Hi,I am doing a project whereby I am simulating a high frequency platform receiving quotes from the market. However, I need some computationally-intensive algorithm, but preferably suited to cash equities or FX (because I am only sending very basic input information into the system- prices)?I don't care if the technique makes money or not- my project is based at assessing the infrastructure capabilities. Ideally the algos/quant methods do a fair amount of vector/matrix manipulation- because this is what my project is partially assessing.Could anyone help? I did look at monte carlo simulation, but that seemed to be geared towards options pricing. The only possible technique I could think of is harmonic oscillation dampening/control theory. I could simply keep track of the last 1000 quotes and do the computations based on this.

You might want to look at Hidden Markov Models. You generate prices (S_t) from a joint statisticalprocess (S_t, C_t) where (C_t) is a Markov chain not observed directly (for example, volatility states).Then, you try to recover process parameters and estimates of the hidden states from what you see. Lots of matrix work. Zucchini & MacDonald is a good intro.

QuoteOriginally posted by: AlanYou might want to look at Hidden Markov Models. You generate prices (S_t) from a joint statisticalprocess (S_t, C_t) where (C_t) is a Markov chain not observed directly (for example, volatility states).Then, you try to recover process parameters and estimates of the hidden states from what you see. Lots of matrix work. Zucchini & MacDonald is a good intro.Hi,So I did some basic reading but I am confused why this would be useful. I looked at the example on:http://en.wikipedia.org/wiki/Viterbi_al ... xampleFrom what I gather, given the latest output this method finds the most probable sequence which caused the output. Don't I want the opposite "given inputs find the most likely output"?

QuoteOriginally posted by: JT77QuoteOriginally posted by: AlanYou might want to look at Hidden Markov Models. You generate prices (S_t) from a joint statisticalprocess (S_t, C_t) where (C_t) is a Markov chain not observed directly (for example, volatility states).Then, you try to recover process parameters and estimates of the hidden states from what you see. Lots of matrix work. Zucchini & MacDonald is a good intro.Hi,So I did some basic reading but I am confused why this would be useful. I looked at the example on:http://en.wikipedia.org/wiki/Viterbi_al ... xampleFrom what I gather, given the latest output this method finds the most probable sequence which caused the output. Don't I want the opposite "given inputs find the most likely output"?All statistical models can be run in two directions: (i) make inference on parameters, given real data, or(ii) create simulated data, given parametersIn HMMs, the "parameters" for (i) are the hidden chain states (C_t) and their transition probabilities (or other parameters)But, for (ii) the "parameters" are simply the chain transitition probabilities, and the output is a random sample (S_t,C_t) The link you cited explains (i), but (ii) is quite easy. In practice before testing any involved model on real data, youusually do (ii) and then (i), using your simulated data.BTW, the Viterbi algorithm is not the only way to handle HMM's -- see the book I cited for simpler approaches. The matrix work I was thinking of for you was not Viterbi, but the so-called forward-and-backward algorithms for HMMs.

QuoteOriginally posted by: AlanQuoteOriginally posted by: JT77QuoteOriginally posted by: AlanYou might want to look at Hidden Markov Models. You generate prices (S_t) from a joint statisticalprocess (S_t, C_t) where (C_t) is a Markov chain not observed directly (for example, volatility states).Then, you try to recover process parameters and estimates of the hidden states from what you see. Lots of matrix work. Zucchini & MacDonald is a good intro.Hi,So I did some basic reading but I am confused why this would be useful. I looked at the example on:http://en.wikipedia.org/wiki/Viterbi_al ... xampleFrom what I gather, given the latest output this method finds the most probable sequence which caused the output. Don't I want the opposite "given inputs find the most likely output"?All statistical models can be run in two directions: (i) make inference on parameters, given real data, or(ii) create simulated data, given parametersIn HMMs, the "parameters" for (i) are the hidden chain states (C_t) and their transition probabilities (or other parameters)But, for (ii) the "parameters" are simply the chain transitition probabilities, and the output is a random sample (S_t,C_t) The link you cited explains (i), but (ii) is quite easy. In practice before testing any involved model on real data, youusually do (ii) and then (i), using your simulated data.BTW, the Viterbi algorithm is not the only way to handle HMM's -- see the book I cited for simpler approaches. The matrix work I was thinking of for you was not Viterbi, but the so-called forward-and-backward algorithms for HMMs.Thanks- I will take a look!