# A New Family of Smooth Transition Autoregressive (STAR) Models: Properties and Application of its Symmetric Version to Exchange Rates

## Keywords:

Regime shifts, Time series, Nonstationarity, Power logistic function, smooth transition autoregressive model## Abstract

**Communication in Physical Sciences, 2023, 9(3):310-324**

** ****Authors: Benjamin ^{*} Asuquo Effiong, **

**Emmanuel Wilfred Okereke, Chukwuemeka Onwuzuruike Omekara, Chigozie Kelechi Acha and Emmanuel Alphonsus Akpan**

**Received: 12 May 2023/Accepted 08 July 2023**

A good number of economic variables undergo the process of regime shifts. In modeling such variables, it is necessary to consider a model that has provision for the regime form of nonstationarity. The smooth transition autoregressive (STAR) model is a choice model for time series with regime shifts. Given the role of transition functions in the performance of STAR models, this study introduced a family of transition functions by modifying the conventional logistic function. This new family, called the power logistic transition function, has the symmetric transition function and asymmetric transition function as special cases, making it useful in constructing both symmetric and asymmetric STAR models. The symmetric form of the family and the associated STAR model are extensively explained. The performance of the symmetric version of the power logistic smooth transition autoregressive model was illustrated with a monthly exchange rate of naira to United States dollar and African Financial Community Franc spanning from January 2004 to April 2021, which were extracted from Central Bank of Nigeria statistical bulletin. The numerical results obtained show that the symmetric power logistic smooth transition autoregressive model outperforms the linear autoregressive model and other existing symmetric smooth transition autoregressive models.

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