Chaotic Analysis of the Real Estate Investment Trusts Index Returns: An Application of the Largest Lyapunov Exponent

This paper examines the presence of chaotic dynamics in Real Estate Investment Trusts (REITs) index returns for the United States. Specifically, the paper uses the largest Lyapunov exponent to explores the chaotic behaviors of all, mortgage and equity REITs index returns for the time period running from January 1980 through December 2018. The sample is divided into two (pre-crisis and post-crisis periods) to ascertain the impact of the U.S. subprime mortgage crisis on the dynamic structure ofREITs index returns. The ADF, Phillips-Perron and the KPSS are used to determine the time series properties of the REITs index returns. To test for nonlinearity, the paper implemented the BDS test. The results from the unit root tests indicate that the three REITs index returns have zero order of integration. The BDS test results show that the REITs index return series are nonlinear. The results from the largest Lyapunov exponent test for the full and pre-crisis sample periods provide supportive evidence of chaotic dynamics in REITs index returns. However, for the post-crisis period, the study finds that the behavior of the three REITs index returns is governed by stochastic processes as opposed to chaotic dynamics. The implications of the results are discussed.