In the last decade , there exist two active lines on the investigation of nonlinear time series . one is the autoregressive conditional heteroscedasticity ( arch ) model , the another is the nonstationary ( unit root ) time series model 对非线性时间序列的研究，近几十年来，有两条研究路线非常活跃，其一是自回归条件异方差( arch )模型，其二是非平稳(单位根)时间序列模型。
While it ' s always possible to estimate robust standard errors for ols estimates , if we know something about the specific form of the heteroskedasticity , we can transform the model into one that has homoskedastic errors ? called weighted least squares 对ols估计稳健标准差总是可能办到的，但是，如果我们知道一些关于异方差结构的信息，我们可以将原模型转化为具有同方差的新模型，这称为加权最小二乘法。
The article analyses whether the theory of emh market can explain some phenomena on capital market . we provide some evidence for the non - normal , non - gaussian distribution , auto - correlation , non - linear and heteroskedasticity character of stock price 文章就有效市场假说( emh )对现实资本市场的解释能力进行了分析，发现我国股票市场的股价收益率序列具有非正态性、自相关性、非线性、异方差性等特点。
In the third section three different forms of heteroscedasticity are used in the random simulation and then park test , glejser test and goldfeld - quandt test are compared although the existence of heteroscedasticity does not destroy the unbiasedness of the ols estimators , the variances become larger 异方差的存在虽然并不破坏普通最小二乘估计量的无偏性，但是估计量的方差变大了。由于估计量方差的变大，就使通常假设检验的值不可靠。
Firstly , several methods are used to test if there is heteroscedasticity in the data . then some variance stabilizing transformation methods are applied to the data . finally , it is pointed out that the least squares fitting may be used to the transformed data 先用几种方法对数据是否具有异方差性进行检验，然后选择适当的方法进行变换，最后指出，可以通过对新模型作最小二乘拟合等方法，观察变换后的模型其数据的拟合程度，以确定模型的优劣。
The third chapter " essay of emh on chinese stock market " tested the hypotheses for the emh on chinese stock market , presented that stock price and return rate variance and voiatiiity are not stable . the chapter provided some evidence for the non - - normai 第二章分析了有效市场理论产生的背景，就有效市场理论成立的基本假设进行了检验，提出股票价格收益是不稳定的随机序列，收益分布不是正态分布，股票价格收益表现出非性，序列自相关性，异方差性。
The distributions studied are normal distribution , student - t distribution , skewed student - t distribution and general error distribution . besides this , considering the conditional heteroskedasticity of the time serial in financial market , apply the garch model into the estimation of var 在此基础上，研究了证券市场上时间序列收益率波动的条件异方差性，考虑中国证券市场的风险特征，将garch系列模型与var模型相结合，构造了基于不同分布条件下的var模型。
We will show that not any mean of the revenue rates of the industrial indexes is significantly beyond value zero at confident level 0 . 90 . moreover the mean of the revenue rate of sse 30 index is negative ( though not significant ) . and the fact of " the heritage of variance " appears congruous to the feature of industries represented by the corresponding indexes 第二章，通过分析上海股市各分类指数的收益率序列的特征，得出结论如下：各序列都非正态，有自相关性和异方差存在，相对适宜用garch ( 1 ， 1 )来拟合；除了上证商业( 1b0002 ) ，各分类指数收益率的均值在85的置信度下都不显著地异于0 ，而上证30 ( 1b0007 )的收益率竟小于0 ；在各分类指数中， ”波动继承性”的结果和各分类指数对应行业的特征是相关的。
Granger received the nobel prize , because their cointegration theory had solved two difficult problems , the time - varying volatility and non - stationary in the time series analysis field . in this paper , will introduce the normal knowledge of cointegration theory , and emphatically depict the possibility of applying cointegration algorithm to condition monitoring and fault diagnosis for engineering systems , which are non - stationary processes . it is well known that non - stationary system behavior causes grave difficulties on system modeling and condition monitoring due to the time - dependent statistics 2003年,诺贝尔经济学奖颁给了在时间序列计量经济学研究领域做出突破性贡献的两位美国经济学家,罗伯特?恩格尔( robertf . engle )和克莱夫?格兰杰( clivewj . granger ) ,以表彰他们提出的协整理论解决了时间序列分析中的两个难题,即异方差( time - varyingvolatility )与非平稳性( non - stationary ) 。
