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Tests 13 through 21 examine divergences with the Stochastic oscillator, the RSI, and the MACD. Divergence is a concept used by technical traders to describe something easily perceived on a chart but hard to precisely define and detect algorithmically. Figure 7-l shows examples of divergence. Divergence occurs when, e.g., the market forms a lower valley, while the oscillator forms a higher valley of a pair of valleys, indicating a buy condition; selling is the converse. Because wave forms may be irregular, quantifying divergence is tricky. Although our detection algorithm is elementary and imperfect, when examining charts it appears to work well enough to objectively evaluate the usefulness of divergence. Only buy signals will be discussed; the sells are the exact opposite. The algorithm s logic is as follows: Over a look-back (in the code, len3), the lowest bar in the price series and the lowest bar produced by the oscillator are located. Several conditions are then checked. First, the lowest bar of the price series must have occurred at least one bar ago (there has to be a definable valley), but within the past six bars (this valley should be close to the current bar). The lowest bar in the price series has to occur at least four bars after the lowest bar in the look-back period for the oscillator line (the deepest valley produced by the oscillator must occur before the deepest valley produced by the price). Another condition is that the lowest bar produced by the oscillator line is not the first bar in the look-back period
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(again, there has to be a definable bottom). Finally, the oscillator must have just turned upward (defining the second valley as the signal about to be issued). If all conditions are met, there is ostensibly a divergence and a buy is posted. If a buy has not been posted, a similar set of conditions looks for peaks (instead of valleys); the conditions are adjusted and a sell is posted if the market formed a higher high, while the oscillator formed a lower high. This logic does a reasonable job of detecting divergences seen on charts. Other than the entry orders, the only difference between Tests 13 through 21 is the oscillator being analyzed (in relation to prices) for the presence of divergence. Tests 13 through 15: Stochastic Divergence Mode&. Fast %K was used with the standard entries. Optimization involved stepping the Stochastic length from 5 to 25 in increments of 1 and the divergence look-back from 15 to 25 by 5. The best parameters were length and look-back, respectively, 20 and 15 for open, 24 and 15 for limit, 25 and 15 for stop. This model was among the worst for all orders and in both samples. In-sample, the limit was marginally best; out-of-sample, the stop. In-Sample, across all orders, Unleaded Gasoline, Soybeans, and Soybean Meal were profitable; Gold and Pork Bellies were moderately profitable with a limit. Unleaded Gasoline held up out-of-sample across all orders. Soybeans were profitable out-ofsample for the open and stop. More markets were profitable out-of-sample than insample, with the stop yielding the most markets with profits. The pattern of more profitable trading out-of-sample than in-sample is prima facie evidence that optimization played no role in the outcome; instead, in recent years, some markets have become more tradeable using such models. This may be due to fewer trends and increased choppiness in many markets. Tests 16 through 18: RSI Divergence Models. Optimization stepped the RSI period from 5 to 25 in increments of 1, and the divergence look-back from 15 to 25 by 5. Overall, the results were poor. h-sample, the stop was lest bad, with the limit close behind. Out-of-sample, the stop was also best, closely followed by the open. Given that the RSI has been one of the indicators traditionally favored by traders using divergence, its poor showing in these tests is noteworthy. Heating Oil was profitable for all orders, Unleaded Gasoline WZY significantly profitable for the open and stop, Light Crude for the limit and stop. In-sample, Soybeans traded very profitably across orders; Orange Juice, Corn, Soybean Oil, and Pork Bellies traded well with the stop. Out-ofsample, the oils were not consistently profitable, while Soybeans remained profitable across orders; Orange Juice and Soybean Oil still traded profitably with the stop. Tests 19 through 21: MACD Divergence Mode&. The length of the shorter moving average was stepped from 3 to 15 in increments of 2; the length of the longer moving average from 10 to 40 by 5; and the divergence look-back from 15 to 25, also by 5. Only parameter sets where the longer moving average was actaally longer than the shorter one were examined.
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