithm form the conditional probability distribution, and the Metropolis criterion determines that if reject this candidate sample. Thus, the combinational sampling method can get a Markov chain of these parameters. After the parameter estimation work, the ARIMA(p,d,q)-GARCH(1,1) model which parameters are estimated by MCMC algorithm and PMLE algorithm respec-tively forecasts the twelve load value at every5minture time point of next hour. From experiment result, the ARIMA (p,d,q)-GARCH(1,1) Estimated by MCMC algorithm have higher forecasting accuracy than that estimated by QMLE algorithm. The forecasting errors RMSE and MAPE are far smaller than that of the single ARIMA model.
引文
[1]王信茂.对“十二五”加快电力发展方式转变的思考[J].能源技术经济,2010,22(005)：1-7.
[2]张文泉,高玉君.电力技术经济学的建立与发展[J].电力技术经济,2004,16(003)：4-7.
[3]Alfares H, Nazeeruddin M. Electric load forecasting:literature survey and classifica-tion of methods[J]. International Journal of Systems Science,2002,33(1):23-34.
[4]于尔铿,韩放,谢开,等.电力市场[M].北京：中国电力出版社,1998.
[5]牛东晓.电力负荷预测技术及其应用[M].北京：中国电力出版社,1999.
[6]尚金成,黄永皓,夏清.电力市场理论研究与应用[M].北京：中国电力出版社,2002.
[7]叶彬.混合智能建模技术及其在短期负荷预测中的应用研究[D].杭州：浙江大学,2006.
[8]Taylor J, Buizza R. Neural network load forecasting with weather ensemble predic-tions[J]. Power Systems, IEEE Transactions on,2002,17(3):626-632.
[9]Engle R, Granger C, Rice J, et al. Semiparametric estimates of the relation between weather and electricity sales[J]. Journal of the American Statistical Association,1986, 81(394):310-320.
[10]Hor C, Watson S, Majithia S. Analyzing the impact of weather variables on monthly electricity demand[J]. Power Systems, IEEE Transactions on,2005,20(4):2078-2085.
[11]Parkpoom S, Harrison G. Analyzing the impact of climate change on future electricity demand in Thailand[J]. Power Systems, IEEE Transactions on,2008,23(3):1441-1448.
[12]Liu X, Sweeney J. The impacts of climate change on domestic natural gas consump-tion in the Greater Dublin Region[J]. International Journal of Climate Change Strate-gies and Management,2012,4(2):161-178.
[13]Jardini J, Tahan C, Ahn S, et al. Distribution transformer loading evaluation based on load profiles measurements [J]. Power Delivery, IEEE Transactions on,1997, 12(4):1766-1770.
[14]牛东晓,邢棉.短期电力负荷预测的小波神经元网络模型的研究[J].电网技术,1999,23(4)：21-24.
[15]Jardini J, Tahan C, Gouvea M, et al. Daily load profiles for residential, commercial and industrial low voltage consumers[J]. Power Delivery, IEEE Transactions on,2000, 15(1):375-380.
[16]Chang R, Leou R, Lu C. Distribution transformer load modeling using load research data[J]. Power Delivery, IEEE Transactions on,2002,17(2):655-661.
[17]康重庆,夏清,刘梅,等.应用于负荷预测中的回归分析的特殊问题[J].电力系统自动化,1998,22(10)：3841.
[18]赵宏伟,任震,黄雯莹.基于周期自回归模型的短期负荷预测[J].中国电机工程学报,1997,17(5)：348-351.
[19]Charytoniuk W, Chen M, Van Olinda P. Nonparametric regression based short-term load forecasting[J]. Power Systems, IEEE Transactions on,1998,13(3):725-730.
[20]Papalexopoulos A, Hesterberg T. A regression-based approach to short-term system load forecasting[J]. Power Systems, IEEE Transactions on,1990,5(4):1535-1547.
[21]Broadwater R, Sargent A, Yarali A, et al. Estimating substation peaks from load research data[J]. Power Delivery, IEEE Transactions on,1997,12(1):451-456.
[22]Nazarko J, Zalewski W. The fuzzy regression approach to peak load estimation in power distribution systems[J]. Power Systems, IEEE Transactions on,1999, 14(3):809-814.
[23]Haida T, Muto S. Regression based peak load forecasting using a transformation technique[J]. Power Systems, IEEE Transactions on,1994,9(4):1788-1794.
[24]Ruzic S, Vuckovic A, Nikolic N. Weather sensitive method for short term load fore-casting in electric power utility of Serbia[J]. Power Systems, IEEE Transactions on, 2003,18(4):1581-1586.
[25]Hagan M, Behr S. The time series approach to short term load forecasting[J]. Power Systems, IEEE Transactions on,1987,2(3):785-791.
[26]Chen J, Wang W, Huang C. Analysis of an adaptive time-series autoregressive moving-average (ARMA) model for short-term load forecasting[J]. Electric Power Systems Research,1995,34(3):187-196.
[27]侯志俭,吴际舜,张琦雨,等.电力系统短期负荷预报的几种改进手段[J].电力系统自动化,1996,20(7)：27-31.
[28]叶瑰昀,罗耀华.基于ARMA模型的电力系统负荷预测方法研究[J].信息技术,2002(006)：74-76.
[29]Yang H, Huang C, Huang C. Identification of ARMAX model for short term load forecasting:an evolutionary programming approach[C]//Power Industry Computer Application Conference. Salt Lake City UT:[s.n.],1995:325-330.
[30]Huang C, Huang C, Wang M. A particle swarm optimization to identifying the AR-MAX model for short-term load forecasting[J]. Power Systems, IEEE Transactions on,2005,20(2):1126-1133.
[31]Wang B, Tai N, Zhai H, et al. A new ARMAX model based on evolutionary algorithm and particle swarm optimization for short-term load forecasting [J]. Electric Power Systems Research,2008,78(10):1679-1685.
[32]王晛,张少华.一种应用时间序列技术的短期电力负荷预测模型[J].上海大学学报：自然科学版,2002,8(2)：133-136.
[33]鞠平,姜巍,赵夏阳.96点短期负荷预测方法及其应用[J].电力系统自动化,2001,25(22)：32-36.
[34]张颖,高中文.基于时间序列和神经网络的电力系统负荷预测[J].哈尔滨理工大学学报,2003,8(1)：30-32.
[35]Haykin S. Neural networks:a comprehensive foundation[M]. Michigan:USA:Pren-tice Hall,1999.
[36]Park D, El-Sharkawi M, Marks R, et al. Electric load forecasting using an artificial neural network[J]. Power Systems, IEEE Transactions on,1991,6(2):442-449.
[37]Peng T, Hubele N, Karady G. Advancement in the application of neural networks for short-term load forecasting[J]. Power Systems, IEEE Transactions on,1992, 7(1):250-257.
[38]Khotanzad A, Afkhami-Rohani R, Lu T, et al. ANNSTLF-a neural-network-based electric load forecasting system[J]. Neural Networks, IEEE Transactions on,1997, 8(4):835-846.
[39]Marin F, Garcia-Lagos F, Joya G, et al. Global model for short-term load forecasting using artificial neural networks[J].2002,149(2):121-125.
[40]Senjyu T, Takara H, Uezato K, et al. One-hour-ahead load forecasting using neural network[J]. Power Systems, IEEE Transactions on,2002,17(1):113-118.
