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In our studies of stock or commodity time series data, i.e. a stream of successive daily closes (highs,
lows, volume), we are constantly reminded of moving averages and their application. A moving average is one of the simplest and most often used smoothing or filtering methods available. All that is required is that one choose a number of days, N, that you intend to average your data by and plot that average coincident with the last day of data.
MATHEMATICALLY:
Moving Average= Day1+Day2+Day3+...DayN N
The only variable is, N, the number of days. The 'correct' number of days to use has been researched a great deal, with only one clear indication, that being that each stock issue or commodity tends to have its own characteristic number. There seems to be no agreement on the number or procedures used to derive these numbers (or test them). (For a list of commodity numbers try using "Computerized Trading Techniques 1980" [February '80] by Merrill Lynch.) For the purpose of this discussion we will use five (5) days, although the technique will hold for any number of days.
MOVING AVERAGE AS A FORECASTER:
As a slight extension of the normal moving average procedure we may use moving averages to predict a possible future price. At the point that one runs out of data we plot the last days moving average value one day in the future. For the second day in the future we drop the oldest day and add the first future day during our calculation. This will get us a great prediction if our past prices have been moving sideways, but would intuitively lag behind a rising or falling market.
Let us suppose that the moving average may NOT be a strictly linear relationship. That is, each of the last moving average days (five) MAY not count for an equal amount. Instead of each day accounting for one fifth (20%) of the moving average, each day may be weighed unequally by some other method. This is not a new idea in that almost all smoothing methods use some sort of weighting (See Table 1). Be it exponential, geometric or arithmetic they all weigh past prices in determining a possible future, and some are capable of assigning a probability associated with its future prediction.
MATHEMATICALLY: Weighted Moving Average =
Weight1× Day1+ Weight2 × Day2+...+WeightN× DayN
N
The trick here is coming up with appropriate weights Weight1 through WeightN. In lieu of a crystal ball we have a computer and lots of past price data. It only seems natural that we should be able to go back in time, using our past data, and try a few weights. To test our try-out weights we could check them against the actual next days results, thus determine possible corrections to our original weight guesses. The problem soon resolves itself into a lifetime of trial and error; just the thing for a computer.
The moving average is well known and often used by both stock and commodity traders. The scope of moving average type functions in use is more apparent by studying Table 1. The moving average is generally thought of as simply taking a number (N) of, say, daily closes, adding these values together, and then dividing by the number (N) of days originally taken. With a series of successive calculations, by dropping the oldest data point and adding the next current point, we obtain a 'moving' average of the original series of data points.
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This procedure is more correctly described as a linear moving average because each daily data point is treated (weighted) as being equal. This is certainly not a requirement and may not even represent a desirable result. For example, closer to present days data should (?) be weighted more heavily than older information thereby allowing more recent market information to have a larger impact on the moving average. This would be referred to as a weighted moving average. The variation of weighting schemes is infinite and shall be a topic for additional discussions as well as how and where to plot this average in relation to the original data.
Moving Average Variables:
1) Number (N) of days used in averaging.
2) Weighting scheme used within the (N) number of days.
3) Plot location used relative to original data.
The plot location best fit, to the original data, is midway between the first and last day used to produce the moving average figure. So in our five day (N = 5) moving average example the points would be plotted at the third day of original data, this is called a centered moving average. A centered moving average will appear to ride or fit the general shape inherent in the original price data. Although this is 'Best' both intuitively and mathematically for fitting the data it has the disadvantage of always lagging or trailing the most recent data by one-half (N) number of days. In addition, the centered moving average plot position may not be the best location from a forecast point of view. In reality the fourth day may be a better plot location if one is trying to predict a future price. This approach to moving average plotting will be the subject of a future article.
There is one other bit of confusion with the (N) number of days chosen to use while averaging. It would be very unlikely that the number would remain fixed, for a particular issue, for all time. While five days may work very well, based on the last six months of history, it may be in the process of shifting towards some other, more recent, number such as six days. This sort of anomaly is difficult to automatically assess by using a computer, even the computers speed is limited (e.g. a first test of an Adaptive Filter program took almost four hours to run).
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