Bootstrap choice of non-nested autoregressive model with non-normal innovations

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-07-04 DOI:10.1515/mcma-2023-2010
Sedigheh Zamani Mehreyan
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Abstract

Abstract It is known that the block-based version of the bootstrap method can be used for distributional parameter estimation of dependent data. One of the advantages of this method is that it improves mean square errors. The paper makes two contributions. First, we consider the moving blocking bootstrap method for estimation of parameters of the autoregressive model. For each block, the parameters are estimated based on the modified maximum likelihood method. Second, we provide a method for model selection, Vuong’s test and tracking interval, i.e. for selecting the optimal model for the innovation’s distribution. Our analysis provides analytic results on the asymptotic distribution of the bootstrap estimators and also computational results via simulations. Some properties of the moving blocking bootstrap method are investigated through Monte Carlo simulation. This simulation study shows that, sometimes, Vuong’s test based on the modified maximum likelihood method is not able to distinguish between the two models; Vuong’s test based on the moving blocking bootstrap selects one of the competing models as optimal model. We have studied real data, the S&P500 data, and select optimal model for this data based on the theoretical results.
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具有非正态创新的非嵌套自回归模型的自举选择
摘要基于块的bootstrap方法可用于相关数据的分布参数估计。这种方法的优点之一是它改善了均方误差。这篇论文有两个贡献。首先,我们考虑用移动块自举法估计自回归模型的参数。对于每个块,基于改进的最大似然法估计参数。其次,我们提供了一种模型选择、Vuong检验和跟踪区间的方法,即选择创新分布的最优模型。我们的分析提供了自举估计量渐近分布的解析结果和仿真计算结果。通过蒙特卡罗仿真研究了运动块自举法的一些性质。仿真研究表明,有时,基于改进的极大似然法的Vuong检验不能区分两个模型;Vuong的基于移动阻塞自举的测试选择一个竞争模型作为最优模型。我们研究了实际数据和标准普尔500指数数据,并根据理论结果选择了最优模型。
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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