[41]Satish B, Swarup K, Srinivas S, et al. Effect of temperature on short term load forecast-ing using an integrated ANN[J]. Electric Power Systems Research,2004,72(1):95-101.
[42]谢宏,程浩忠,张国立,et al.基于粗糙集理论建立短期电力负荷神经网络预测模型[J].中国电机工程学报,2004,23(11)：1-4.
[43]程其云,孙才新,周湶,et al.粗糙集信息熵与自适应神经网络模糊系统相结合的电力短期负荷预测模型及方法[J].电网技术,2004,28(17)：72-75.
[44]罗治强,张焰,朱杰.粗集理论在电力系统负荷预测中的应用[J].电网技术,2004,28(3)：29-32.
[45]雷绍兰,孙才新,周湶,et al.模糊粗糙集理论在空间电力负荷预测中的应用[J].电网技术,2005,29(9)：26-30.
[46]王志勇,郭创新,曹一家.基于模糊粗糙集和神经网络的短期负荷预测方法[J].中国电机工程学报,2005,25(19)：7-11.
[47]Xiao Z, Ye S, Zhong B, et al. BP neural network with rough set for short term load forecasting[J]. Expert Systems with Applications,2009,36(1):273-279.
[48]庞清乐.基于粗糙集理论的神经网络预测算法及其在短期负荷预测中的应用[J].电网技术,2010,34(12)：168-173.
[49]牛东晓,陈志业.遗传神经网络优化预测方法研究及其应用[J].华北电力大学学报,2001,28(1)：1-5.
[50]Ling S, Leung F, Lam H, et al. Short-term electric load forecasting based on a neural fuzzy network[J]. Industrial Electronics, IEEE Transactions on,2003,50(6):1305-1316.
[51]谢宏,陈志业,牛东晓,et al.基于小波分解与气象因素影响的电力系统日负荷预测模型研究[J].中国电机工程学报,2001,21(5)：5-10.
[52]张大海,江世芳,毕研秋,et al.基于小波神经网络的电力负荷预测方法[J].电力自动化设备,2003,23(8)：29-32.
[53]徐军华,刘天琪.基于小波分解和人工神经网络的短期负荷预测[J].电网技术,2004,28(8)：30-33.
[54]Nengling T, Stenzel J, Hongxiao W. Techniques of applying wavelet transform into combined model for short-term load forecasting[J]. Electric power systems research, 2006,76(6):525-533.
[55]Bakirtzis A, Theocharis J, Kiartzis S, et al. Short term load forecasting using fuzzy neural networks[J]. Power Systems, IEEE Transactions on,1995,10(3):1518-1524.
[56]Papadakis S, Theocharis J, Kiartzis S, et al. A novel approach to short-term load forecasting using fuzzy neural networks[J]. Power Systems, IEEE Transactions on, 1998,13(2):480-492.
[57]Kim K, Youn H, Kang Y. Short-term load forecasting for special days in anomalous load conditions using neural networks and fuzzy inference method[J]. Power Systems, IEEE Transactions on,2000,15(2):559-565.
[58]Song K, Baek Y, Hong D, et al. Short-term load forecasting for the holidays us-ing fuzzy linear regression method[J]. Power Systems, IEEE Transactions on,2005, 20(1):96-101.
[59]Khan M, Abraham A. Short Term Load Forecasting Models in Czech Republic Using Soft Computing Paradigms[J]. arXiv preprint cs/0405051,2004.
[60]Liao G, Tsao T. Application of fuzzy neural networks and artificial intelligence for load forecasting[J]. Electric Power Systems Research,2004,70(3):237-244.
[61]Liao G, Tsao T. Application of a fuzzy neural network combined with a chaos genetic algorithm and simulated annealing to short-term load forecasting[J]. Evolutionary Computation, IEEE Transactions on,2006,10(3):330-340.
[62]Mamlook R. Fuzzy set methodology for evaluating alternatives to compare between different power production systems[J]. Journal of Applied Sciences,2006,6(9):1686-1691.
[63]Mamlook R, Badran O, Abdulhadi E. A fuzzy inference model for short-term load forecasting[J]. Energy Policy,2009,37(4):1239-1248.
[64]Chenthur Pandian S, Duraiswamy K, Christober Asir Rajan C, et al. Fuzzy approach for short term load forecasting[J]. Electric Power Systems Research,2006,76(6):541-548.
[65]Hinojosa V, Hoese A. Short-term load forecasting using fuzzy inductive reasoning and evolutionary algorithms[J]. Power Systems, IEEE Transactions on,2010,25(1):565-574.
[66]Al-Kandari A, Soliman S, El-Hawary M. Fuzzy short-term electric load forecast-ing[J]. International journal of electrical power & energy systems,2004,26(2):111-122.
[67]Vapnik V. The nature of statistical learning theory[M]. New York:Springer Verlag, 1999.
[68]Smola A J, Scholkopf B. A tutorial on support vector regression[J]. Statistics and computing,2004,14(3):199-222.
[69]Suykens J, Vandewalle J. Least squares support vector machine classifiers [J]. Neural processing letters,1999,9(3):293-300.
[70]Chang M, Chen B, Lin C. EUNITE network competition:Electricity load forecast-ing[C]//National Taiwan University. Taipei, Taiwan:[s.n.],2001.
[71]Chen B, Chang M, et al. Load forecasting using support vector machines:A study on EUNITE competition 2001 [J]. Power Systems, IEEE Transactions on,2004, 19(4):1821-1830.
[72]Mohandes M. Support vector machines for short-term electrical load forecastingfJ]. International Journal of Energy Research,2002,26(4):335-345.
[73]Bao Z, Pi D, Sun Y. Short-term load forecasting based on self-organizing map and support vector machine[J]. Advances in Natural Computation,2005:688-691.
[74]Hsu C, Wu C, Chen S, et al. Dynamically optimizing parameters in support vector regression:An application of electricity load forecasting[C]//System Sciences,2006. HICSS'06. Proceedings of the 39th Annual Hawaii International Conference on. Tai-wan:[s.n.],2006,2:30-37.
[75]牛东晓,谷志红,邢棉,et al.基于数据挖掘的SVM短期负荷预测方法研究[J].中国电机工程学报,2006,26(18)：6-12.
[76]Espinoza M, Suykens J, De Moor B. Load forecasting using fixed-size least squares support vector machines[J]. Computational Intelligence and Bioinspired Systems, 2005:488-527.
[77]Wu H, Zhang S. Power load forecasting with least squares support vector machines and chaos theory[C]//Neural Networks and Brain,2005. ICNN&B'O5. International Conference on. Dalian:China:[s.n.],2005,2:1020-1024.
[78]唐杰明,刘俊勇,杨可,et al.基于灰色模型和最小二乘支持向量机的电力短期负荷组合预测[J].电网技术,2009,33(3)：63-68.
[79]King G. Variance specification in event count models:From restrictive assumptions to a generalized estimator[J]. American Journal of Political Science,1989:762-784.
[80]Naylor J, Smith A. Econometric illustrations of novel numerical integration strategies for Bayesian inference[J]. Journal of Econometrics,1988,38(1):103-125.
[81]Tierney L, Kadane J. Accurate approximations for posterior moments and marginal densities[J]. Journal of the American Statistical Association,1986,81(393):82-86.
[82]Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,1984,17(6):721-741.
[83]Gelfand A, Smith A. Sampling-based approaches to calculating marginal densities[J]. Journal of the American statistical association,1990,85(410):398-409.
