开发 FIGARCH 模型的样本外预测公式

Q4 Mathematics
Debopam Rakshit, R. Paul
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引用次数: 0

摘要

波动性是时间序列建模所关注的一个问题。它提供了有关变量随时间变化的波动性和稳定性的宝贵见解。历史数据中的波动模式可以为预测未来行为提供有价值的信息。自回归条件异方差(ARCH)和 ARCH 模型的广义版本,即广义 ARCH(GARCH)模型等非线性时间序列模型常用于捕捉时间序列的波动性。任何时间序列的实现都可能与其远期的对应序列存在显著的统计依赖关系。这种现象被称为长记忆过程。波动率中也可能存在长记忆结构。分数积分波动率模型,如分数积分 GARCH(FIGARCH)模型,可以用来捕捉波动率中的长记忆。本文通过条件期望和条件方差的递归使用,推导出了 AR (1) -FIGARCH (1, d, 1) 模型的样本外预测公式和预测误差方差。为了进行实证说明,使用了印度德里、拉萨尔冈和班加罗尔市场的洋葱模态现货价格以及标准普尔 500 指数(收盘价)数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Development of out-of-sample forecast formulae for the FIGARCH model
Volatility is a matter of concern for time series modeling. It provides valuable insights into the fluctuation and stability of concerning variables over time. Volatility patterns in historical data can provide valuable information for predicting future behaviour. Nonlinear time series models such as the autoregressive conditional heteroscedastic (ARCH) and the generalized version of the ARCH model, i.e. generalized ARCH (GARCH) models are popularly used for capturing the volatility of a time series. The realization of any time series may have significant statistical dependencies on its distant counterpart. This phenomenon is known as the long memory process. Long memory structure can also be present in volatility. Fractionally integrated volatility models such as the fractionally integrated GARCH (FIGARCH) model can be used to capture the long memory in volatility. In this paper, we derived the out-of-sample forecast formulae along with the forecast error variances for the AR (1) -FIGARCH (1, d, 1) model by recursive use of conditional expectations and conditional variances. For empirical illustration, the modal spot prices of onion for Delhi, Lasalgaon and Bengaluru markets, India and S&P 500 index (close) data are used.
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来源期刊
Model Assisted Statistics and Applications
Model Assisted Statistics and Applications Mathematics-Applied Mathematics
CiteScore
1.00
自引率
0.00%
发文量
26
期刊介绍: Model Assisted Statistics and Applications is a peer reviewed international journal. Model Assisted Statistics means an improvement of inference and analysis by use of correlated information, or an underlying theoretical or design model. This might be the design, adjustment, estimation, or analytical phase of statistical project. This information may be survey generated or coming from an independent source. Original papers in the field of sampling theory, econometrics, time-series, design of experiments, and multivariate analysis will be preferred. Papers of both applied and theoretical topics are acceptable.
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