Tracing the Source of Long Memory in Volatility

We study the effects of trade duration properties on dependence in counts (number of trans-actions) and thus on dependence in volatility of returns. A return model is established to link counts and volatility. We present theorems as well as a conjecture relating properties of durations to long memory in counts and thus in volatility. We then apply several parametric durationmodels to empirical trade durations and discuss our findings in the light of the theorems and conjecture