[84]Besag J, Green P. Spatial statistics and Bayesian computation[J]. Journal of the Royal Statistical Society. Series B (Methodological),1993:25-37.
[85]Bishop C. Pattern recognition and machine learning[M]. Vol.4. New York:USA: springer New York,2006.
[86]Andrieu C, De Freitas N, Doucet A, et al. An introduction to MCMC for machine learning[J]. Machine learning,2003,50(1):5-43.
[87]Kass R E, Carlin B P, Gelman A, et al. Markov chain monte carlo in practice:A roundtable discussion[J]. The American Statistician,1998,52(2):93-100.
[88]Chen M, Shao Q, Ibrahim J. Monte Carlo methods in Bayesian computation[M]. New York, USA:Springer Verlag,2000.
[89]Brooks S. Markov chain Monte Carlo method and its application[J]. Journal of the Royal Statistical Society:Series D (The Statistician),1998,47(1):69-100.
[90]Putter H, Heisterkamp S, Lange J, et al. A Bayesian approach to parameter estimation in HIV dynamical models[J]. Statistics in Medicine,2002,21(15):2199-2214.
[91]Huang Y, Liu D, Wu H. Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system[J]. Biometrics,2005,62(2):413-423.
[92]Lancaster T. An introduction to modern Bayesian econometrics[M]. USA:Wiley-Blackwell,2004.
[93]Geweke J, Whiteman C. Bayesian forecasting[J]. Handbook of Economic Forecast-ing,2006,1:3-80.
[94]Koop G. Bayesian econometric Methods[M]. Econometric Exercises, vol.23. UK: Cambridge University Press,2007.
[95]Harrison P, Stevens C. A Bayesian approach to short-term forecasting[J]. Operational Research Quarterly,1971:341-362.
[96]Zellner A, Chen B, et al. Bayesian modeling of economies and data requirements [J]. Macroeconomic Dynamics,2001,5(5):673-700.
[97]Brav A. Inference in Long-Horizon Event Studies:A Bayesian Approach with Appli-cation to Initial Public Offerings[J]. The Journal of Finance,2002,55(5):1979-2016.
[98]Harvey A, Trimbur T, Van Dijk H. Trends and cycles in economic time series:A Bayesian approach[J]. Journal of Econometrics,2007,140(2):618-649.
[99]Lahiri K, Sheng X. Learning and heterogeneity in GDP and inflation forecasts [J]. International Journal of Forecasting,2010,26(2):265-292.
[100]Geweke J, Amisano G. Comparing and evaluating Bayesian predictive distributions of asset returns[J]. International Journal of Forecasting,2010,26(2):216-230.
[101]Douglas A P, Breipohl A M, Lee F N, et al. The impacts of temperature forecast uncertainty on Bayesian load forecasting[J]. Power Systems, IEEE Transactions on, 1998,13(4):1507-1513.
[102]Lauret P, Fock E, Randrianarivony R, et al. Bayesian neural network approach to short time load forecasting[J]. Energy Conversion and Management,2008,49(5):1156-1166.
[103]Saini L M. Peak load forecasting using Bayesian regularization, Resilient and adaptive backpropagation learning based artificial neural networks[J]. Electric power systems research,2008,78(7):1302-1310.
[104]Cottet R, Smith M. Bayesian modeling and forecasting of intraday electricity load[J]. Journal of the American Statistical Association,2003,98(464):839-849.
[105]付桂琴,李运宗.气象条件对电力负荷的影响分析[J].气象科技,2009,36(6)：795-800.
[106]康重庆,周安石,王鹏,et al.短期负荷预测中实时气象因素的影响分析及其处理策略[J].电网技术,2006,30(7)：5-10.
[107]谢宏,陈志业.短期电力负荷预测的数据主成份分析[J].电网技术,2000,24(1)：43-46.
[108]Srinivasan D. Evolving artificial neural networks for short terra load forecasting[J]. Neurocomputing,1998,23(1):265-276.
[109]罗慧,巢清尘,李奇,et al.气象要素在电力负荷预测中的应用[J].气象,2005,31(6)：15-18.
[110]汪峰,于尔铿,阎承山,et al.基于因素影响的电力系统短期负荷预报方法的研究[J].中国电机工程学报,1999,19(8)：54-58.
[111]Hippert H, Pedreira C. Estimating temperature profiles for short-term load forecast-ing:neural networks compared to linear models[J].2004,151(4):543-547.
[112]秦海超,王玮,周晖,et al.人体舒适度指数在短期电力负荷预测中的应用[J].电力系统及其自动化学报,2006,18(2)：63-66.
[113]刘旭.基于实时气象因素的短期负荷预测方法研究[D].湖南：湖南大学,2009.
[114]Robinson P J. Modeling utility load and temperature relationships for use with long-lead forecasts[J]. Journal of Applied Meteorology,1997,36(5):591-598.
[115]Bernardo J, Ramon J. An introduction to Bayesian reference analysis:inference on the ratio of multinomial parameters[J]. Journal of the Royal Statistical Society:Series D (The Statistician),1998,47(1):101-135.
[116]Jaynes E, Bretthorst G. Probability theory:the logic of science[M]. UK:Cambridge University Press,2003.
[117]Krogh A, Vedelsby J. Neural network ensembles, cross validation, and active learn-ing[J]. Advances in neural information processing systems,1995,7:231-238.
[118]Goutte C. Note on free lunches and cross-validation[J]. Neural Computation,1997, 9(6):1245-1249.
[119]Kohavi R. A study of cross-validation and bootstrap for accuracy estimation and model selection[C]//International joint Conference on artificial intelligence. Mon-treal,Canda:[s.n.],1995,14:1137-1145.
[120]Andrieu C, Doucet A, Holenstein R. Particle markov chain monte carlo methods[J]. Journal of the Royal Statistical Society:Series B (Statistical Methodology),2010, 72(3):269-342.
[121]Rubinstein R, Kroese D. Simulation and the Monte Carlo method[M]. Vol.707. Hoboken, New Jersey:John Wiley & Sons,2011.
[122]Meteopolis N, Ulam S. The monte carlo method[J]. Journal of the American statistical association,1949,44(247):335-341.
[123]Gilks W, Richardson S, Spiegelhalter D. Markov Chain Monte Carlo in practice: interdisciplinary statistics[M]. Vol.2. New York, USA:Chapman & Hall,1995.
[124]Hastings W. Monte Carlo sampling methods using Markov chains and their applica-tions[J]. Biometrika,1970,57(1):97-109.
[125]Gelfand A, Sahu S. On Markov chain Monte Carlo acceleration[J]. Journal of Com-putational and Graphical Statistics,1994:261-276.
[126]Neal R. Bayesian learning for neural networks[M]. Lecture Notes in Statistics Series, vol.118. New York, USA:Springer Verlag,1996.
[127]Gamerman D. Markov chain Monte Carlo for dynamic generalised linear models[J]. Biometrika,1998,85(1):215.
[128]Jeffreys H. Theory of probability[M]. USA:Oxford University Press,1998.
[129]George E, Makov U, Smith A. Conjugate likelihood distributions[J]. Scandinavian Journal of Statistics,1993:147-156.
[130]Arnold B, Castillo E, Sarabia J. Priors with convenient posteriors[J]. A Journal of Theoretical and Applied Statistics,1996,28(4):347-354.
