On 1 Oct 2003 at 17:14, Tamas Papp wrote: > I need to find a computationally simple process for the movement of > interest rates. In this simplified model, an interest rate can have > 3--5 possible values, and its movement is characterized by a matrix of > transition probabilities (ie, it is a Markov process). > > I would like to estimate this process from a given set of data. > > For example, let the interest rate time series be: > > 7 3 8 2 5 9 6 > > Assume that the discretized variable can take the following values: > (3, 5, 8), then we find the nearest discrete point and give its index: > > 3 1 3 1 2 3 2 > > Then estimate the transition probabilities. > > I have the following questions: > > - how should I select the discrete set of values that the variable can > assume? Eg simply get the maximum and minimum, and divide this > interval into, say, three pieces? Or estimate the mean, and make the > other two values mean plus-minus one standard deviation? >
?Try with simulation what is best, after yuou have solved the estimation problem? > - once the variable is discretized, how do I transform each data point > to its discretized value (its index)? > > - the most important: how should I estimate the transition > probabilities? > > References to introductory literature on estimating Markov chains like > this would be welcome. A good reference covering this is U. Narayan Bhat: "Elements of Applied Stochastic Processes". For an almost ML solution, condition on the first observation, then take each transition i -> somewhere as an observation from the multinomial distribution given by the i'th row of the transition matrix, and use the multinomial estimates. Kjetil Halvorsen Most importantly, I need to know how robust an > estimation is to selecting the discrete points, or is there a simple > "goodness of fit" estimation. > > Thanks, > > Tamas Papp > > -- > Tam�s K. Papp > E-mail: [EMAIL PROTECTED] (preferred, especially for large messages) > [EMAIL PROTECTED] > Please try to send only (latin-2) plain text, not HTML or other garbage. > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
