本文系统研究了一种预测金融时间序列波动率的非模型方法，NoVaS，通过对金融收益率序列做变换使其收益率正态化以及方差稳定化，并通过变换后的序列进行波动率的单步预测。我们选取了S&P500 股票市场指数（1983-2008），美元兑日元汇率（1993-2008），以及个股Bear Stearns Co.（1985-2008）的日收益率三种不同类型的金融收益率数据进行研究，通过分块自抽样方法我们比较NoVaS 和一系列GARCH，EGARCH，以及GJR 模型预测的日波动率相对于历史波动率的误差。我们发现，在以波动率之差的绝对值为误差度量（MAD）的情况下，NoVaS 模型的预测能力显著优于GARCH/EGARCH/GJR 模型；而在在以波动率之差的平方(MSE)为误差度量的情况下，NoVaS 模型的预测能力则显著劣于GARCH 系列模型。通过细致的对比NoVaS 方法和GARCH/ARCH 系列模型的波动率预测分布，以及预测误差分布，我们理解了随着误差度量的阶数增高，NoVaS相对于GARCH/ARCH 的优势减弱的原因。在预测历史波动率的分布中，GARCH/ARCH 系列模型系统性的高估了波动率较小的那些天的值，而NoVaS 高估这部分波动率的程度显著低于GARCH/ARCH 模型，因此对于波动率分布的主体，NoVaS 有更佳的预测能力。而对于波动率较大一端的厚尾分布，NoVaS 低估的程度高于GARCH/ARCH 模型。随着误差度量的阶数增加，波动率厚尾部分误差较大的点所占权重增大，NoVaS 的相对优势下降。这些结论在使用指数衰减的NoVaS 方法时同样成立。关于在实际用中如何选择波动率预测模型，我们进行了如下讨论。当投资者更倾向于关心波动率预测的主体部分或波动率的高阶效应对收益-风险影响较小时，NoVaS 方法比GARCH/ARCH 方法更适合于波动率预测，例如：对于投资于证券组合或证券市场指数的投资者，或者对于投资组合的组合。此外，当市场处于相对平缓时期，不处于突发事件邻域内时，NoVaS 方法预测能力更佳，适宜采用。对于直接涉及波动率的单一交易策略，先有证据尚不能确定NoVaS 或GARCH/ARCH 哪一个能提供够好的波动率预测，这需要进行模拟来研究。但可以推断的是，对于进行波动率交易的投资组合，随着投资组合分散风险作用的增强，单一交易策略中的极值点对整个组合的风险- 收益的影响将减少， 因而， NoVaS 比GARCH/ARCH 能带来更好的投资效果的可能性也将增大。此外，我们发现在现有的用于比较一组波动率模型的预测能力方法中，模型置信集方法由于有以下优点而能够在不同的GARCH/ARCH 模型中很好的应用：该方法包含显著性等级，可以从若干模型中选出预测能力较好的一组而不是单一模型，在应用MAD 误差时模型区分度很高。因此我们研究了模型置信集方法在加入NoVaS 预测方法之后的效果如何，并发现该方法在此时失去了效果，不能有效的区分出预测能力不同的模型。由于在我们所选用的三类金融收益率数据中包含收益率和波动率的字相关结构随时间的演化，特别的，包含1987 年市场崩溃和2008 年BearStearns. Co.被美联储援助及被JP Morgan 收购事件，因此我们研究NoVaS和GARCH/ARCH 两类模型的预测能力之差别在不同市场环境和波动率情况下有和不同。具体的我们研究了表示两模型预测能力之差的统计量随历史波动率的演化，并发现历史波动率大的时期，NoVaS 对于GARCH/ARCH的优势较小，而历史波动率小的时期，NoVaS 对于GARCH/ARCH 的优势较大，并且这种区别在统计意义上是显著的。这与前文中所发现的NoVaS和GARCH/ARCH 对波动率分布的主题和厚尾部份预测能力的差别是相符合的。

This paper presents a systematic research on NoVaS, a model-freemethod used for volatility forecast in financial time series. The financial return series are varied for a normal distribution and for a stabilized square deviation, so as to make a one-step-ahead forecast of the volatility through the varied series. S&P500 index, the exchange rate of US Dollars against Japanese Yen, and the daily returns of an individual stock, Bear Stearns Co. are used for the research. We compare the errors in the volatility forecastsby NoVas and other models such as GARCH, EGARCH and GJR with theerrors of historical volatility by using the method of block bootstrap. It is found that the NoVaS model is significantly better than GARCH, EGARCH and GJR models for its forecasting ability when the absolute value of the difference in volatility is error measurement, whereas this does not hold when the square of the difference in volatility is error measurement. Through a detailed comparison of NoVaS with the GARCH/ARCH-type models for the volatility forecasting distributions as well as the distribution offorecast errors, we now understand why the forecasting ability of NoVas is reducing compared with GARCH/ARCH-type models when the error estimation is increasing. In forcasting the daily volatility,GARCH/ARCH-type models systermatically overestimate volatility, whereas the degree of overestimation of NoVaS is statistically significantly smaller. Hense for the majority of the volatility distribution, NoVaS provdes a better forcast than GARCH/ARCH-type models. On the other hand, for large volatility at the fat tail of the distribution, the degree of underestimated forcast by NoVaS is larger than GARCH/ARCH. Therefore the relative advantage of NoVAS to GARCH/ARCH decreases when the order of the error measurement increases. These conclusions also hold for exponential-decayNoVaS.We discussed how to choose volatility forcast model in practice. When the investors are more interesting in the majority of the volatility distribution, they should choose NoVaS methods, e.g., for investment of a stock portfolio or market index portfolio, and also for fund of fund inverstment. In addition, when the market is relatively calm and has no cras, NoVaS would provide better volatility forcast than GARCH/ARCH. For single volatility tradingstrategy, there is no evidence yet on which model can provide a better forcast. This requires further study and simulation. Nevertheless, we can infer when a portfolio of volatility stradegies are traded, the risk diversify effect would decrease the impact of extreme values in volatility forcast. Consequently, thepossibility for NoVaS to provide a better forcase would increase with the usage of portfolio.Furthermore, our research also shows that the model confidence intervals method of comparing forecasting abilities, will be of no effect when the NoVas forecasting method is added to it. It then can not identify the different models with different forecasting abilities. During the research of the two types of models for their forecasting ability’s change along with time and historical volatility, it is found that NoVas has less advantage over GARCH/ARCH in a historical period of high volatility and that it has more advantage over them in a historical period of low volatility. And such a difference has statistical significance.