Stochastic Permanent Breaks

This paper aims to bridge the gap between processes where shocks are permanent and those with transitory shocks by formulating a process in which the long run impact of each innovation is time varying and stochastic. Frequent transitory shocks are supplemented by occasional permanent shifts. The stochastic permanent breaks (STOPBREAK) process is based on the premise that a shock is more likely to be permanent if it is large than if it is small. This formulation is motivated by a class of processes that undergo random structural breaks. Consistency and asymptotic normality of quasi maximum likelihood estimates is established and locally best hypothesis tests of the null of a random walk are developed. The model is applied to relative prices of pairs of stocks and significant test statistics result