Dear Allin and GRETL-users,
Thank you for your kind response. I have read chapter 17, Maximum Likelihood
Estimation, but still not sure from which angle I have to start. I never did
this before and have a very minimal exposure on programming, except for some
Macro at Excel. I give some description of what the PIN (Probability of Informed
Trading)model is about and the parameter.
This model assumed that each day can be classified into either a day with
information (with the probability x) or a day without information (with the
If the day is categorized as day without information, then only uninformed
traders will do transactions (buy and sell) during that day; the buy arrival
rate of is eb and the sell arrival rate is es.
If it is a day with information, there are further possibilities:
(1)The news is bad with probability d
(2)The news is good with probability (1-d)
If the case is day with good news, then the sell arrival rate is es and the buy
arrival rate is u + eb.
If the case is day with bad news, then the buy arrival rate is eb and the sell
arrival rate is u + es.
To be brief, u is the arrival rate of informed traders. These traders only act
to buy (sell) if the day has good (bad) news. While eb is the buy arrival rate
of uninformed traders and es is the sell arrival rate of uninformed traders.
We want to estimate this x,u,eb,es, and d using maximum likelihood estimation.
The data that we have to estimate them comes from the daily number of buyer
initiated trades (B) and daily seller initiated trades (S) over the period P
days. In my case I have 240 days, so I have B1 till B240 and S1 till 240 as my
L(0|B,S) = (1-x)e^-eb (eb^B/B!) e^-es (es^S/S!) +
xde^-eb (eb^B/B!)e^-(u+es) (((u+es)^S)/S!)+
x(1-d)e^-(u+eb) ((u+eb)^B!)e^-es ((es^S)/S!)
The model also has an assumption that arrival rates of informed and uninformed
traders follow independent Poisson processes.
I would be glad if there are people on the list who can give me a clue on how to
start, as I am not sure what is alpha, beta and gamma in this model. Many thanks
in advance for your kind attention.
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