  # Re: Moving Average Crossover

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#1988

1) It is not using the weighted average (instead of AR) that causes the complexity of the optimization problem. Fitting AR(p) is still an optimization problem (unconstrained) with (p + 2) parameters except that the objective function is much simpler. If we denote the original process by $${X_t}$$, then AR(p) minimizes $$sum(X_t – hat{X}_t)^2$$; whereas in our configuration, the objective function is strategy specific and is of a much more complex form $$f(X_t, hat{Y}_t, mathcal{F}_{t-})$$, where $$hat{Y}_t$$ is the (fitted) indicator at time t and $$mathcal{F}_{s}$$ represents the filtration at time s.
2) Fitting an AR model to the original price process wouldn’t help much in generating this kind of indicators, since $${Y_t}$$ is different from the original price process $${X_t}$$ and $${Y_t}$$ itself is not expected to be AR. (We could use ArmaModel.armaMean to generate the indicators though, since $$Y_t = sum{a_i X_{t-i}}$$.) In fact, if the original price process $${X_t}$$ were indeed a stationary AR process, we wouldn’t expect to make much money at all using this strategy. A mean-reverting strategy would probably be much better. Also, for an AR(p2) model, there are actually (p2 + 2) parameters to estimate (including the constant and the variance of error) not just 1.