[131]McCulloch W, Pitts W. A logical calculus of the ideas immanent in nervous activity [J]. Bulletin of mathematical biology,1943,5(4):115-133.
[132]Lee K, Cha Y, Park J. Short-term load forecasting using an artificial neural network[J]. Power Systems, IEEE Transactions on,1992,7(1):124-132.
[133]Ho K, Hsu Y, Yang C. Short term load forecasting using a multilayer neural network with an adaptive learning algorithm[J]. Power Systems, IEEE Transactions on,1992, 7(1):141-149.
[134]Papadokonstantakis S, Lygeros A, Jacobsson S. Comparison of recent methods for inference of variable influence in neural networks[J]. Neural networks,2006, 19(4):500-513.
[135]Cataltepe Z, Abu-Mostafa Y, Magdon-Ismail M. No free lunch for early stopping[J]. Neural computation,1999, 11(4):995-1009.
[136]Efron B, Tibshirani R. An introduction to the bootstrap[M]. Monographs on statistics and applied probabilities, vol.57. Boca Raton, Florida:Chapman & Hall/CRC, 1993.
[137]Chernick M. Bootstrap Methods:A Guide for Practitioners and Researchers[M]. Wiley Series in Probability and Statistics. Hoboken, New Jersey:Wiley-Interscience, 2011.
[138]Titterington D. Bayesian methods for neural networks and related models[J]. Statis-tical Science,2004,19(1):128-139.
[139]Vila J, Wagner V, Neveu P. Bayesian nonlinear model selection and neural net-works:A conjugate prior approach[J]. Neural Networks, IEEE Transactions on,2000, 11(2):265-278.
[140]Lampinen J, Vehtari A. Bayesian approach for neural networks-review and case stud-ies[J]. Neural Networks,2001,14(3):257-274.
[141]Penny W, Roberts S. Bayesian neural networks for classification:how useful is the evidence framework?[J]. Neural Networks,1999,12(6):877-892.
[142]Buntine W, Weigend A. Bayesian back-propagation[J]. Complex systems,1991, 5(6):603-643.
[143]MacKay D. Bayesian interpolation[J]. Neural computation,1992,4(3):415-447.
[144]MacKay D. A practical Bayesian framework for backpropagation networks[J]. Neural computation,1992,4(3):448-472.
[145]Barber D, Bishop C. Bayesian model comparison by monte carlo chaining[J]. Ad-vances in neural information processing systems,1997:333-339.
[146]Chua C, Goh A. A hybrid Bayesian back-propagation neural network approach to multivariate modelling[J]. International journal for numerical and analytical methods in geomechanics,2003,27(8):651-667.
[147]Liang F. Bayesian neural networks for nonlinear time series forecasting[J]. Statistics and Computing,2005,15(l):13-29.
[148]Nocedal J, Wright S. Numerical optimization[M]. Springer series in operations re-search. New York, USA:Springer verlag,1999.
[149]Poggio T, Girosi F. Networks for approximation and learning[J]. Proceedings of the IEEE,1990,78(9):1481-1497.
[150]Weigend A, Rumelhart D, Huberman B. Generalization by weight-elimination with application to forecasting[J]. Advances in neural information processing systems, 1991,3(875-882).
[151]Girosi F, Jones M, Poggio T. Regularization theory and neural networks architec-tures[J]. Neural computation,1995,7(2):219-269.
[152]Williams P. Bayesian regularization and pruning using a Laplace prior[J]. Neural Computation,1995,7(1):117-143.
[153]Polycarpou M, Ioannou P. Learning and convergence analysis of neural-type struc-tured networks[J]. Neural Networks, IEEE Transactions on,1992,3(1):39-50.
[154]Atiya A, Ji C. How initial conditions affect generalization performance in large net-works[J]. Neural Networks, IEEE Transactions on,1997,8(2):448-451.
[155]Wang C, Venkatesh S, Judd J. Optimal Stopping and E ective Machine Complexity in Learning[J]. Advances in neural information processing systems,1994,6:303-310.
[156]Venkatesh C. Temporal Dynamics of Generalization in Neural Networks [J]. Advances in neural information processing systems 7,1995,7:263.
[157]Reed R. Pruning algorithms-a survey[J]. Neural Networks, IEEE Transactions on, 1993,4(5):740-747.
[158]Kwok T, Yeung D. Constructive algorithms for structure learning in feedforward neural networks for regression problems[J]. Neural Networks, IEEE Transactions on, 1997,8(3):630-645.
[159]Maniezzo V. Genetic evolution of the topology and weight distribution of neural networks[J]. Neural Networks, IEEE Transactions on,1994,5(1):39-53.
[160]Murata N, Yoshizawa S, Amari S. Network information criterion-determining the number of hidden units for an artificial neural network model [J]. Neural Networks, IEEE Transactions on,1994,5(6):865-872.
[161]Browne M W, Cudeck R. Single sample cross-validation indices for covariance struc-tures[J]. Multivariate Behavioral Research,1989,24(4):445-455.
[162]Box G E, Jenkins G M, Reinsel G C. Time series analysis:forecasting and control[M]. Vol.734. New Jersey:Prentice-Hall,1994.
[163]Shumway R H, Stoffer D S, Stoffer D S. Time series analysis and its applications[M]. Vol.549. New York, USA:Springer verlag,2000.
[164]Kalman R, et al. A new approach to linear filtering and prediction problems[J]. Journal of basic Engineering,1960,82(1):35-45.
[165]Durbin J, Koopman S. Time series analysis by state space methods[M]. Vol.24. New York, USA:Oxford Univ Press,2001.
[166]Odell P, Feiveson A. A numerical procedure to generate a sample covariance ma-trix[J]. Journal of the American Statistical Association,1966,61(313):199-203.
[167]Everson P, Morris C. Simulation from Wishart distributions with eigenvalue con-straints[J]. Journal of Computational and Graphical Statistics,2000,9(2):380-389.
[168]Sailor D. Relating residential and commercial sector electricity loads to climate eval-uating state level sensitivities and vulnerabilities [J]. Energy,2001,26(7):645-657.
[169]Engle R. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica:Journal of the Econometric Society, 1982:987-1007.
[170]Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of econometrics,1986,31(3):307-327.
[171]Nelson D. Stationarity and persistence in the GARCH (1,1) model[J]. Econometric theory,1990,6(03):318-334.
[172]Bougerol P, Picard N. Stationarity of GARCH processes and of some nonnegative time series[J]. Journal of Econometrics,1992,52(1):115-127.
[173]Lee S, Hansen B. Asymptotic theory for the GARCH (1,1) quasi-maximum likeli-hood estimator[J]. Econometric theory,1994,10:29-29.
[174]Lumsdaine R. Consistency and asymptotic normality of the quasi-maximum likeli-hood estimator in IGARCH (1,1) and covariance stationary GARCH (1,1) models[J]. Econometrica:Journal of the Econometric Society,1996:575-596.
[175]Berkes I, Kokoszka P, et al. GARCH processes:structure and estimation[J]. Bernoulli, 2003,9(2):201-227.
[176]Berkes 1, Horvath L. The efficiency of the estimators of the parameters in GARCH processes[J]. The Annals of Statistics,2004,32(2):633-655.
[177]Francq C, Zakoian J. Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes[J]. Bernoulli,2004,10(4):605-637.
[178]Brandt A. The stochastic equation Yn+1= AnYn+Bn with stationary coefficients[J]. Advances in Applied Probability,1986:211-220.
