[R] fitting Markov chains

[Tamas Papp]

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?

- 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. 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

-- 
Tamás K. Papp
E-mail: tpapp at axelero.hu (preferred, especially for large messages)
        tpapp at westel900.net
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