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Statistical Process Control Techniques in Technical Analysis

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Statistical Process Control Techniques in Technical Analysis Statistical Process Control Techniques in Technical Analysis Leonard H. Smith, CMT SOT in a trending period. and quantifiable methodscan be used Abstract to take trending systemsout of the market during non-trending This paper addresses Statistical Process Control (SPC) tech- drawdownperiods, thereby improving mechanicalsystem timing. niques applied to Technical Analysis. The premise is that simple The challengefor the market technician is to determine whirh methods from manufacturing Statistical Process Control can be market behavior is worth trading with zdzattechnique. Statistical used to determine when a statistically significant tradable event methods can be applied to the market and lead to a trending or has occurred. non-trending conclusiononce a threshold probability assumption This paper proposes an Orderliness Indicator that has predic- is selected. A trading method can be selected once the market tire value on expected LACK of price change. has been categorized as trending or non-trending. One strateg) SPC-derived trading systems are shown that use: would be used for a random or non-trending market. X different Rule 1: Price movement outside a range of expected prices is trading strategy would be designed for trending markets. One usedas a trade setup, and application might be to sell options when the end of a trend is Rule 4: X moving average technique will be introduced, and signaled.The end of a trend usuall!; has high option premiums R Rule: Price change as an entry stop in combination with a and selling them with appropriate risk control could be quanti- simple exit rule. fied. SPC methods offer a simple way of evaluating market trend behaviors with statisticaltechniques. Introduction Bollinger Bands and Statistics StatisticalProcess Control (SPC) is usedin manufacturing pro- Bollinger Bands have been used as a market volntili~yindica- cessesto detect significant deviations from normal conditions so tion for a number of Tears.They also graphically depict statistical that process control and manufacturing products can be im- bands. Bollinger Bands use a moving average for the indicator proved. Simple methods that represent complex statisticalanal:- backbone while standard deviation multiples are spannedoff of sisrules have been developed and applied to many processes.It 1s the average. natural that these general techniques are applicable to todav’s The general form of Bollinger Bandsis: markets. Upper band: a moving average plus a multiple (X) of stan- The first step in Manufacturing SPCis to selectproduct mea- dard deviation suresand calculate statisticallv significant variations b? standard Lower baud: a moving averageminus the samemultiple (X) methods. The most importan; change for the Financial Markets of standard deviation and the most obvious measure is price change. However, the X statistical relationship explains the natural multiple to use changecould just aseasily be in an indicator. or variation between for the previously empirically derived band multiples. F\‘hen a 20- a model and results. The thesis of this paper is this: Statistical period average is used, the significance of one data point being ProcessControl methodscan lead to profitable trading opportu- significantly different from the rest of the population represents nities. 5% chance. If more than one in 20 happens to be outside 95% Random Walk and Statistics confidence limits, the event is not explained by random statistics Random Walk suggeststhat market movements can be de- and something significant probably happened. scribed by purely rundom events.Although the Random1Valk the- If only one event occurred outside the confidence limit, then sisis currently on the decline, statisticsshares a common assump- it may haye been a small chance occurrence or it may have been tion. Statisticsalso relies on the assumptionof ,-n&m behavior. significant. Statisticsmakes the assumptionthat the data set has a random It is no accident that two standarddeviations work well with a variation around an averagevalue. The difference is that random 20-period average.TWO times standard deviation spannedaround walk is a model for unfolding price, while statisticalmethods are the average represents93% confidence limits in random statis- the basisfor assessingsignificance of unfolding events and can tics. For eachaverage length, there is an implied confidence limit signal a non-random event. and probability. The probability is one divided by the number of events counted in the average.The standarddeviation multiplier Market Phases: Trends and Accumulation/Distribution is correlated to a statisticalconfidence limit and probability and Pring and others have suggestedthat the behavior of market is shownin Appendix A. The confidence limit implied bp the av moves can be characterized in segments.Markets exhibit non- erage length can also be usedin SPC. trending Accumulation or Distribution phasesand change to a During Accumulation and Distribution phases,the