Spurious Relationship of Long Memory Sequences in Presence of Trends Breaks

This article extends the theoretical analysis of spurious relationship and considers the situation where the deterministic components of the processes generating the individual series are long memory sequences with structural changes. Show it by using the ordinary least squares estimator, the t-statistics become divergent and pseudo correlation. However, two long memory time series having change points can produce spurious regression. In the presence of structural change points, confirm the rate of t-statistic tends to infinity increased with the increase in sample size. Numerical simulation results show that when structural changes are a feature of the data, the presence of spurious relationship is unambiguous. And the spurious regression not only depends on long memory indexes, but also for trend of model is also very sensitive.