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摘要翻译：
离散时间GARCH方法对时间序列异方差性的建模产生了如此深远的影响，它直观地很好地激发了捕捉关于金融序列的许多“程式化事实”的动机，现在几乎在广泛的情况下经常使用，经常包括一些数据不是在等间隔时间内观察到的情况。然而，用连续时间模型分析这些数据更合适，它保留了成功的GARCH范式的基本特征。一个可能的推广是Nelson的扩散极限，但这是有问题的，因为离散时间的GARCH模型和它的连续时间的扩散极限在统计上是不等价的。作为替代方案，KL\“{u}ppelberg等人。最近介绍了一个连续时间版本的GARCH（“Cogarch”过程），它是直接从驱动L{e}vy过程的背景中构造的。本文介绍了如何用离散时间GARCH方法来拟合不规则间隔的时间序列数据，方法是用一个嵌入的离散时间GARCH序列来逼近COGARCH,随着离散逼近网格的细化，该序列在很强的意义上（在概率上，在Skorokhod度量上）收敛于连续时间模型。此属性在某些其他应用程序中也特别有用，如期权定价。然后，对COGARCH模型使用类似于GARCH模型的统计技术，并利用股票指数数据进行了实证研究。
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英文标题：
《GARCH modelling in continuous time for irregularly spaced time series
data》
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作者：
Ross A. Maller, Gernot M\"uller, Alex Szimayer
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now almost routinely used in a wide range of situations, often including some where the data are not observed at equally spaced intervals of time. However, such data is more appropriately analyzed with a continuous-time model which preserves the essential features of the successful GARCH paradigm. One possible such extension is the diffusion limit of Nelson, but this is problematic in that the discrete-time GARCH model and its continuous-time diffusion limit are not statistically equivalent. As an alternative, Kl\"{u}ppelberg et al. recently introduced a continuous-time version of the GARCH (the `COGARCH' process) which is constructed directly from a background driving L\'{e}vy process. The present paper shows how to fit this model to irregularly spaced time series data using discrete-time GARCH methodology, by approximating the COGARCH with an embedded sequence of discrete-time GARCH series which converges to the continuous-time model in a strong sense (in probability, in the Skorokhod metric), as the discrete approximating grid grows finer. This property is also especially useful in certain other applications, such as options pricing. The way is then open to using, for the COGARCH, similar statistical techniques to those already worked out for GARCH models and to illustrate this, an empirical investigation using stock index data is carried out.
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PDF链接：
https://arxiv.org/pdf/0805.2096
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