In a poisson distribution the number of events, e.g big declines in a time period occurs with a specific average rate, regardless of the time that has elapsed. For example, the average number of big declines per month is two. How likely is it to have 2 declines in the month, 3 declines. The time between such events, follows an exponential distribution. What is the distribution of time that elapses between such events? The time between events has a mean of 1 / the average rate, e.g. 1/2 a month in the above example. The variance is also 1/2.

Mr. Vince proposes that the rate and average elapsed time changes conditional on what has happened in the most recent period, a very good proposal, which can be modeled most practically by the use of survival statistics that all here are familiar with, i.e. what is the average duration between declines based on what the most recent event has been. Vince proposes that one look at the likely variations in that time, which may be skewed to the near term or long term.

Rocky Humbert writes: 

My stats are rusty but I believe poison specifies an average time between events (lambda) as a parameter and further specifies that's the actual time between events is random. Others please correct me, but I believe volatility in stocks experience clustering and so the independence assumption of poison is violated.

Ralph Vince writes: 

I'm talking about modelling the times between declines of x% with the fishy distribution, determining lambda. Then testing various past time windows vs futures ones to find a window length such that lambda settles and converges.

Gary Rogan writes: 

Why would it be a reasonable theory that a process where actual sentient being react to a previous decline in some way resemble a process where every event has no informational connection to not only the prior event but any other?

Ralph Vince replies: 

Why not? Has dependency been proven here?


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