[179]Wei G, Tanner M. Posterior computations for censored regression data[J]. Journal of the American Statistical Association,1990,85(411):829-839.
[180]Carlin B, Gelfand A. An iterative Monte Carlo method for nonconjugate Bayesian analysis[J]. Statistics and Computing,1991,1(2):119-128.
[2]张文泉,高玉君.电力技术经济学的建立与发展[J].电力技术经济,2004,16(003)：4-7.
[3]Alfares H, Nazeeruddin M. Electric load forecasting:literature survey and classifica-tion of methods[J]. International Journal of Systems Science,2002,33(1):23-34.
[4]于尔铿,韩放,谢开,等.电力市场[M].北京：中国电力出版社,1998.
[5]牛东晓.电力负荷预测技术及其应用[M].北京：中国电力出版社,1999.
[6]尚金成,黄永皓,夏清.电力市场理论研究与应用[M].北京：中国电力出版社,2002.
[7]叶彬.混合智能建模技术及其在短期负荷预测中的应用研究[D].杭州：浙江大学,2006.
[8]Taylor J, Buizza R. Neural network load forecasting with weather ensemble predic-tions[J]. Power Systems, IEEE Transactions on,2002,17(3):626-632.
[9]Engle R, Granger C, Rice J, et al. Semiparametric estimates of the relation between weather and electricity sales[J]. Journal of the American Statistical Association,1986, 81(394):310-320.
[10]Hor C, Watson S, Majithia S. Analyzing the impact of weather variables on monthly electricity demand[J]. Power Systems, IEEE Transactions on,2005,20(4):2078-2085.
[11]Parkpoom S, Harrison G. Analyzing the impact of climate change on future electricity demand in Thailand[J]. Power Systems, IEEE Transactions on,2008,23(3):1441-1448.
[12]Liu X, Sweeney J. The impacts of climate change on domestic natural gas consump-tion in the Greater Dublin Region[J]. International Journal of Climate Change Strate-gies and Management,2012,4(2):161-178.
[13]Jardini J, Tahan C, Ahn S, et al. Distribution transformer loading evaluation based on load profiles measurements [J]. Power Delivery, IEEE Transactions on,1997, 12(4):1766-1770.
[14]牛东晓,邢棉.短期电力负荷预测的小波神经元网络模型的研究[J].电网技术,1999,23(4)：21-24.
[15]Jardini J, Tahan C, Gouvea M, et al. Daily load profiles for residential, commercial and industrial low voltage consumers[J]. Power Delivery, IEEE Transactions on,2000, 15(1):375-380.
[16]Chang R, Leou R, Lu C. Distribution transformer load modeling using load research data[J]. Power Delivery, IEEE Transactions on,2002,17(2):655-661.
[17]康重庆,夏清,刘梅,等.应用于负荷预测中的回归分析的特殊问题[J].电力系统自动化,1998,22(10)：3841.
[18]赵宏伟,任震,黄雯莹.基于周期自回归模型的短期负荷预测[J].中国电机工程学报,1997,17(5)：348-351.
[19]Charytoniuk W, Chen M, Van Olinda P. Nonparametric regression based short-term load forecasting[J]. Power Systems, IEEE Transactions on,1998,13(3):725-730.
[20]Papalexopoulos A, Hesterberg T. A regression-based approach to short-term system load forecasting[J]. Power Systems, IEEE Transactions on,1990,5(4):1535-1547.
[21]Broadwater R, Sargent A, Yarali A, et al. Estimating substation peaks from load research data[J]. Power Delivery, IEEE Transactions on,1997,12(1):451-456.
[22]Nazarko J, Zalewski W. The fuzzy regression approach to peak load estimation in power distribution systems[J]. Power Systems, IEEE Transactions on,1999, 14(3):809-814.
[23]Haida T, Muto S. Regression based peak load forecasting using a transformation technique[J]. Power Systems, IEEE Transactions on,1994,9(4):1788-1794.
[24]Ruzic S, Vuckovic A, Nikolic N. Weather sensitive method for short term load fore-casting in electric power utility of Serbia[J]. Power Systems, IEEE Transactions on, 2003,18(4):1581-1586.
[25]Hagan M, Behr S. The time series approach to short term load forecasting[J]. Power Systems, IEEE Transactions on,1987,2(3):785-791.
[26]Chen J, Wang W, Huang C. Analysis of an adaptive time-series autoregressive moving-average (ARMA) model for short-term load forecasting[J]. Electric Power Systems Research,1995,34(3):187-196.
[27]侯志俭,吴际舜,张琦雨,等.电力系统短期负荷预报的几种改进手段[J].电力系统自动化,1996,20(7)：27-31.
[28]叶瑰昀,罗耀华.基于ARMA模型的电力系统负荷预测方法研究[J].信息技术,2002(006)：74-76.
[29]Yang H, Huang C, Huang C. Identification of ARMAX model for short term load forecasting:an evolutionary programming approach[C]//Power Industry Computer Application Conference. Salt Lake City UT:[s.n.],1995:325-330.
[30]Huang C, Huang C, Wang M. A particle swarm optimization to identifying the AR-MAX model for short-term load forecasting[J]. Power Systems, IEEE Transactions on,2005,20(2):1126-1133.
[31]Wang B, Tai N, Zhai H, et al. A new ARMAX model based on evolutionary algorithm and particle swarm optimization for short-term load forecasting [J]. Electric Power Systems Research,2008,78(10):1679-1685.
[32]王晛,张少华.一种应用时间序列技术的短期电力负荷预测模型[J].上海大学学报：自然科学版,2002,8(2)：133-136.
[33]鞠平,姜巍,赵夏阳.96点短期负荷预测方法及其应用[J].电力系统自动化,2001,25(22)：32-36.
[34]张颖,高中文.基于时间序列和神经网络的电力系统负荷预测[J].哈尔滨理工大学学报,2003,8(1)：30-32.
[35]Haykin S. Neural networks:a comprehensive foundation[M]. Michigan:USA:Pren-tice Hall,1999.
[36]Park D, El-Sharkawi M, Marks R, et al. Electric load forecasting using an artificial neural network[J]. Power Systems, IEEE Transactions on,1991,6(2):442-449.
[37]Peng T, Hubele N, Karady G. Advancement in the application of neural networks for short-term load forecasting[J]. Power Systems, IEEE Transactions on,1992, 7(1):250-257.
[38]Khotanzad A, Afkhami-Rohani R, Lu T, et al. ANNSTLF-a neural-network-based electric load forecasting system[J]. Neural Networks, IEEE Transactions on,1997, 8(4):835-846.
[39]Marin F, Garcia-Lagos F, Joya G, et al. Global model for short-term load forecasting using artificial neural networks[J].2002,149(2):121-125.
[40]Senjyu T, Takara H, Uezato K, et al. One-hour-ahead load forecasting using neural network[J]. Power Systems, IEEE Transactions on,2002,17(1):113-118.
[41]Satish B, Swarup K, Srinivas S, et al. Effect of temperature on short term load forecast-ing using an integrated ANN[J]. Electric Power Systems Research,2004,72(1):95-101.
[42]谢宏,程浩忠,张国立,et al.基于粗糙集理论建立短期电力负荷神经网络预测模型[J].中国电机工程学报,2004,23(11)：1-4.
