As far as I know, switching models are Markovian. But can somebody provide me with paper references - if any - about non-Markov switching models which would have been developed in the financial markets area ? I suppose it could exist, e.g. for high frequency dataBy the way, chartism(technical analysis) could belong to such a category, isn' it ? (which doesn't mean I defend technical analysis!)thanks a lot,Alain

When people say they have a "markov switching" model they seem to just mean "I have a model, it switches, it has n variables". Under that definition it is not clear to me what would qualify as non-markov. Maybe one could distinguish between models with hidden variables under the risk neutral vs just the objective measure (i.e. variables that only affect drift)? The latter would be relevant to technicians who might be looking to isolate "excess" risk premium. If you mean the former, its not clear to me what would qualify as non-markov. Would you be referring to "hidden" variables like stochastic vol (as opposed to additional variables like yesterday's price)? Regards,Karsten

Don't know if this is what you are thinking about, but:Consider a stochastic process x that you think can be modelled in terms of two other stochastic processes y,z. Neither y nor z can be deduced from the current value of x, but, depending on your model, estimates may be obtainable from the recent history of x. If those estimates provide useful values for estimating the future process x, then x is non-Markovian, even if y and z are themselves Markovian.

QuoteOriginally posted by: alainruttiensAs far as I know, switching models are Markovian. But can somebody provide me with paper references - if any - about non-Markov switching models which would have been developed in the financial markets area?I am not sure that it is what you are looking for but...you may look at Fractional Brownian Motion models in finance with Hurst parameter 0.5 < H < 1.

Models with time varying transition probabilitities could generate non-Markovian regime switching models (if that is what you are looking for). Although they can be still estimated and filtered using maximum likelihood, one would have difficulties in forecasting without Monte Carlo. In many cases non-Markovian models can be transformed into Markovian ones by some change of variable or some extension of the state space.K.

T o raise up further (useful) comments:When I talk about possible "non-Markov" switching models, I mean (in my view) : (double or multiple) switching models involve, first, a set of minimum 2 stochastic models, with their specific parameters; the "switching" is then modelized, to fit with specific circumstances, e.g. switching models in spot market, with a switch depending on central bank interventions. There is no problem that the "sub-models" be Markovian, but - here is the point - usually, the switching function is usually purely probalistic, and, if depending on exogeneous events, naturally Markovian. But, if we suppose that a market could be modelized with a set of different Markovian "sub-models", to what extent do some research presents a switching component which would not be Markovian? hence - like for example an autoregressive model, with some lag >1 - indicating which one of the Markovian submodels would be concerned in some market conditions.It is in this sense that a made the somewhat provocative comparison with technical analysis: besides the ungrounded features of the technical analysis, at least this is an approach involving the idea that, depending on prevailing market conditions, the market behaviour is supposed to follow different possible ways, translated by the different "models" of technical analysis.So, I wonder if there exist a grounded scientific approach having considered a possible set of stochastic processes, like diffusion processes, whom the selection would depend on several previous data, and not random as well. If such theories exist, I suppose, they would have been developped within the framework of a very short term horizon, for very liquid instruments, and based on (relatively) high-frequency data. If any of the vast and competent set of the Wilmott forum participants (including the most prominent of them, as for example Paul Wilmott himself) have heard about such works, I am very interested in their output. However, usual references research, including on the Internet, have given no result to me up to now...

QuoteOriginally posted by: alainruttienshence - like for example an autoregressive model, with some lag >1 - indicating which one of the Markovian submodels would be concerned in some market conditions.How do you want to model the transitional period? If it is an instantaneous switch I think you can just attach two consecutive processes to the initial one as a "fork".

Agreed. The question is, with Markovian switching, the transition is actually defined by a distribution probability, saying (for 2 sub-processes) "there is a p proba to go to sub-process 1 and (1-p) proba going to sub-process 2, with respect to a (Gaussian or not) distribution probability". I wonder if it exists other approachs, defining the transition based on some (previous) data (non-Markov feature), or at least by a process having both a deterministic and a probabilistic components. If it exists, I'd like to see further how it runs !

Maybe this work http://links.jstor.org/sici?sici=0162-1 ... .CO%3B2-7I think you are talking about regimen switching models with observable variables, such like the article, threshold auto regressive models.