When prices rise above the upper band or fall below the lower band, a change in direction may occur when the price penetrates the band after a small reversal from the opposite direction.

Remember, because only previous data is used to compute a Moving Average, it will always lags behind the actual prices. As a result, Moving Averages will not predict a change in trend, but rather follow behind the current trend. Use them for trend identification and trend following purposes and not for prediction.

The MACD is simple and reliable. It uses moving averages to include trend-following characteristics. These lagging indicators are turned into a momentum oscillator and plotted as a line that moves above and below zero with no upper or lower limits. The MACD proves most effective in studying wide-swinging trading markets.

Three popular ways to use the MACD are crossovers, overbought/oversold conditions and divergences.

• Crossovers:
  The basic MACD trading rule is sell when the MACD falls below its signal line and buy when the MACD rises above it. It is also common to buy/sell when the MACD goes above/below zero.

• Overbought/Oversold Conditions:
  The MACD is also can be used as an overbought/oversold indicator. If the shorter moving average pulls away dramatically from the longer moving average and the MACD rises it is likely that the security price is overextended and will soon return to more realistic levels.

• Divergences:
  Expect the end a current trend may be near when the MACD diverges from the price of a security. A bearish divergence occurs when the MACD is making new lows while prices fail to match these lows. Likewise, a bullish divergence occurs when the MACD is making new highs while prices fail to follow suit. Both of these divergences are most significant when they occur at relatively overbought/oversold levels.

A buy signal is generated as the histogram crosses above the zero point. A sell signal is generated as the histogram crosses below zero.

The calculation for the MFI is:

In his book Trading Chaos, Williams identified four types of trading sessions: Fakes, Fades, Squats, and Greens.

The combination of lowered volume with a rising MFI is known as a "Fake." As there is no real foundation for change behind a stock except for market activity on the floor, the price eventually reverses itself.

A "Fade" is when volume is down and the MFI is also down. In essence, the market is bored and interest in the stock fades. Expect the price to move in the opposite direction.

When volume is up while the MFI is down, the condition is referred to as a "Squat." Think of the stock crouching down like a sprinter before a race. Movement after the squat gives a clue to future to direction.

When volume and the MFI are both up, the situation is "Green." This is a strong signal to follow the trendline.

A significant pattern to watch for is the "reversal bulge." These occur when on a 25-period plot the Mass Index surpasses 27 then falls past 26.5.

A 9-period Exponential Moving Average of prices is often used to determine if the reversal bulge indicates a buying or selling. If a reversal bulge occurs, buy if the moving average is trending down (in anticipation of the reversal) and sell if it is trending up.

Similar to MACD, the McClellan Oscillator is a breadth indicator that uses advances and declines to determine the amount of participation in the movement of the stock market. One sign of a healthy bull market is a large number of stocks making moderate upward advances in price. A small number of stocks making large advances in price is a sign of a weakening bull market. This situation gives the false appearance that all is well and is the type of divergence that often signals an end to a bull market.

The oscillator fluctuates around a zero line usually ranging between +100 to-100. A McClellan Oscillator reading between +70 to +100 which then turns down is an overbought or sell signal. Buy signals are when the oscillator falls into the oversold area of -70 to -100 and then turns up. Any reading that goes beyond these areas (rising above +100 or falling below -100) is a sign of an extremely overbought or oversold condition. These extreme readings are usually a sign of a continuation of the current trend. Crossings above and below the zero line can also interpreted as short to intermediate term buying and selling signals respectively.

The McClellan Oscillator is calculated taking the difference between 10% (approximately 19-day) and 5% (approximately 39-day) Exponential Moving Averages of advancing minus declining issues:

Information provided by John Murphy, author of Technical Analysis of the Financial Markets and The Visual Investor.

The interpretation of the McClellan Summation is similar to that of the McClellan Oscillator except that it is more suited to major trend reversals as it is a long-term version of the Oscillator.

The McClellans suggest the following rules for use with the Summation:

The beginning of a significant bull market is indicated when the McClellan Summation crosses above +1,900 after moving upward more than 3,600 points from its prior low.

As with other price adjustment functions, the median price provides a simplified view of the trading prices for the day. It can be used to smooth out some of the volatility of the closing price since it includes information for the entire trading day rather than specifically the end of the day.

The median price can be used anywhere a closing price or other single price field would be used.

One useful attribute of the MESA Sine Wave indicator is that it will anticipate cycle mode turning points rather than waiting for confirmation as is seen with most other oscillators. The indicator has the additional advantage that trend mode whipsaw signals are minimized.

The indicator consists of two plots - one line displaying the Sine of the measured phase angle over time and the other the Sine of the phase angle advanced by 45 degrees (the Lead Sine). Together the crossings of the Sine and Lead Sine give clear advanced indication of cycle mode turning points.