[43]程其云,孙才新,周湶,et al.粗糙集信息熵与自适应神经网络模糊系统相结合的电力短期负荷预测模型及方法[J].电网技术,2004,28(17)：72-75.
[44]罗治强,张焰,朱杰.粗集理论在电力系统负荷预测中的应用[J].电网技术,2004,28(3)：29-32.
[45]雷绍兰,孙才新,周湶,et al.模糊粗糙集理论在空间电力负荷预测中的应用[J].电网技术,2005,29(9)：26-30.
[46]王志勇,郭创新,曹一家.基于模糊粗糙集和神经网络的短期负荷预测方法[J].中国电机工程学报,2005,25(19)：7-11.
[47]Xiao Z, Ye S, Zhong B, et al. BP neural network with rough set for short term load forecasting[J]. Expert Systems with Applications,2009,36(1):273-279.
[48]庞清乐.基于粗糙集理论的神经网络预测算法及其在短期负荷预测中的应用[J].电网技术,2010,34(12)：168-173.
[49]牛东晓,陈志业.遗传神经网络优化预测方法研究及其应用[J].华北电力大学学报,2001,28(1)：1-5.
[50]Ling S, Leung F, Lam H, et al. Short-term electric load forecasting based on a neural fuzzy network[J]. Industrial Electronics, IEEE Transactions on,2003,50(6):1305-1316.
[51]谢宏,陈志业,牛东晓,et al.基于小波分解与气象因素影响的电力系统日负荷预测模型研究[J].中国电机工程学报,2001,21(5)：5-10.
[52]张大海,江世芳,毕研秋,et al.基于小波神经网络的电力负荷预测方法[J].电力自动化设备,2003,23(8)：29-32.
[53]徐军华,刘天琪.基于小波分解和人工神经网络的短期负荷预测[J].电网技术,2004,28(8)：30-33.
[54]Nengling T, Stenzel J, Hongxiao W. Techniques of applying wavelet transform into combined model for short-term load forecasting[J]. Electric power systems research, 2006,76(6):525-533.
[55]Bakirtzis A, Theocharis J, Kiartzis S, et al. Short term load forecasting using fuzzy neural networks[J]. Power Systems, IEEE Transactions on,1995,10(3):1518-1524.
[56]Papadakis S, Theocharis J, Kiartzis S, et al. A novel approach to short-term load forecasting using fuzzy neural networks[J]. Power Systems, IEEE Transactions on, 1998,13(2):480-492.
[57]Kim K, Youn H, Kang Y. Short-term load forecasting for special days in anomalous load conditions using neural networks and fuzzy inference method[J]. Power Systems, IEEE Transactions on,2000,15(2):559-565.
[58]Song K, Baek Y, Hong D, et al. Short-term load forecasting for the holidays us-ing fuzzy linear regression method[J]. Power Systems, IEEE Transactions on,2005, 20(1):96-101.
[59]Khan M, Abraham A. Short Term Load Forecasting Models in Czech Republic Using Soft Computing Paradigms[J]. arXiv preprint cs/0405051,2004.
[60]Liao G, Tsao T. Application of fuzzy neural networks and artificial intelligence for load forecasting[J]. Electric Power Systems Research,2004,70(3):237-244.
[61]Liao G, Tsao T. Application of a fuzzy neural network combined with a chaos genetic algorithm and simulated annealing to short-term load forecasting[J]. Evolutionary Computation, IEEE Transactions on,2006,10(3):330-340.
[62]Mamlook R. Fuzzy set methodology for evaluating alternatives to compare between different power production systems[J]. Journal of Applied Sciences,2006,6(9):1686-1691.
[63]Mamlook R, Badran O, Abdulhadi E. A fuzzy inference model for short-term load forecasting[J]. Energy Policy,2009,37(4):1239-1248.
[64]Chenthur Pandian S, Duraiswamy K, Christober Asir Rajan C, et al. Fuzzy approach for short term load forecasting[J]. Electric Power Systems Research,2006,76(6):541-548.
[65]Hinojosa V, Hoese A. Short-term load forecasting using fuzzy inductive reasoning and evolutionary algorithms[J]. Power Systems, IEEE Transactions on,2010,25(1):565-574.
[66]Al-Kandari A, Soliman S, El-Hawary M. Fuzzy short-term electric load forecast-ing[J]. International journal of electrical power & energy systems,2004,26(2):111-122.
[67]Vapnik V. The nature of statistical learning theory[M]. New York:Springer Verlag, 1999.
[68]Smola A J, Scholkopf B. A tutorial on support vector regression[J]. Statistics and computing,2004,14(3):199-222.
[69]Suykens J, Vandewalle J. Least squares support vector machine classifiers [J]. Neural processing letters,1999,9(3):293-300.
[70]Chang M, Chen B, Lin C. EUNITE network competition:Electricity load forecast-ing[C]//National Taiwan University. Taipei, Taiwan:[s.n.],2001.
[71]Chen B, Chang M, et al. Load forecasting using support vector machines:A study on EUNITE competition 2001 [J]. Power Systems, IEEE Transactions on,2004, 19(4):1821-1830.
[72]Mohandes M. Support vector machines for short-term electrical load forecastingfJ]. International Journal of Energy Research,2002,26(4):335-345.
[73]Bao Z, Pi D, Sun Y. Short-term load forecasting based on self-organizing map and support vector machine[J]. Advances in Natural Computation,2005:688-691.
[74]Hsu C, Wu C, Chen S, et al. Dynamically optimizing parameters in support vector regression:An application of electricity load forecasting[C]//System Sciences,2006. HICSS'06. Proceedings of the 39th Annual Hawaii International Conference on. Tai-wan:[s.n.],2006,2:30-37.
[75]牛东晓,谷志红,邢棉,et al.基于数据挖掘的SVM短期负荷预测方法研究[J].中国电机工程学报,2006,26(18)：6-12.
[76]Espinoza M, Suykens J, De Moor B. Load forecasting using fixed-size least squares support vector machines[J]. Computational Intelligence and Bioinspired Systems, 2005:488-527.
[77]Wu H, Zhang S. Power load forecasting with least squares support vector machines and chaos theory[C]//Neural Networks and Brain,2005. ICNN&B'O5. International Conference on. Dalian:China:[s.n.],2005,2:1020-1024.
[78]唐杰明,刘俊勇,杨可,et al.基于灰色模型和最小二乘支持向量机的电力短期负荷组合预测[J].电网技术,2009,33(3)：63-68.
[79]King G. Variance specification in event count models:From restrictive assumptions to a generalized estimator[J]. American Journal of Political Science,1989:762-784.
[80]Naylor J, Smith A. Econometric illustrations of novel numerical integration strategies for Bayesian inference[J]. Journal of Econometrics,1988,38(1):103-125.
[81]Tierney L, Kadane J. Accurate approximations for posterior moments and marginal densities[J]. Journal of the American Statistical Association,1986,81(393):82-86.
[82]Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,1984,17(6):721-741.
[83]Gelfand A, Smith A. Sampling-based approaches to calculating marginal densities[J]. Journal of the American statistical association,1990,85(410):398-409.
[84]Besag J, Green P. Spatial statistics and Bayesian computation[J]. Journal of the Royal Statistical Society. Series B (Methodological),1993:25-37.
[85]Bishop C. Pattern recognition and machine learning[M]. Vol.4. New York:USA: springer New York,2006.
