Exploring Maintained in AR(1) Model with Finite Mixture of Gaussian Innovations
Abstract
The idea of using mixture distribution for Innovations in time series models has come into the picture in recent years as this approach allows flexible modelling in cases where the observations are multimodal. However, with limited research on this notion, there is a vast range of time series models yet to be explored. In this regard, we studied the time series model with a maintained trend. The theory is developed on AR(1) process with Innovations following K-component finite mixture distribution. The approach allows us to capture the multimodal aspect of the time series along with trend estimation. To support the idea a simulation study is conducted for different cases of the model specifying the order of maintained trend and number of components in mixture distribution. Further, to show the application, an empirical analysis is done on a real-time data set along with a realization study that justifies the proposed theory.
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