Tuesday, July 16, 2013

2013.07.14 DJIA Cycle Model

Saving the least predictive cycle model for last, here is the update for the DJIA. I probably should preface this particular model with some comments about what it represents.  The inputs to  the cycle models rely on  historical data. History rhymes and sometimes even repeats itself. However, the Fed asset buying and bailouts over the past four years are unprecedented in scope, so the model falls apart because there is no way to predict future Fed actions, and right ow the market is focused on Fed actions, rather than underlying business cycle fundamentals like credit, international capital flows, industrial production, etc.  And the market rules.

So why continue to run this model?  Well,  one way to interpret the prediction is that while on a historical basis there is very strong downward pressure on prices, the Fed has successfully, at least for now, inflated equity prices with enough liquidity to push back on seasonal, yearly and decadal patterns of business cycles, all of which have been pointing down for 4 years. Nevertheless, the model might give some quantitative indication of the amount of "pressure" the Fed has to exert to prevent the normal business cycles from re-exerting themselves.  If you look carefully at the Z-score charts, you will see that negative divergences in the  Z-score coincide with Fed bailouts and QE (n+1) announcements. So, if this hypothesis is correct, we should see the Fed announcing a creative way to continue to add liquidity to the banking system without spooking bond holders,  probably in the next few weeks. If the Fed does inject enough liquidity, and the bond markets do not get spooked, then it will provide another point of divergence for the model predictions.  However, if the Fed does nothing, or even thinks about removing liquidity by setting a timeline, the downward pressure on equity prices will reassert itself. 

For those not familiar with Z-scores, it is a way to look at how much variance there is between the predictions and the actual prices over time. A positive Z-score of 2 or 3  indicates that the predictions have exceeded actual prices by that margin 2.2 % of the time and 0.13% respectively.  The reverse operating for negative scores.  The Wiki page is good for a refresher course. The blue line on the second chart shows where we are with the Z-score at the moment, and you can see that on a historical basis it is quite remarkable. But does it mean an equity meltdown is coming up? I don't know, I guess I'll keep my eye on the Fed, like everyone else.


zimzeb said...

Fascinating work--is there anywhere you could direct me that describes your methodology (what data is used as the training set, etc.)?


Paolo said...

Thanks zimzeb. The cycle model was originally a sub-model of a larger structural model. However, as seen in my previous posts, that model got a failing grade because of non-convergence and low accuracy. The structural model included bond prices, derivatives of equity time series of non-US markets, measures of capital flows, as well as fractal parameters associated with the time series, like the Hurst exponent, etc. The cyclical model is much simpler, and it is the one charted here. For the DJIA, the input data is the time series of closing prices since 1896.

The time series is log transformed, and then analyzed using a Multi-Taper Method described by Mann (1). I wrote the analytic routines in Matlab. Statistically robust cycle periods are collected, and then used to seed the cyclical structural model which has the form: P(t) = a1(cos[(t-b1)(2Pi)/c1]) + a2(cos[(t-b2)(2Pi)/c2]) where a,b,c are model parameters, in this case shown for two cycles. I use an SAS platform for this stage.

It is a somewhat tedious process, since the final model has multiple cycles. I think it probably took me around 500-600 hours for the iterative process: find robust cycle, add to model, test model, remove pseudocycles, lather, rinse and repeat. Upkeep is minimal unless the model fails to converge.

All that said, I am pondering why the other three models, gold, silver and oil, seem to be doing relatively well in terms of predictive accuracy, unlike the DJIA model.

Your question inspired me to put up a page for a bibliography, so if you check back in a few weeks, it should be up. if not, feel free to give me a shout. Good luck!

1. Mann, M.E. and Lees, J.M., 1996: Robust estimation of background noise and signal detection in climatic time series, Clim. Change., 33, 409-445.

zimzeb said...

Appreciate the detailed response Paolo! Looking forward to checking back for the bibliography (and other updates too).

Not possible to automate the lathering and rinsing?