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An oscillator is like a pendulum. As you may know from observing grandfather clocks, the pendulum swings back and forth about a line of stability that goes straight down from the suspension point -- i.e., about the gravity line. In a similar way, the oscillator swings above or below a reference line.

The oscillator gives a trading signal when its value reaches unusually high values. Applying a reference line equal to zero, it provides a caution signal for:

1. A long position when a price advance is accompanied by a lower positive momentum reading.
2. A short position when a price decrease is accompanied by a greater negative momentum reading.

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In Introduction to Momentum, Martin L Pring understands market momentum to mean, in one sense, a percentage rate of change of price over a specified period of time. It compares today's close with the close some number of trading periods ago.

This requires picking a suitable interval of time in the chart of a stock and comparing the beginning price on the interval with the end price on the interval. It's done on a moving basis, and therefore involves computing the percentage change for each position of the interval.  

Say we're dealing with a weekly chart and the momentum computation interval is 10 weeks. In this format we have a computation at the end of every week. So, for any week, we compute the percentage rate of change momentum using the latest interval of ten weeks and plot it below this week's price. For the next week we would repeat the computation using the new endpoints with the interval shifted over one position on the chart. This continues indefinitely. The running series of points shows the fluctuation of momentum.

It's worth noting that Bauer and Dahlquist say the momentum indicator displays the rate of change of price. But they differ from Pring in saying it gives the rate of change as a ratio, that the Rate of Change indicator itself gives the rate of change as a percentage.

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A property of the oscillator described here is that it's without bounds and therefore can have very large values. For instance, if the price changes from $2 to $6 in the interval, the percentage change is 300 %. Because of the possibility of even higher values, the oscillator is difficult to interpret. This makes it less valuable as a predictive tool.

The potentially large readings can be eliminated by applying a transformation formula limiting the values to a range between plus and minus one. Intuitively, the process packs large quantities into a small space. If we let the pre-normalized momentum be U, the normalized momentum, N, is:

N = 100(U/(U + 1)).

No matter how large U becomes, either positively or negatively, U/(U + 1) never gets larger than 1. And as U approaches zero, N approaches 0/1, which is zero. So N is always between zero and one.

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Momentum as calculated for the normalized oscillator may be too erratic to be of value. One way to improve the situation is to use a moving average of the momentum to smooth the computation. Say you applied a three-week average to the momentims you computed above on a ten-week interval.

To start the process, you would compute the raw momentum on three successive weeks in the regular way. But on the third week you would also average the three values and plot this average as your first momentum point.

When the fourth week is completed, you would use the raw momenta from the second, third, and fourth weeks to get a new three-day average and the second plot. Continuing that way each week thereafter, you would drop the oldest of the previous three raw values and add the new one to compute the average. This smoothes the results by putting less emphasis on individual raw data.

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The successive values of momentum can be averaged to give more weight to the more recent data. According to Martin L Pring, the added sensitivity yields more timely results.

Let's take a simple example. Suppose the successive bits of data are 1, 4, and 2, and say the weightings were 1, 2, and 3, respectively. A weight of three, for example, is like counting the weighted value three times. You would then compute the weighted average by adding the products 1x1, 2x4, and 3x2 and dividing by the total number of elements, namely 6. So the weighted average is:

(1 + 4 + 4 + 2 + 2 + 2)/6 = 2.5.

For comparison, the unweighted average of 1, 4, and 2 is 7/3 = 2.033.

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The view of momentum developed by Welles Wilder has the property that its values can be very large, making it less valuable as an oscillator. But Wilder corrected this by developing a normalized version that varied between 100 and 0. Following the practice of Wilder, letting this momentum be represented by rs, the normalizing formula is as follows:

rsi = 100 - [100rs/(rs + 1)].

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