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In a previous study (Katz and McCormick, June 1997), we found that lunar cycles could be used to profitably trade the NYFE. From 1990 to 1997, a simple lunar system produced a net profit of $75,550. There were 170 trades, 60% profitable. The average one contract trade made $444.41; the return-on-account was 365% (not annualized). The long side performed better (520%) than the short (-37%). The signals often marked turning points to the very day. Silver also responded well, with signals picking off exact tops and bottoms; both longs and shorts were profitable with a 190% return over the same period as for the NYFE. Even Wheat traded profitably long and short with a 242% return. Given only one parameter (a displacement in days since the full or new moon), and many trades, the results are impressive and probably robust. Our results were encouraging enough to justify further study of entries based on these phenomena. The study will involve the phases of tbe moon, i.e., full moon, fast quarter, last quarter, new moon, and all phases in between. Can the lunar phase predict whether the market is bottoming or topping Do bottoms (or tops) form at the time of the full moon, or perhaps five days before the full moon, or at the new moon Since the lunar cycle may affect different markets differently, the adaptive approach taken with seasonality is again used.
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GENERATING LUNAR ENTRIES
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There are many ways to time entries based on the lunar rhythm. Two approaches are employed in the tests: momentum and crossover. To calculate momentum, a series of price changes is computed and then a centered smoothing (one that induces no delays or phase shifts) is applied. For normalization, each price change in the smoothed series is divided by the 50-day average true range. For each bar, we ask: What phase is the moon in currently As many past instances as possible are found in which the moon was in the identical phase and the momentum of prices on the corresponding bars is examined. The average of the momentums becomes the value placed in the lunar momentum series, which reflects the expected rate-of-change (momentum) in prices at a given time based on historical price movement at the phase of the moon existing on the current bar. Each number in the lunar momentum series is determined only by events about 27 or more days ago; this is why centered smoothing, and other techniques
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that look ahead in time relative to any specified bar, are permissible. Entries are taken when momentum crosses above a positive threshold (a buy signal is issued), or when momentum crosses below a negative threshold (a sell is posted). Buying or selling can take place at the open, on a limit, or on a stop. The momentum calculations and generation of entries closely follow those for seasonality, but, instead of looking to previous instances of the same date in earlier years, previous instances of the moon having a phase identical to that on the target bar are examined. Entries can also be generated by computing the price differences, normalizing them, and integrating the series to obtain a pseudo-price series based on previous instances of the correct lunar phase. A moving average crossover model is then applied to that series. Because the value at any bar in the series is determined only by bars roughly 27 or more days ago, the delay in the crossovers can be compensated for by looking ahead a small number of bars. Both methods are adaptive in that no specific information is required about the phase of the moon on which to place a buy or sell order. The adaptive quality is important because different markets respond to the moon differently, as seen in our earlier study. Both methods differ from the previous research, where buys or sells occurred a fixed number of days before or after a full or a new moon. Several rules for handling confirmations and inversions are also tested to determine whether better results can be obtained over the basic models. An example of co@mation is the following: If a buy signal occurs on a given bar and everything behaves as expected, the market should bottom around the time of the buy; if instead it tops, the buy signal might be suspect, i.e., the market may not be adhering to its typical seasonal or lunar timing. The crossover with cunfirmurion model implements the crossover model with an additional rule that must be satisfied before a buy or sell can be issued. lf a buy signal occurs, the Slow %K on the signal bar must be less than 25%, meaning the market is near the bottom of its recent historical range. Likewise, if the model generates a sell signal, a check is made to see whether Slow %K is greater than 75%, indicating that the market is near the top of its range, as would be expected if it is responding to lunar influence. The con@nation and inversion model adds another element: If a buy is signalled, and the market is near the top of its range (Slow %K greater than 75%), then an inversion is assumed and, instead of issuing a buy, a sell order is posted. If a sell is signalled, but the market is near the bottom of its recent range, a buy order is issued. The characteristics of lunar entries are similar to seasonal entries: Both are predictive, rather than responsive, and thus lend themselves to countertrend trading. And, as with any predictive entry, they may be out of tune with market behavior. As with seasonal entries, cycle or rhythm inversions may occur.
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