The main idea of this talk was to present NKS ideas for modeling time series. The standard model for financial time series: Random walks, random walks with trends. All the randomness seen in such processes is explicitly introduced into the system at each step (see NKS Ch.7). There are all kinds of statistics that can be done on such models.
NKS, Ch. 8 offers an alternative: use a simple CA based model to encode randomness generation in financial markets. The NKS model uses rule 90. White cells are buy orders, black cells sell orders. One cell represents one trader, who respond to the input of his neighbors. Price series correspond to the number black cells in each state. Note that the randomness in the rule 90 system in encoded in the initial conditions of the system (not at each step as in conventional stochastic models.) The series has "memory": it depends on previous steps.
Extensions of the model: other ECA rules, 3-color totalistic CA's, 2k 2r, 3 color totalistic, 3 color general, uneven cell weights, second difference / acceleration series. Interactive Cellular Automata approach: mix multiple rules. ICA's apply one of two CA rules at a given step, as determined by an external function of time t. ICA's generate richer time series distributions, and by changing rules and interaction functions it is possible to fit time series from financial markets into their behavior.
An explicit experiment is presented by trying to fit the time series for Goldman Sachs (NYSE:GS). Results were found that very closely track the behavior of the stock.
Comments