[量化金融] 确定性趋势对…估计参数的影响 GARCH(1,1）模型 [推广有奖]

摘要翻译：
金融时间序列的对数收益率通常采用平稳的GARCH(1,1）随机过程或其推广方法来建模，不能很好地描述原始序列的非平稳确定性成分。通过蒙特卡罗模拟分析了确定性趋势对GARCH(1,1）参数的影响。统计系综包含由叠加在确定性趋势上的GARCH(1,1）噪声组成的数值生成的时间序列。一年以上金融时间序列的GARCH(1,1）参数特征不受去中心误差的影响。当ARCH系数大于GARCH系数时，估计的GARCH(1,1）参数依赖于趋势中单调部分的数目以及趋势与噪声振幅的比值。
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英文标题：
《Influence of deterministic trend on the estimated parameters of
  GARCH(1,1) model》
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作者：
Calin Vamos, Maria Craciun ("T. Popoviciu" Institute of Numerical
  Analysis, Romanian Academy, Romania)
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最新提交年份：
2007
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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：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  The log returns of financial time series are usually modeled by means of the stationary GARCH(1,1) stochastic process or its generalizations which can not properly describe the nonstationary deterministic components of the original series. We analyze the influence of deterministic trends on the GARCH(1,1) parameters using Monte Carlo simulations. The statistical ensembles contain numerically generated time series composed by GARCH(1,1) noise superposed on deterministic trends. The GARCH(1,1) parameters characteristic for financial time series longer than one year are not affected by the detrending errors. We also show that if the ARCH coefficient is greater than the GARCH coefficient, then the estimated GARCH(1,1) parameters depend on the number of monotonic parts of the trend and on the ratio between the trend and the noise amplitudes.
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PDF链接：
https://arxiv.org/pdf/0709.1536