There was a question regarding momentum during today’s real-time trading session.
I did a quick google search and found an answer at Investopedia that most traders are probably familiar with:

One of the main goals of every trader using technical analysis is to measure the strength of an asset’s momentum and the likelihood that it will continue. This is the primary purpose of indicators such as the moving average convergence divergence (MACD), stochastics, price rate of change (ROC) and the relative strength index (RSI).
Most of the indicators used to measure momentum are interpreted by using certain values that suggest the asset may be getting overbought or oversold. The strength of current momentum is considered to be getting weaker when indicators such as the ones mentioned above have values that demonstrate overbought or oversold conditions. For example, many traders suggest that an asset with an RSI below 30 or a stochastic value below 20 may experience a reduction in the amount of downward momentum and is a likely candidate for a reversal.
You may notice that many momentum indicators are bound between two extreme levels, usually 0 to 100 or -100 to +100. This is important because a cross through the center line of the indicator is interpreted to mean that momentum is either increasing or decreasing, depending on the direction. For example, momentum is said to be increasing when the ROC indicator crosses above the 0 line, and decreasing when it crosses down through 0.
In addition to the methods we’ve already mentioned, traders can also monitor the crossing of certain moving averages to confirm the strength of a price move. Momentum is said to be increasing when a short-term average crosses above a longer-term average. This is the premise behind the MACD indicator, which uses a 12-day exponential moving average and a 26-day EMA. When this indicator has a value greater than 0, it means that the shorter-term average is above the longer-term average, and it may suggest that momentum is increasing.

Next, I found an eSignal handout [DOWNLOAD PDF] from August 2000.
 
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Then, from Bloomberg:

Stock Momentum Measure Signals More Gains: Technical Analysis
March 11 (Bloomberg) — The yearlong rally in the U.S. market has pushed the number of stocks showing unusually sharp daily gains to the highest level at least since 1994, a sign that more gains may come, according to Concept Capital.
The New York-based institutional broker defined “overbought” as when a stock’s 21-day stochastic reading exceeds 80. On March 9, 77 percent of the companies in the Standard & Poor’s 1500 Composite index reached that threshold, exceeding the previous high of 74 percent in April, Concept Capital said.
“While a sign of a short-term overbought condition, which could usher in a pause, readings this extreme have historically led to higher prices over the next several months,” John Kolovos and Craig Peskin, technical analysts at Concept Capital, wrote in a note to clients yesterday.
Using stochastics, which analyzes momentum to capture a security’s turns in direction, Kolovos and Peskin identified the previous nine most overbought conditions from 1994 to the present and found that, following these days, the S&P 1500 on average rose 1.9 percent in one month, 4.7 percent in three months, and 8.5 percent over the next six months.
The current spike in the S&P 500’s level of overbought stocks is the fourth highest dating back to 1990, the Concept strategists said.

And finally, CXO references another definition of momentum, namely “(1) nearness to the one-year high of the fund share net asset value; (2) prior six-month fund return; and, (3) fund sensitivity to stock return momentum.”

Defining the Problem

Is this another classic technical analysis urban legend coming on? Perhaps the best thing to do is define the problem. Recall high school physics: momentum = mass * velocity. This can’t be the “momentum” traders have in mind.
Some questions. What do we want to know? Momentum? Speed? Velocity? Acceleration? How do we measure it? Rate of change? Stochastics? MACD? What do these indicators measure? How do we interpret the data?
Back to basics. A stock chart with price bars plotted against time is a position-time graph while the indicator most people have in their mind (even if it’s the wrong one) is probably a velocity-time graph.
Speed, velocity, acceleration? Perhaps one of these is suitable, but let’s not forget the kinematics fine print.

I think the answer is straight out of the first few lectures on derivatives from first year calculus. Isn’t what you want the slope of the derivative, aka, the second derivative? You want to know if the function is concave up or concave down, but honestly, I think “visual inspection” OF THE ACTUAL PRICE CHART will tell us that. And yes, I just took a picture of my TV screen since I have these DVDs handy at all times. 😉

We looked at this 5-minute E-mini S&P chart this morning with SmarterSwings applied. Note the pattern of higher swing highs and higher swings lows. The upswings are larger in magnitude than the downswings. THIS IS UP. Click the chart to see a larger image.

As I said this morning in the real-time session, the big downswing at the beginning of the day broke the pattern. This is all you need to know. Click the chart to see a larger image.
So there we have it. Before taking an indicator on faith and trying to interpret it, I think it would be best to step back and look at what it is that we’re trying to measure, define it and then decide what equation to apply.