提出了一种新的概率函数计算方法，用于研究金融时间序列在方差波动方面的多重分形特征。
A new probabilistic function for studying the multi-fractal features on the volatility of variance of financial time series is proposed.
他们把高居不下的食品价格和幅度较大的食品价格波动(最好定义为食品价格水平的方差)混为一谈。
They conflated high food prices with greater food price volatility, which is best defined as variance around the food price level.
股票价格的频繁波动是股票市场最明显的特征之一，自回归条件异方差类模型可以很好地预测金融资产收益率的方差。
Frequent volatility is a feature of stock market. Autoregressive Conditional Heteroscedasticity (ARCH) model is often used to forecast the variance of the benefit of financial capitals.
然后，利用自回归条件异方差模型系统研究了我国封闭式基金市场的价格波动特性，分析了基金市场的风险特征。
Then, it studies the characteristic of price volatility and risk in closed-end securities investment fund market by use of ARCH models.
本文所研究的这种波动性指的是资产收益的方差随时间不断变化，这在计量经济学中称之为异方差问题。
Volatility in the article is the variance of asset return, which varies with time going, and this is also called heteroscedasticity in Econometrics.
我们首先提出了一个带arma(1,1)条件异方差相关的随机波动模型，它是基本的随机波动模型的一个自然的推广。
In this paper, we extended the basic stochastic volatility models to a stochastic volatility models with ARMA (1, 1) conditional heteroskedasticity and correlated errors.
广义自回归条件异方差(GARCH)模型具有描述时间序列波动性的能力。
The generalized autoregressive conditional heteroscedasticity (GARCH) model has the ability to describe the volatility of time series.
进一步研究表明，波动性和相关性的多尺度变化导致了最小方差对冲比率及对冲效率呈相似规律的多尺度变化。
The empirical results suggested that the correlation and volatility ratio between index futures and spot vary over various time scales.
目前，很多有关金融风险的研究都是针对均值、方差、相关性，很少有人关注极端的波动情况。
Nowadays, most of the empirical studies and models concern average properties like expected returns, volatility, or correlations, and little attention has been given to the extreme movements.
研究了负荷时间序列波动性，考虑方差时变特征，提出了基于随机波动（SV）模型的短期负荷预测方法。
The volatility of load time series is analyzed, and the short-term load forecasting based on SV(Stochastic Volatility) models is presented with the consideration of the time-varying characteristics.
分析结果显示：我国股市日收益率具有明显的异方差性、波动性、聚集性、持续性和杠杆效应。
The results showed that the daily yield of China' s stock market had obvious heteroscedasticity, volatility, aggregation, sustainability and leverage effect.
实证结果表明：我国股价波动具有尖峰厚尾特征、异方差性特征和波动的持续性和非对称特征；
My results show that there are significantly volatility, excess kurtosis and heteroskedasticity, persistence and asymmetric effect in Chinese Stock Market.
关于调整印花税对噪声收益波动性的影响，研究方法是方差齐次检验，结果是调整证券交易印花税对小组合的影响是显著的。
The results of the study show that the DBMD models can capture the persistence of return volatility, and reveal the joint dynamic relations between price volatility and trading volume.
然后 ，指出了多个变量波动之间协同关系的研究方法 ：分数维协整和方差协同持续 ，并介绍了各自的建模方法。
Then we go on with the correlation between multi-variable: fractional co-integration and co-persistence in variance, and discuss their modeling method.
然后 ，指出了多个变量波动之间协同关系的研究方法 ：分数维协整和方差协同持续 ，并介绍了各自的建模方法。
Then we go on with the correlation between multi-variable: fractional co-integration and co-persistence in variance, and discuss their modeling method.
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