[86]Andrieu C, De Freitas N, Doucet A, et al. An introduction to MCMC for machine learning[J]. Machine learning,2003,50(1):5-43.
[87]Kass R E, Carlin B P, Gelman A, et al. Markov chain monte carlo in practice:A roundtable discussion[J]. The American Statistician,1998,52(2):93-100.
[88]Chen M, Shao Q, Ibrahim J. Monte Carlo methods in Bayesian computation[M]. New York, USA:Springer Verlag,2000.
[89]Brooks S. Markov chain Monte Carlo method and its application[J]. Journal of the Royal Statistical Society:Series D (The Statistician),1998,47(1):69-100.
[90]Putter H, Heisterkamp S, Lange J, et al. A Bayesian approach to parameter estimation in HIV dynamical models[J]. Statistics in Medicine,2002,21(15):2199-2214.
[91]Huang Y, Liu D, Wu H. Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system[J]. Biometrics,2005,62(2):413-423.
[92]Lancaster T. An introduction to modern Bayesian econometrics[M]. USA:Wiley-Blackwell,2004.
[93]Geweke J, Whiteman C. Bayesian forecasting[J]. Handbook of Economic Forecast-ing,2006,1:3-80.
[94]Koop G. Bayesian econometric Methods[M]. Econometric Exercises, vol.23. UK: Cambridge University Press,2007.
[95]Harrison P, Stevens C. A Bayesian approach to short-term forecasting[J]. Operational Research Quarterly,1971:341-362.
[96]Zellner A, Chen B, et al. Bayesian modeling of economies and data requirements [J]. Macroeconomic Dynamics,2001,5(5):673-700.
[97]Brav A. Inference in Long-Horizon Event Studies:A Bayesian Approach with Appli-cation to Initial Public Offerings[J]. The Journal of Finance,2002,55(5):1979-2016.
[98]Harvey A, Trimbur T, Van Dijk H. Trends and cycles in economic time series:A Bayesian approach[J]. Journal of Econometrics,2007,140(2):618-649.
[99]Lahiri K, Sheng X. Learning and heterogeneity in GDP and inflation forecasts [J]. International Journal of Forecasting,2010,26(2):265-292.
[100]Geweke J, Amisano G. Comparing and evaluating Bayesian predictive distributions of asset returns[J]. International Journal of Forecasting,2010,26(2):216-230.
[101]Douglas A P, Breipohl A M, Lee F N, et al. The impacts of temperature forecast uncertainty on Bayesian load forecasting[J]. Power Systems, IEEE Transactions on, 1998,13(4):1507-1513.
[102]Lauret P, Fock E, Randrianarivony R, et al. Bayesian neural network approach to short time load forecasting[J]. Energy Conversion and Management,2008,49(5):1156-1166.
[103]Saini L M. Peak load forecasting using Bayesian regularization, Resilient and adaptive backpropagation learning based artificial neural networks[J]. Electric power systems research,2008,78(7):1302-1310.
[104]Cottet R, Smith M. Bayesian modeling and forecasting of intraday electricity load[J]. Journal of the American Statistical Association,2003,98(464):839-849.
[105]付桂琴,李运宗.气象条件对电力负荷的影响分析[J].气象科技,2009,36(6)：795-800.
[106]康重庆,周安石,王鹏,et al.短期负荷预测中实时气象因素的影响分析及其处理策略[J].电网技术,2006,30(7)：5-10.
[107]谢宏,陈志业.短期电力负荷预测的数据主成份分析[J].电网技术,2000,24(1)：43-46.
[108]Srinivasan D. Evolving artificial neural networks for short terra load forecasting[J]. Neurocomputing,1998,23(1):265-276.
[109]罗慧,巢清尘,李奇,et al.气象要素在电力负荷预测中的应用[J].气象,2005,31(6)：15-18.
[110]汪峰,于尔铿,阎承山,et al.基于因素影响的电力系统短期负荷预报方法的研究[J].中国电机工程学报,1999,19(8)：54-58.
[111]Hippert H, Pedreira C. Estimating temperature profiles for short-term load forecast-ing:neural networks compared to linear models[J].2004,151(4):543-547.
[112]秦海超,王玮,周晖,et al.人体舒适度指数在短期电力负荷预测中的应用[J].电力系统及其自动化学报,2006,18(2)：63-66.
[113]刘旭.基于实时气象因素的短期负荷预测方法研究[D].湖南：湖南大学,2009.
[114]Robinson P J. Modeling utility load and temperature relationships for use with long-lead forecasts[J]. Journal of Applied Meteorology,1997,36(5):591-598.
[115]Bernardo J, Ramon J. An introduction to Bayesian reference analysis:inference on the ratio of multinomial parameters[J]. Journal of the Royal Statistical Society:Series D (The Statistician),1998,47(1):101-135.
[116]Jaynes E, Bretthorst G. Probability theory:the logic of science[M]. UK:Cambridge University Press,2003.
[117]Krogh A, Vedelsby J. Neural network ensembles, cross validation, and active learn-ing[J]. Advances in neural information processing systems,1995,7:231-238.
[118]Goutte C. Note on free lunches and cross-validation[J]. Neural Computation,1997, 9(6):1245-1249.
[119]Kohavi R. A study of cross-validation and bootstrap for accuracy estimation and model selection[C]//International joint Conference on artificial intelligence. Mon-treal,Canda:[s.n.],1995,14:1137-1145.
[120]Andrieu C, Doucet A, Holenstein R. Particle markov chain monte carlo methods[J]. Journal of the Royal Statistical Society:Series B (Statistical Methodology),2010, 72(3):269-342.
[121]Rubinstein R, Kroese D. Simulation and the Monte Carlo method[M]. Vol.707. Hoboken, New Jersey:John Wiley & Sons,2011.
[122]Meteopolis N, Ulam S. The monte carlo method[J]. Journal of the American statistical association,1949,44(247):335-341.
[123]Gilks W, Richardson S, Spiegelhalter D. Markov Chain Monte Carlo in practice: interdisciplinary statistics[M]. Vol.2. New York, USA:Chapman & Hall,1995.
[124]Hastings W. Monte Carlo sampling methods using Markov chains and their applica-tions[J]. Biometrika,1970,57(1):97-109.
[125]Gelfand A, Sahu S. On Markov chain Monte Carlo acceleration[J]. Journal of Com-putational and Graphical Statistics,1994:261-276.
[126]Neal R. Bayesian learning for neural networks[M]. Lecture Notes in Statistics Series, vol.118. New York, USA:Springer Verlag,1996.
[127]Gamerman D. Markov chain Monte Carlo for dynamic generalised linear models[J]. Biometrika,1998,85(1):215.
[128]Jeffreys H. Theory of probability[M]. USA:Oxford University Press,1998.
[129]George E, Makov U, Smith A. Conjugate likelihood distributions[J]. Scandinavian Journal of Statistics,1993:147-156.
[130]Arnold B, Castillo E, Sarabia J. Priors with convenient posteriors[J]. A Journal of Theoretical and Applied Statistics,1996,28(4):347-354.
[131]McCulloch W, Pitts W. A logical calculus of the ideas immanent in nervous activity [J]. Bulletin of mathematical biology,1943,5(4):115-133.
[132]Lee K, Cha Y, Park J. Short-term load forecasting using an artificial neural network[J]. Power Systems, IEEE Transactions on,1992,7(1):124-132.
