Analyzing Markovian and Non-Markovian Behaviour with Censored Continuous-Time Observations in Islamic Financing Contracts

Memoryless properties of Markov first order have been powerful enough to cast light upon rating movement behavior. Further, Laplace transform is used to generate transition matrix, with homogenous continuous time assumption from discretized generator matrix. Various metric testing, i.e.: eigen value and eigen vector analysis, as well as MAGL and MSVD metric, were unable to distinctively accept or reject the above assumption of homogenous transition matrix. Furthermore, this research also analyzes non-Markovian behavior issue on particular transition, i.e: previous downgrade (upgrade) momentum as well as waiting time on the original rating of present downgrade (upgrade). The estimation result of Cox semi-parametric linier regression shows that waiting time significantly affects present rating downgrade (upgrade) on negative way. In the same way, previous downgrade (upgrade) momentum also proves to provide positive effect, except to D-M (downgrade) and D-KL (upgrade), which shows negative effect. Expansion of Markov chain process definition used to analyze the length of waiting time required for each rating before experience downgrade (upgrade). Generally, the result shows that the longer the waiting time, more descend the downgrade (upgrade) probability will be. This result is consistant with previous Cox's model estimation result