Thanks for the suggestion. To write a concise summary I need first some financial and economical interpretation of the results.
This computational work is a numerical implementation of the theoretical work of Carl Futia “INVARIANT DISTRIBUTIONS AND THE LIMITING BEHAVIOR OF MARKOVIAN ECONOMIC MODELS” to estimate the transition probability matrix using Machine Learning Tools(MLTs).
As illustrated in your work, “SOME STABILITY RESULTS FOR MARKOVIAN ECONOMIC SEMIGROUPS” , you provided two transition probability matrices that are derived from economical hypotheses-concepts.
I use MLTs to figure out the transition probability matrix directly from the historical data and to convey financial-economical information.
Only finite number of states are considered. The chapter 4 in your book, “Economic Dynamics Theory and Computation” provides substantial theoretical results as the existence of the stationary distribution and so on …
When applied to daily data from stock markets using the last 90 days, as the posted one related to Indices, it is relatively easy to interpret the results and moreover the obtained stationary distribution is not changing rapidly on the biweekly updated data(less sensitive to the perturbation).
When applied to daily FED interest rates to assess Term Structure Of Interest Rates, the estimated transition probability matrix provides a comprehensible
Term Structure Network. However, the values of the associated stationary distribution are changing rapidly on the biweekly updated data:
2-1) Temporal Interest Rates
2-2) Term Structure Network( transition probability matrix)
2-3) Associated Stationary Distribution
Mathematically, this stationary distribution is extremely sensitive to perturbations of some entries of the transition probability matrix, but insensitive to others.
Any economical interpretation?