When the market is in cycle mode, a buy signal is given as the Sine plot crosses above the Lead Sine plot. The sell signal is given when the Sine plot crosses below the Lead Sine plot.

When the market is in the trend mode, trade the trend. Basic moving average crossovers may be useful for entering and exiting positions in this type of market.

While the mathematics are straightforward (subtract the closing price n days ago from the closing price today), do not underrate its value because of its simplicity.

Use the Momentum indicator as a trend-following oscillator similar to the MACD and buy when the indicator bottoms and turns up. Sell when the indicator peaks and turns down. When the Momentum indicator reaches extremely high or low values (relative to historical values) assume a continuation of the current trend.

A second usage for the Momentum indicator is as a leading indicator. As a market peaks, the Momentum indicator will climb sharply before falling off. At a market bottom, the plot will drop sharply and then climb well ahead of prices.

Information provided by Charles LeBeau's Technical Traders Guide to Computer Analysis of the Futures Market.

So:

if P_t today's price and P_t-n the price n days ago,

Momentum is calculated as:

So if you define MO_max the highest absolute value of the momentum, the Momentum % is:

The interpretation for Momentum % is the same as that for Momentum, purchase when Momentum % changes from negative positive and sell when it is the reverse.

The equation for Money Flow calculation is simply:

Money Flow values can be used as an independent measurement or as part of the Money Flow Index equation.

The calculation of the Money Flow Index requires multiple steps. First, determine the period's Typical Price:

Calculate Money Flow (not the Money Flow Index) by multiplying the period's Typical Price by the volume:

If today's Typical Price is greater than yesterday's Typical Price, it is considered Positive Money Flow. If today's price is less, it is considered Negative Money Flow. Positive Money Flow is the sum of the Positive Money over the specified number of periods. Negative Money Flow is the sum of the Negative Money over the specified number of periods.

Then finally:

Use the Money Flow Index to look for divergence between the indicator and the price action. If the price trends higher and the MFI trends lower (or vice versa), a reversal may be imminent.

Look for market tops to occur when the MFI > 80. Look for bottoms to when the MFI < 20.

The underlying concept is that overzealous buyers and sellers will drive prices toward the upper or lower band. Look for the price to penetrate the band followed by a small reversal to predict a large change in direction. This is similar to the interpretation of Bollinger Bands.

Information provided by John Murphy, author of Technical Analysis of the Financial Markets and The Visual Investor.

While the first number in the study specifies the period of a simple moving average (e.g., 28 days), the second parameter specifies the shift period (e.g., 5 days); enter a negative number to shift the moving average back (e.g., -14 days). When the moving average is shifted back, the remaining portion of the study is computed with the moving average based on the available data for each day (e.g., 13 days, 12 days, etc.)

The mathematics of a moving average will always force it to follow or lag the actual price data. By centering the moving average, you will have a more accurate picture of the moving average relative to the current price on the chart. A Displaced Moving Average study could be quite useful in locating and estimating cycles.

The Double Exponential Moving Average can be applied in the same manner as the Simple Moving Average or Exponential Moving Average. When price crosses the moving average and increases, a continuing uptrend can be expected.

The DEMA is calculated via:

where EMA = exponential moving average

A buy signal occurs when the short and intermediate term averages cross from below to above the longer term average. Conversely, a sell signal is issued when the short and intermediate term averages cross from above to below the longer term average. Use longer term averages when trading only two exponential moving averages in a crossover system.

It may be worth noting that a 5-day exponential moving average normally will include more than 5 days worth of data and could include data from the entire life of a futures contract. In fact, these moving averages might be better identified by their actual "smoothing constants," since the number of days of data in the calculation is the same for a so-called 5-day average as for a 10-day average. Exponential calculations can arrive at different moving average values depending on your starting point.

Information provided by Charles LeBeau's Technical Traders Guide to Computer Analysis of the Futures Market.

Note that because the Simple Moving Average gives equal weight to each daily price, the longer the time period studied the greater the smoothing out of recent market volatility. Long-term moving averages smooth out all the minor fluctuations showing only longer-term trends. Shorter-term moving averages will show shorter term trends but at the expense of the long term.

Most of the time prices are on one side or the other of the moving average. As trends develop, the moving average will slope in the direction of the trend, showing the trend direction and some indication of its strength based on the steepness of the slope.

Information provided by Charles LeBeau's Technical Traders Guide to Computer Analysis of the Futures Market.

Most methods for calculating Moving Averages are unable to compensate for sideways moving prices versus trending markets and often produce numerous false signals. When prices move up and down over an extended period, longer term moving averages are slow to react to reversals in trend. By automatic adjustment of the smoothing constant, a Variable Moving Average adjusts its sensitivity and enables it to perform better in either type of market conditions.

To calculate the Variable Moving Average:

The average is calculated by multiplying each of the previous day's data by a weight factor. That factor is based upon the number of days past the first day used in the Moving Average, for example use five times more weight to today's price than to a price five days ago.