With liquid products like SPY the volume@price and time@price profiles are "honest". I use quotes around honest because efficient markets tend to be priced correct (in terms of number of people agreeing on value) more often than not, hence the profiles are good indicators of value. It's a bit tougher when one moves to a multi-market model, especially when trading less liquid markets.
Quote from Mike805:[/i] "That's a good question and I don't have a definitive answer. What I try to quantify is the stabilization of price and what a subsequent reversal/reversion setup trades like. So far, price simply moving a certain distance away from the low is good enough for me. " So for example in a downward spike, that would be zone where the shorts have placed profit-taking stops, "X" number of tics up off the low. You are saying aim to enter just as those stops are beginning to hit, right? I use that method also, but then there those times we have a spike down and prices drift up into that "stop zone", the stops are hit, price pauses, and sure enough the selling starts in again. So the another approach is to aim at entering at the extreme low of the push, or close to it. This way one has more cushion should selling continue then you would have entering higher at the "stops zone".
Very interesting topic! I've only taken an elementary stats course, and a lot of this stuff is over my head but I do enjoy reading MAESTRO's and others posts. Keep it up
Maestro, LoLatency, Others: Help me out, here is a very simple strat using the boxed version of WMA. Top/Bottom ticks eliminated, 0.01 commish, and no optimization. Profitability seems robust across some random parameters I selected. How can Splines or other forms of curve-fitting improve this? PM if you like...
I never said ARMA was the end all be all. ARMA assumes weak stationarity, and that's not guaranteed on stock prices. It's somewhat reasonable to assume integration on the order of 1 , or to assume the returns [or log returns] are weak stationary. ARMA can provide a better fit under weak stationarity than a flat-weighted MA. The reason is because returns and prices are not independent of each other. If you're talking about those 3sigma stochastic shocks, and you carry no hedge, there's not much you can do. You can try to hedge, pair up, etc. Trading a pure MA strategy unhedged means you carry the risk of a shock.
What do all the different items on this graph mean? No way to tell you how to improve the strategy without looking at the strategy in more detail.
Perhaps I'm not asking my question correctly and I am sincere in my question: I can see how a more stable distribution about some line will result in more efficient results. IOW, I have 2 systems: 1) I short X+SMA and buy SMA-X, cover @ SMA. 2) I short X+F(x) and buy F(x)-X, cover @ F(x); where F(x) is some method of curve-fitting (ARMA, Spline, etc.) I would expect that equity curve of 2 to be more efficient (profitability/distribution/both) then #1. Is this correct? BUT regardless of how good F(x) might be, if the security in question is not a semi-stationary process then no system will work. And hence any true profitability comes from your ability to filter stocks for stationary and NOT due to finding the best method to curve-fit. Furthermore, your ability to generate longer term gains comes from knowing when a stock switches regimes. P.S. This could apply to pairs and baskets as well.... The figure posted is the following: 1) Green area is equity curve 2) Green line is profit of long component 3) Red line is profit of short component
If by stationary you mean normally distributed then you have your answer: use a filter (or entry F(x) calc.) that incorporates non-linear (non-normal) behavior. I find raw vola. filters to be very useful for this, something as simple as filtering for higher vola. might work. Also, why curve fit the mean, F(x) or anything? It provides little forward-looking value IMO. What you have already is likely to be more representative of real world results that any "fit" model you chose to implement. Mike
You're right. Improved F(X) would just give you a better estimate of the mean in the presence of correlation at various lags. IOW, you would know more readily whether price is trading in a region that could be considered far from the mean. In theory, your system would be more accurate in the presence of stationarity. [Recall, however, that the confidence interval for small n on the prediction of the mean even in ARMA is still ridiculously wide.] But, again, you're right -- how do you even know if you've got stationarity? This is one of the reasons why they have terms like weak stationarity and strong stationarity. Strong stationarity implies the joint distribution of two disjoint, sequentially time-ordered subsets of a time series are the same. No serious market participant would ever bet on strong stationarity being present in the markets. Weak stationarity just assumes a constant mean and variance at every time-step, which we also KNOW is a bogus assumption. But to address your question of knowing whether the regime changed, you could mathematically detect such a thing -- but it would take some time for the formal test to register. Whether this time is long enough for you to save yourself depends on your strategy. I mean, one possible way to figure out whether your regime has changed is to take the two disjoint time-ordered subsets of the same time-series and do a non-parametric comparison of the CDFs of the two subsets. If the CDFs don't match, you've got a different underlying distribution and no longer have stationarity. In theory, you could do this all day long for every tick. You could also use something like Brown-Forsythe or Modified-Levine test on the residuals -- non-parametric tests to assess there is homoscedascity. The real question is -- what is breaking that stationarity? It's almost certainly the volatility parameter of the stock price process that changes. ARMA models and the like assume homoscedascity. Your regime changes are going to come from the fact that you are almost assured that the volatility of the price process itself changes -- or, what they call like heteroscedascity. The genius in pairs trading is that two correlated, stochastic processes will evolve in a similar fashion. The pair-hedge accounts for the simultaneous shift in paradigm, so your reversion happens within the context of whatever distribution currently determines the empirically determined probability distribution function, or what you're calling "the regime."
Fix this graph and plot a few other things: 1) Historical volatility of the stock for each time step in the graph 2) Implied volatility for the nearest at-the-money call at each step 3) mean of the returns 4) sample variance of the residuals for a given time window as t->inf