Spurious long memory in estimating financial risk: An application on S&P 500

The slowly decaying autocorrelations of squared returns imply that shocks are long-range dependent. However, this behavior is easily confused with the behavior of volatility when exposed to structural breaks that is described as spurious long memory. The study aims at investigating whether long memory in the volatility of S&P 500 can be explained by spurious reasons. The study utilizes both time domain and frequency domain estimations. In the time domain, the data is filtered for outliers using a recently developed wavelet-based procedure. Structural breaks are detected using a modified ICSS algorithm. Then, symmetric and asymmetric GARCH models are estimated for the data before and after filtering. In the frequency domain, the degree of integration is computed using Local Whittle estimation, then two tests of spurious long memory are performed. The empirical results indicate that the long memory in the volatility of S&P500 is at least partially spuriously caused by volatility shifts. It was found that ignoring outliers can lead to misspecified GARCH models. Furthermore, the long memory parameter estimated in the frequency domain is not consistent over time. This indicates that return series might be better described by several regimes rather than by one fractionally integrated process of a consistent degree of integration (d)