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- Title
A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution.
- Authors
Jiang, Yunlu; Zhuang, Zehong
- Abstract
In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods.
- Subjects
LAPLACE distribution; AUTOREGRESSIVE models; TIME series analysis; HANG Seng Index; EXPECTATION-maximization algorithms; GAUSSIAN distribution
- Publication
Axioms (2075-1680), 2023, Vol 12, Issue 2, p196
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms12020196