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Exponential Moving Average (EMA)
The following is an update of an important indicator in my 820-page research book, Exponential Smoothing Colby, Robert W., , Second Edition,The Encyclopedia of Technical Market Indicators McGraw-Hill Publishing, 2003 (click here for a description). The Exponential Moving Average (EMA) is a popular data smoothing method that is a key component of many technical market indicators. Behaviorally, in its responsiveness to new data being generated by the markets, the EMA represents a compromise between the overly sensitive weighted moving average and the overly sluggish simple moving averages. Compared to other averaging techniques, the EMA follows the trend of the current data smoothly and seamlessly, minimizing jumps, wiggles, and lags. Computationally, the EMA is the simplest and most streamlined of moving average techniques. The EMA requires the fewest calculations, the least data handling, and the least data history. The EMA requires numerical values for only two data periods: the most recently available raw data and the immediate past period's EMA. For example, working with daily data, we need only today's observed, unprocessed data and yesterday's EMA in order to calculate today's EMA. Thus, the EMA eliminates the need to keep and handle long lists of historical data. A significant advantage of this computational method is that the EMA is never distorted by old data suddenly dropping out of the calculation. Old data is never suddenly dropped because it is not actually part of the calculation. For practical purposes, the effect of past data fades away gradually due to the ever decreasing weighting of yesterday's EMA. The EMA's method of calculation correctly avoids the problem of erratic current movement caused solely by irrelevant and obsolete data dropping out of the calculation. An Exponential Moving Average is calculated as follows: EMA = (C - Ep)K + Ep where EMA = the Exponential Moving Average for the current period. C = the closing price for the current period. Ep = the Exponential Moving Average for the previous period. K = the exponential smoothing constant, equal to 2 / ( n+1). n = the total number of periods in a simple moving average to be roughly approximated by the EMA. The exponential smoothing constant formula, K = 2/( n+1), allows an approximate comparison of any EMA to the more sluggish Simple Moving Average of length n. As the number of days n increases, the value of K grows ever smaller, and the EMA becomes increasingly less sensitive to the newer data.
[My table for converting from simple n days to exponential smoothing constants (K), and back, can be seen on page 262 of my book.]
When first starting a new EMA, it takes approximately length n days of calculations for an accurate reading. For a quick startup of a EMA, on the first day of calculation we may use a n-day simple moving average to approximate the previous day's EMA (Ep) in the formula, EMA = (C - Ep)K + Ep. After that first day, we will never need any data other than yesterday's EMA and today's fresh data to maintain our EMA.
[My table illustrating how to compute an EMA of four periods, which is also known as a 40% EMA, named for the exponential smoothing constant, K, can be seen on page 263 of my book.] Indicator Strategy Examples for Exponential Moving Average (EMA) Crossover
Based on the daily closing prices for the Dow-Jones Industrial Average from 1897 through 2002, Exponential Moving Average Crossover Strategies of all lengths from 2 days through 300 days would have produced substantial profits, indicating that a very simple form of trend following would have been an effective strategy over that past period of 105 years. Since 10/21/2002, when cumulative equity hit its peak, the stock market has become much more choppy and prone to day-to-day reversals, with a much greater frequency of significant overnight gaps in the opposite direction from the previous day's trend. Because of these changes, simple trend following has not been profitable since 2002. Trading based on all short-length EMA crossovers, using EMAs from 2 to 35 days, actually would have lost money, and longer-length EMA crossover signals produced mixed results. No trend-following EMA crossover signal produced substantial, consistent, and robust performance from 2002 through 2011. This finding suggests a major change in stock market behavior since year 2002. The cause of this change in market behavior is not clear, but I suspect that the rise of computer algorithmic and high-frequency trading has something to do with it. In addition, with increasing globalization of trading, many more short-term trend changes start in Asia and Europe while U.S. markets are closed for the night. When markets finally open in U.S. time zones, they open on price gaps that are too often in the opposite direction from the previous day's trend. Check out this finding yourself using the following system trading rules: The MetaStock(R) System Testing rules are written as follows: Enter long: CLOSE > Mov(CLOSE,opt1,E) Close long: CLOSE < Mov(CLOSE,opt1,E) Enter short: CLOSE < Mov(CLOSE,opt1,E) Close short: CLOSE > Mov(CLOSE,opt1,E) where "opt1" is a variable corresponding to the number of days used to compute a simple moving average of similar but less sensitivity than an EMA. For example, this "opt1" value can be allowed to vary from 1 day to 300 days, by a step size of 1 day, in software programs such as MetaStock(R). To try this powerful research tool, at no risk, phone:
1-800-882-3040 toll free within the U.S.
or 1-801-265-9996 international Be sure to mentionto order this powerful software at a "Offer Code COLBY".
special discount priceOr, order online here: http://www.MetaStock.com/colbyto buy MetaStock(R) XVII software at the same significant price discount. Translation of
MetaStock(R)
code into English: Trading Rules for EMA Crossover Strategy
Enter Long (Buy) at the current daily price close of the Dow-Jones Industrial Average when this close is greater than the variable-day exponential moving average of the daily closing prices.
Close Long (Sell) at the current daily price close of the Dow-Jones Industrial Average when this close is less than the variable-day exponential moving average of the daily closing prices.
Enter Short (Sell Short) at the current daily price close of the Dow-Jones Industrial Average when this close is less than the variable-day exponential moving average of the daily closing prices.
Close Short (Cover) at the current daily price close of the Dow-Jones Industrial Average when this close is greater than the variable-day exponential moving average of the daily closing prices.
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