An Application of a Random Level Shifts Model to the Volatility of Peruvian Stock and Exchange Rates Returns

The literature has shown that the volatility of Stock and Forex rate market returns shows the characteristic of long memory. Another fact that is shown in the literature is that this feature may be spurious and volatility actually consists of a short memory process contaminated with random level shifts. In this paper, we follow the approach of Lu and Perron (2010) and Li and Perron (2013) estimating a model of random level shifts (RLS) to the logarithm of the absolute value of Stock and Forex returns. The model consists of the sum of a short term memory component and a component of level shifts. The second component is speci.ed as the cumulative sum of a process that is zero with probability 1- α and is a random variable with probability α. The results show that there are level shifts that are rare but once they are taken into account, the characteristic or property of long memory disappears. Also, the presence of GARCH e¤ects is eliminated when included or deducted level shifts. An exercise of out-of-sample forecasting shows that the RLS model has better performance than traditional models for modeling long memory such as the models ARFIMA (p,d,q).

Keywords

Returns, Volatility, Long Memory, Random Level Shifts, Kalman Filter, Forecasting

JEL Classification

C22