A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture multimodality of data. However, traditional methods usually need assume that error follows a specific distribution not adaptive dataset. This paper proposes via asymmetric exponential power distribution, which includes normal skew-normal generalized Laplace and uniform as special cases. Therefore, proposed method can be seen generalization some existing model, adapt unknown structures improve prediction accuracy, even in case fat tail asymmetry. addition, expectation-maximization algorithm applied implement optimization problem. The finite sample performance approach illustrated numerical simulations. Finally, we apply methodology analyze daily return Hong Kong Hang Seng Index. results indicate more robust distributions than other methods.