bandscon- Trending phaseand back to an Accumulation/Distribution phase. tract and usuallv contain the price. During Accumulation and During the Accumulation/Distribution phase, price exhibits a Distribution phases,markets behave more randomly and are more more random behavior. likelp to be explained by random statistics.Conversel!; when the Profitable systemshave been documented, like the Donchian market beginsto trend, price may NOT be contained by the bands 20-davI systemI and Breakout systems,that capitalize on the trend- and indicate a non-random event in the market. During trending ing (non-random) periods. Drawdownsoccur when the market is phasesthe bandswiden and the moving averagefollows the trend. MTA JOURVAL 0 \\‘inter SpringI999 19 SPC compared to Bollinger Bands Figure 1 NYSE Orderliness 1988-1996 SPC charts in the manufacturing process are similar to Bollinger Band charts. Bollinger Bands plot a Price average and an upper and lower band separated from an average by some mul- tiple of standard deviation over the same period. Similarly, SPC charts are plotted with an average and upper and lower band. 2.00 The difference between Bollinger Bands and the SPC tech- P : nique is the measure used to separate the bands from a central ; 1.50 average. The calculation of Statistical Process Control Limits uses z the average difference behveen consecutive values and multiplies 1.00 a factor based on the number of observations to arrive at a “natu- 0.50 ral control limit.” The key SPC measure is price difference from one dav to the next, rather than standard deviation. A&her difference is that SPC uses the significance of event sequences to arrive at another more detailed look at probabili- ties. For example, if hvo 90% probabiliE events failed to occur sequentially, their combined probability would be about 1%. Standard Deviation Compared to SPC Variation 20% , Measures A basic measure of Bollinger Bands is standard deviation. Stan- 10% dard deviation is a variation measure of the whole population. SPC $ usesa different measureof data variation in that it measuresthe ; 5% sequentialvariation {R value),which can be significantly different ! 0% from the standard deviation. .c 0 C The sequentialR values are calculated by taking the absolute i -5% e value of the change in values.For example, the absolutevalue of u -10% t the sequence3,5 is the sameas the sequence5, 3 and is equal to -15% 2. The R-Bar value, the R value for the whole period, is calculated by averaging the sequential R values over a suitable number of -20% J data values.The procedure for calculating R-Barvalues is included Standard Deviation4R.Bsr*2.656) asa part of Appendix B. A random set of 20 values illustrates difference between stan- SPC Rules dard deviation and the R-Bar value. The standard deviation of 20 SPC hasa number of simplified “rules” that imply statistically values doesn’t change no matter how you order the values. How- ignificant events. These rules include: eyer, the R-Barvalue changesand will be significantly lower when Rule 1: Trade when OSE value is outside an Upper or Lower the values are ordered from highest to lowest and much larger Limit at 3 standard deviations above or 3 standard deviations when the consecutive values are ordered from one extreme to below the averagevalue. the other and back. One set ofvalues ordered differently can have Rule 2: Trade when TM’0 out of 3 consecutive values exceed many different R-Bar values. limits at 2 standard deviations above or 2 standard deviations below the averagevalue. Orderliness Index (Sigma/R) Suggested Rule 3: Trade when FOUR out of 5 consecutivevalues exceed The ratio of Sigma, the standard deviation, over R-Bar, the av- limits at one standard deviation above or one standard devia- erage point to point variation, can give additional information tion below the averagevalue. about the market. Note that the indicator does not imply direc- Rule 4: Trade when EIGHT consecutivevalues exceed the av- tion. erage or EIGHT consecutirevalues are lessthan the average. The Orderliness Index data in Figure 1 are calculated from R Rule: Trade when the change from one value to the next (re- the NYSE index from 1988to 1996.In fact, the OrderlinessIndex gardlessof increasingchange, decreasingchange, or relation- shown in Figure 1 showsthat for relatively high values, greater ship to the average) - expressedas a positive number - ex- than 1.75, a trend in the next 20 days is NOT expected. In this ceedsan Upper Limit. case, the price 20 days from a date where the index is greater h common choice of confidence level in manufacturing is 99%. than 1.75, the price is expected to change lessthan 2%. The de- 100data points are recommendedto derive 99% confidence lim- velopment of the Orderliness Index is beyond the scope of this ts. If 20 data points are used, uncertainty is about one in 20 or paper and is left for future study. 5%. Since uncertainty is 5%, this suggeststhat only a 95% confi- lence limit is warranted. A 95% confidence limit correspondsto 1 Z score of approximately 2. This suggeststhat t/- 2 standard deviationsshould be used when working with 20 data points in :he average.
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