[133]Ho K, Hsu Y, Yang C. Short term load forecasting using a multilayer neural network with an adaptive learning algorithm[J]. Power Systems, IEEE Transactions on,1992, 7(1):141-149.
[134]Papadokonstantakis S, Lygeros A, Jacobsson S. Comparison of recent methods for inference of variable influence in neural networks[J]. Neural networks,2006, 19(4):500-513.
[135]Cataltepe Z, Abu-Mostafa Y, Magdon-Ismail M. No free lunch for early stopping[J]. Neural computation,1999, 11(4):995-1009.
[136]Efron B, Tibshirani R. An introduction to the bootstrap[M]. Monographs on statistics and applied probabilities, vol.57. Boca Raton, Florida:Chapman & Hall/CRC, 1993.
[137]Chernick M. Bootstrap Methods:A Guide for Practitioners and Researchers[M]. Wiley Series in Probability and Statistics. Hoboken, New Jersey:Wiley-Interscience, 2011.
[138]Titterington D. Bayesian methods for neural networks and related models[J]. Statis-tical Science,2004,19(1):128-139.
[139]Vila J, Wagner V, Neveu P. Bayesian nonlinear model selection and neural net-works:A conjugate prior approach[J]. Neural Networks, IEEE Transactions on,2000, 11(2):265-278.
[140]Lampinen J, Vehtari A. Bayesian approach for neural networks-review and case stud-ies[J]. Neural Networks,2001,14(3):257-274.
[141]Penny W, Roberts S. Bayesian neural networks for classification:how useful is the evidence framework?[J]. Neural Networks,1999,12(6):877-892.
[142]Buntine W, Weigend A. Bayesian back-propagation[J]. Complex systems,1991, 5(6):603-643.
[143]MacKay D. Bayesian interpolation[J]. Neural computation,1992,4(3):415-447.
[144]MacKay D. A practical Bayesian framework for backpropagation networks[J]. Neural computation,1992,4(3):448-472.
[145]Barber D, Bishop C. Bayesian model comparison by monte carlo chaining[J]. Ad-vances in neural information processing systems,1997:333-339.
[146]Chua C, Goh A. A hybrid Bayesian back-propagation neural network approach to multivariate modelling[J]. International journal for numerical and analytical methods in geomechanics,2003,27(8):651-667.
[147]Liang F. Bayesian neural networks for nonlinear time series forecasting[J]. Statistics and Computing,2005,15(l):13-29.
[148]Nocedal J, Wright S. Numerical optimization[M]. Springer series in operations re-search. New York, USA:Springer verlag,1999.
[149]Poggio T, Girosi F. Networks for approximation and learning[J]. Proceedings of the IEEE,1990,78(9):1481-1497.
[150]Weigend A, Rumelhart D, Huberman B. Generalization by weight-elimination with application to forecasting[J]. Advances in neural information processing systems, 1991,3(875-882).
[151]Girosi F, Jones M, Poggio T. Regularization theory and neural networks architec-tures[J]. Neural computation,1995,7(2):219-269.
[152]Williams P. Bayesian regularization and pruning using a Laplace prior[J]. Neural Computation,1995,7(1):117-143.
[153]Polycarpou M, Ioannou P. Learning and convergence analysis of neural-type struc-tured networks[J]. Neural Networks, IEEE Transactions on,1992,3(1):39-50.
[154]Atiya A, Ji C. How initial conditions affect generalization performance in large net-works[J]. Neural Networks, IEEE Transactions on,1997,8(2):448-451.
[155]Wang C, Venkatesh S, Judd J. Optimal Stopping and E ective Machine Complexity in Learning[J]. Advances in neural information processing systems,1994,6:303-310.
[156]Venkatesh C. Temporal Dynamics of Generalization in Neural Networks [J]. Advances in neural information processing systems 7,1995,7:263.
[157]Reed R. Pruning algorithms-a survey[J]. Neural Networks, IEEE Transactions on, 1993,4(5):740-747.
[158]Kwok T, Yeung D. Constructive algorithms for structure learning in feedforward neural networks for regression problems[J]. Neural Networks, IEEE Transactions on, 1997,8(3):630-645.
[159]Maniezzo V. Genetic evolution of the topology and weight distribution of neural networks[J]. Neural Networks, IEEE Transactions on,1994,5(1):39-53.
[160]Murata N, Yoshizawa S, Amari S. Network information criterion-determining the number of hidden units for an artificial neural network model [J]. Neural Networks, IEEE Transactions on,1994,5(6):865-872.
[161]Browne M W, Cudeck R. Single sample cross-validation indices for covariance struc-tures[J]. Multivariate Behavioral Research,1989,24(4):445-455.
[162]Box G E, Jenkins G M, Reinsel G C. Time series analysis:forecasting and control[M]. Vol.734. New Jersey:Prentice-Hall,1994.
[163]Shumway R H, Stoffer D S, Stoffer D S. Time series analysis and its applications[M]. Vol.549. New York, USA:Springer verlag,2000.
[164]Kalman R, et al. A new approach to linear filtering and prediction problems[J]. Journal of basic Engineering,1960,82(1):35-45.
[165]Durbin J, Koopman S. Time series analysis by state space methods[M]. Vol.24. New York, USA:Oxford Univ Press,2001.
[166]Odell P, Feiveson A. A numerical procedure to generate a sample covariance ma-trix[J]. Journal of the American Statistical Association,1966,61(313):199-203.
[167]Everson P, Morris C. Simulation from Wishart distributions with eigenvalue con-straints[J]. Journal of Computational and Graphical Statistics,2000,9(2):380-389.
[168]Sailor D. Relating residential and commercial sector electricity loads to climate eval-uating state level sensitivities and vulnerabilities [J]. Energy,2001,26(7):645-657.
[169]Engle R. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica:Journal of the Econometric Society, 1982:987-1007.
[170]Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of econometrics,1986,31(3):307-327.
[171]Nelson D. Stationarity and persistence in the GARCH (1,1) model[J]. Econometric theory,1990,6(03):318-334.
[172]Bougerol P, Picard N. Stationarity of GARCH processes and of some nonnegative time series[J]. Journal of Econometrics,1992,52(1):115-127.
[173]Lee S, Hansen B. Asymptotic theory for the GARCH (1,1) quasi-maximum likeli-hood estimator[J]. Econometric theory,1994,10:29-29.
[174]Lumsdaine R. Consistency and asymptotic normality of the quasi-maximum likeli-hood estimator in IGARCH (1,1) and covariance stationary GARCH (1,1) models[J]. Econometrica:Journal of the Econometric Society,1996:575-596.
[175]Berkes I, Kokoszka P, et al. GARCH processes:structure and estimation[J]. Bernoulli, 2003,9(2):201-227.
[176]Berkes 1, Horvath L. The efficiency of the estimators of the parameters in GARCH processes[J]. The Annals of Statistics,2004,32(2):633-655.
[177]Francq C, Zakoian J. Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes[J]. Bernoulli,2004,10(4):605-637.
[178]Brandt A. The stochastic equation Yn+1= AnYn+Bn with stationary coefficients[J]. Advances in Applied Probability,1986:211-220.
[179]Wei G, Tanner M. Posterior computations for censored regression data[J]. Journal of the American Statistical Association,1990,85(411):829-839.
[180]Carlin B, Gelfand A. An iterative Monte Carlo method for nonconjugate Bayesian analysis[J]. Statistics and Computing,1991,1(2):119-128.