Simple Moving Average
SMA = SUM(PRICE, n)
/ n
where n = Period
Weighted Moving Average
WMA = ( PRICE * n + PRICE(1) *
n1 + ... PRICE(n1) * 1) / ( n * (n + 1) / 2 )
n = Period
Exponential Moving Average
EMA = EMA.1 + (PRICE  EMA.1 ) *
K
or
EMA = K * PRICE + (1  K) * EMA.1
where...
K = 2 /
(n + 1)
n = Period
Zero Lag Exponential Moving Average
("Zero Lag" is an option within the
Exponential Moving Average indicator)
EMA = K * ( 2 * PRICE  PRICE.X) +
(1  K) * EMA.1
where...
K = 2 /
(n + 1)
n = Period
x = lag = (n  1) /
2
Wilder Moving Average
WiMA = ( PRICE + (n  1) * WiMA.1
) / n
Least Square Moving Average
LSMA = Endpoint of Regression
Line including current bar and previous n  1 bars
Adaptive Moving Average
Click here
Endpoint Moving Average
Triangular Moving Average
(example of 5 period
triangular moving average, more details below)
TMA = (PRICE + 2 * PRICE.1 + 3 * PRICE.2 + 2 * PRICE.3
+ PRICE.4 ) / 9
Sine Weighted Moving Average
Hull Moving Average
HMA = WMA(2*WMA(PRICE, n/2)  WMA(PRICE,
n), sqrt(n))
where...
n = Period
Smoothed Moving Average
The first value of this smoothed moving average is
calculated as the simple moving average (SMA):
SUM.1 = SUM(CLOSE, n)
SMMA.1 = SUM.1 / n
The second and succeeding moving averages are
calculated according to this formula:
SMMA = (SUM.1  SMMA.1+CLOSE) / n
Modified Moving Average  Click here
MESA Adaptive Moving Average  Click here
Elastic Volume Weighted Moving Average  Click here
Indicator Adjusted Average  Click here
Indicator Weighted Average  Click here
Triple Smoothing  Click here
T3  Click here

Moving averages provide different options for smoothing data. Data
is smoothed in order to help reduce the effect of bartobar price
fluctuations and help identify longer term emerging trends. A moving average reveals the general direction and strength of a stock's price trend over a given period.
The term "Moving" is used to refer to the fact that the window of
bars that we are considering remain fixed in width (Period) but moves
forward with subsequent bar. Some of the averaging methods however are
not so much "Moving" as they are "Cumulative"
(exponential for one).
The following Price options are available as the input data for each
smoothing type: Open, Close, High, Low, HI+LO/2, HI+LO+CL/3,
O+H+L+C/4, %Change, or OP+CL/2. In addition, the MA token can be used
in RTL to smooth just about anything. For instance, if you wanted to
smooth Rate of Change, you would simply use the syntax MA(ROC).
The moving average technical indicator in Investor/RT now supports nine distinct moving
average types. Four new moving average types were added to Investor/RT 3.8. The
Adaptive Moving Average is described in detail on p. 34 of the 1998 Bonus Issue of Stocks
and Commodities Magazine, while the other 3 moving averages are described in detail in the
June 1999, p. 18.
Adaptive Moving Average  This moving average moves
slowly when prices are moving sideways and moves swiftly when prices move swiftly.
Triangular Moving Average  The triangular moving
average derives its name from the way the weighting factors are applied to the un smoothed
data. For example, for a 7 period moving average, the weighting factors are 1, 2, 3, 4, 3,
2, 1.
Endpoint Moving Average  The endpoint moving average
uses a least squares (linear regression) fit to derive each point on the moving average
line based on the preceding period.
SineWeighted Average  The sineweighted moving
average is similar in concept to the triangle moving average, but the weighting factors
are based on a sine calculation instead.
These new moving averages may be used as overlay indicators showing the moving average of
some price type for an instrument, or they may be used as smoothing options in conjunction
with other technical indicators. For example, the Adaptive moving average could be used to
smooth the CCI, RSI, or MACD indicator.
