【作者】 王宇；

【导师】 叶俊；

【作者基本信息】 清华大学 ， 应用统计（专业学位）， 2021， 硕士

【摘要】 时间序列分析中,传统的模型一般假定时间是等间隔的,如AR(p)、MA(q)、ARMA(p,q)、ARCH(q)、AR(p)-ARCH(q)等。然而在现实中很多时间序列数据会出现不规则的时间间隔。如果使用传统的等间距模型分析不规则时间间隔的数据,会丢失数据所携带一些重要信息,或忽略数据所反映的特殊的时间规律,导致参数估计存在偏差、预测低效。本文首先综述了处理不规则时间间隔数据的传统方法,包含插值法补充数据、平滑化方法、均匀采样等方法,并依据所处理不同数据类型对这些方法加以分类概括。文章接着介绍了近些年来专门针对不规则时间间隔时间序列的模型,包括连续时间下一阶自回归模型(continuous-time first-order autoregressive model–CAR(1)),离散情况下的不规则时间间隔的一阶自回归模型(IAR(1)),以及不规则自回归模型ISAR(p)和不规则AR(p)-ARCH(q)等模型。本文还论述针对时间间隔规律一些研究,介绍Engle和Russell在1998年提出的ACD(autoregressive conditional duration)模型。该模型将时间的间隔定义成持续期,是金融领域研究交易行为和微观结构的重要方法。鉴于参数估计在模型现实应用中的重要性,本文对上述不规则时间序列模型进行理论推导的同时,也研究了相应的参数估计方法,包括极大似然估计,最小二乘估计,贝叶斯估计等。文中采用随机模拟得到的数据,对讨论的模型进行拟合,对比分析不同估计方法的效果,讨论其相应的适用范围。最后,文章使用现实的时间序列数据,进行实证分析,论证了文章中提出模型的有效性,也为金融市场高频交易数据提供了良好的分析方法。在研究过程中,进行了大量的计算机编程工作,对相应算法进行了优化,对模型的实际应用有着重要作用。更多还原

【Abstract】 In time series analysis,traditional models assume that time is equally spaced,such as AR(p),MA(q),ARMA(p,q),ARCH(q),AR(p)-ARCH(q),etc.In reality,however,many time series have irregular intervals,to which the application of the traditional space models would lead to biased estimation and inefficient prediction since important information carried by data is lost,or some special pattern in the series is ignored.This thesis first surveys the traditional methods to handle time series with irregular time intervals,including interpolation method to supplement data,smoothing method,uniform sampling and other methods,which are classified and summarized according to the types of data.Then this thesis introduces some recent models specifically for time series with irregular time intervals,such as the continuous time first-order autoregressive model(CAR(1)),the first order autoregressive model(IAR(1))for irregular time intervals in discrete cases,the irregular autoregressive model ISAR(p)and irregular AR(p)-ARCH(q).This thesis also reviews the recent researches on time series with irregular time intervals and focus on ACD(Autoregressive Conditional Duration)model proposed by Engle and Russell(1998),in which time interval is taken as duration.The ACD model has become an important method in the study of transaction behavior and microstructure in finance.Given the importance of parameter estimation in the application of models to real data,this thesis also studies the corresponding methods for parameter estimation in the models reviewed above.This thesis applys different methods such as maximum likelihood estimation,least square estimation,Bayesian estimation to simulated data in the models discussed,in order to evaluate their efficiency and discusses their applicable range.Finally,empirical analysis is carried out with real data.In the process of research,a lot of computer programming work is carried out,and the corresponding algorithm is optimized,which plays an important role in the practical application of the model.更多还原