Self Similarity in Long Horizon Returns

Daily return distributions are limit laws associated with pure jump processes. The processes are a combination of identically distributed increments and a selfsimilar distribution. The presence of a selfsimilar component... [ view full abstract ]

Daily return distributions are limit laws associated with pure jump processes. The processes are a combination of identically distributed increments and a selfsimilar distribution. The presence of a selfsimilar component with a scaling coefficient  above a half  is shown to halt the converge to a normal distribution. Estimations conducted on 214 equity underliers over the period January 2007 to February 2017 support this lack of convergence to normality at very long horizons. In the long run markets are perpetual motion machines creating the information of their necessary movements and then responding to these with an exponential decay.