The five preexisting moving averages are Simple, Weighted, Exponential, Welles Wilder,
and Least Square. Below we'll take a closer look at these 5 averaging
methods. Simple Moving Average (SMA)
 This is probably the most commonly used smoothing type. The
Simple method gives equal weighting to each price point over the period
considered. Let's assume we are considering a 10period simple average
of the close. The SMA value at each bar will be computed by taking the
close of that bar, and the close of the previous 9 (Period  1) bars, adding
them together, and then dividing by 10 (Period), to get the average. Each
time you add a new price point to the simple MA, you drop the oldest price
point. Simple MA's have a memory of only the last X bars (X being the
period). Exponential Moving Average
(EMA)  Exponential averages address two problems that are
experienced with Simple Moving Averages: SMAs give equal weight to
each price in the period, and SMAs change twice with every new bar (new
price added while old price is dropped). The calculation method used
by exponential averages is cumulative, meaning that all previous bars have
some effect on the EMA value, although that effect diminishes greatly with
time. It is similar to other moving averages however in that the
smaller the period, the more responsive the MA will be, as the most recent
bar will have a greater effect. EMAs place more weight on recent prices
than other moving averages such as SMA. For example, if you choose an
EMA period of 7, then the current bar is going to get a weighting factor of
2(n+1) or 2(7+1) in our case, which is 0.25. So the current bar will
be weighted 25% while the previous value of EMA (EMA.1) will be weighted
75%. The previous value of EMA is built using each of the previous
bars (or prices) to some degree. In a comparable SMA with a period of
7, the current bar and the previous 6 bars all get an equal weighting factor
or approximately 14.3% and the bars preceding these 7 bars aren't considered
at all. The EMA period is really less of a "period" and more
of a conversion factor used in determining the weighting factor or the
current bar. Larger periods apply more weighting to past bars, while
smaller periods apply more weighting to the current bar (and therefore make
the indicator more responsive). Something else that must be considered
when using cumulative indicators such as the EMA, is that the values can
change slightly depending on how much data is loaded and considered in the
population. This is inherent in the fact that each EMA value considers
all past prices to some degree. So if you are using 40 bars to compute
the EMA value, then the EMA value of the last bars is based on only those 40
bars, and can be different from an EMA that had 200 prior bars available for
calculation. The difference in this case should be rather small and
probably insignificant, but this can be an issue when running scans or using
custom indicators in custom columns, as Investor/RT optimizes to load the
minimum bars necessary. Charts, on the other hand, generally have many
more bars at its disposal. This can account for small discrepancies
between scan result values and chart values when EMAs are involved.
Beginning
in version 5.4.4, Investor/RT has added the ability to allow floating point
periods for exponential moving averages. Exponential Moving Average
(EMA) has been added as a stand alone technical indicator, and can be
reference in RTL with the token EMA. The standard moving average
indicator allows only integer values to be used for the period. This
new EMA allows numbers such as 2.33, 3.5, or 5.2 to be used as the
period. Some traders prefer this option to allow more precise control
over the weighting of the current bar. Weighted
Moving Average (WMA)  Weighted
MAs share characteristics of both Simple and Exponential Averages.
Like Simple MAs, WMA has a fixed window equal to the period specified.
In other words, if the period is 10, then only the previous 10 bars will be
considered (noncumulative). Like Exponential MAs, WMA places more
emphasis, or heavier weighting, on more recent prices. As can be seen
in the formula at the top of this page, the most recent price gets a
weighting factor equal to the period. The weighting factor then
decreases by 1 for each of the subsequent bars all the way back to a factor
of 1 for n  1 bars back (n being the period). For comparison, consider a
10 period moving average. For an SMA, the weighting of the current bar
would be 10% (1 / 10). For an EMA, the weighting of the current bar
would be approximately 18.18% (2 / [10 + 1]). For a WMA, the weighting
of the current bar would be approximately 18.2% (10 / [(10 * 11) / 2]).
Volume
Weighted
Moving Average (VWMA)  The Volume Weighted Moving Average weights the price of each bar with the volume of that bar. In this way, bars with higher volume will be more heavily weighted in the computation of the average. For example, a 5period VWMA first sum the product of the volume and the price for each of the last 5 bars. This product is then divided by the sum of the volumes to give the resulting average. Many indicators in Investor/RT allow the user to specify the smoothing type. The “Volume Weighted” option can now be found at the bottom of the list of smoothing types. The VWMA can also be accessed in the scan language by simply using the token “MA” and choosing for the smoothing type of the MA to be “Volume Weighted”.
New
in Version 6.0
The Moving Average (MA) and Exponential Moving Average (EMA) indicators have been enhanced by providing options for drawing type. This enhancement will open up MA and EMA lines to be drawn as Two Color Lines, Stepped Lines, and Histograms. These advanced drawing type options, which already exist in a number of indicators including Custom Indicators, will be rolled out to many others in the near future. If an indicator currently does not support these drawing options, it still may be possible to implement the drawing of this indicator by first create a Custom Indicator that simply represents the indicators value. The drawing types are then available to Custom Indicators. 