movavg

Moving average of a financial time series

Syntax

ma = movavg(Data,type,windowSize)

ma = movavg(___,initialPoints)

ma = movavg(Data,type,weights)

ma = movavg(___,initialPoints)

Description

ma = movavg(Data,type,windowSize) computes the moving average (MA) of a financial time series.

ma = movavg(___,initialPoints) adds an optional argument for initialPoints.

ma = movavg(Data,type,weights) computes the moving average (MA) of a financial time series using a 'custom' type and weights.

ma = movavg(___,initialPoints) adds an optional argument for initialPoints.

Examples

Calculate the Moving Average for a Data Series

Load the file SimulatedStock.mat and compute the moving average using simulated closing price data.

load SimulatedStock.mat
type = 'linear';
windowSize = 14;
ma = movavg(TMW_CLOSE,type,windowSize)

ma = 1000×1

  100.2500
  100.3433
  100.8700
  100.4916
   99.9937
   99.3603
   98.8769
   98.6364
   98.4348
   97.8491
      ⋮

Calculate the Leading and Lagging Moving Averages for a Data Series

Load the file SimulatedStock.mat and compute the moving average using simulated closing price data.

load SimulatedStock.mat 
type = 'linear';
mashort_term=movavg(TMW_CLOSE,type,3) % Short-term moving average

mashort_term = 1000×1

  100.2500
  100.3580
  101.0900
  100.4300
   99.3183
   97.8217
   97.0833
   97.1950
   97.4133
   96.1133
      ⋮

malong_term=movavg(TMW_CLOSE,type,20) % Long-term moving average

malong_term = 1000×1

  100.2500
  100.3423
  100.8574
  100.4943
  100.0198
   99.4230
   98.9728
   98.7509
   98.5688
   98.0554
      ⋮

Plot the long-term and short-term moving averages.

plot(TMW_CLOSE(1:100))
hold on
plot(malong_term(1:100))
plot(mashort_term(1:100))
hold off
legend('Actual','Long-term','Short-term')

Input Arguments

Data — Data for a financial series

matrix | table | timetable

Data for a financial series, specified as a column-oriented matrix, table, or timetable. Timetables and tables must contain variables with only a numeric type.

Data Types: double | table | timetable

type — Type of moving average to compute

character vector with value of 'simple', 'square-root', 'linear', 'square', 'exponential', 'triangular', 'modified', or 'custom' | string with value of "simple", "square-root", "linear", "square", "exponential", "triangular", "modified", or "custom"

Type of moving average to compute, specified as a character vector or string with an associated value. The types of moving average are:

• "simple" — The simple moving average (SMA) is calculated by summing up a specified number of data points and dividing the sum by the number of data points. The SMA gives equal importance to each data point within the specified period. The resulting value represents the average price over the specified period.

• "square-root" — In the square root method, the weights assigned to each data point decrease in a square root fashion as the data points move further back in time. The most recent data point has the highest weight, and the weights decrease progressively for older data points.

• "linear" — The linear method assigns weights to each data point that decrease in a linear fashion as the data points move further back in time. This method can be useful for capturing trends and price movements while minimizing the impact of outliers or extreme values.

• "square" — The square method assigns weights to each data point that decrease in a square fashion as the data points move further back in time. The most recent data point has the highest weight, and the weights decrease progressively for older data points.

• "exponential" — An exponential moving average (EMA) places a greater weight and significance on the most recent data points. The exponential moving average is also referred to as the exponentially weighted moving average. An exponentially weighted moving average reacts more significantly to recent price changes than a simple moving average (SMA), which applies an equal weight to all observations in the period.

• "triangular" — The triangular moving average (TMA) is a variation of the SMA that assigns weights to the data points in a triangular pattern. This method aims to give more weight to the data points in the middle of the moving average period and less weight to the data points at the beginning and end of the period.

• "modified" — A modified moving average (MMA) is an indicator that shows the average value of a security's price over a period of time. It is also known as the running moving average (RMA) or smoothed moving average (SMMA). Modified moving averages are similar to simple moving averages, but all subsequent points are calculated by first adding the new price and then subtracting the last average from the resulting sum.

• "custom" — A moving average using a custom method is a type of moving average that uses a custom measure of weights to calculate the average, instead of just taking the close price of each bar as most other moving averages do. The custom measure calculates the difference between the lowest lows and highest highs over different data points.

Data Types: char | string

windowSize — Number of observations of the input series to include in moving average

positive integer

Number of observations of the input series to include in moving average, specified as a scalar positive integer. The observations include (windowSize - 1) previous data points and the current data point.

Note

The windowSize argument applies only to moving averages whose type is 'simple', 'square-root', 'linear', 'square', 'exponential', 'triangular', or 'modified'.

Data Types: double

weights — Custom weights used to compute moving average

vector

Custom weights used to compute the moving average, specified as a vector.

Note

The length of weights (N) determines the size of the moving average window (windowSize). The weights argument applies only to a 'custom' type of moving average.

To compute moving average with custom weights, the weights (w) are first normalized such that they sum to one:

W(i) = w(i)/sum(w), for i = 1,2,...,N

The normalized weights (W) are then used to form the N-point weighted moving average (y) of the input Data (x):

y(t) = W(1)*x(t) + W(2)*x(t-1) + ... + W(N)*x(t-N)

The initial moving average values within the window size are then adjusted according to the method specified in the name-value pair argument initialPoints.

Data Types: double

initialPoints — Indicates how moving average is calculated at initial points

'shrink' (default) | character vector with values of 'shrink', 'fill', or 'zero' | string with values of "shrink", "fill", or "zero"

(Optional) Indicates how the moving average is calculated at initial points (before there is enough data to fill the window), specified as a character vector or string using one of the following values:

• 'shrink' - Initializes the moving average such that the initial points include only observed data

• 'zero' - Initializes the initial points with 0

• 'fill' - Fills initial points with NaNs

Note

The initialPoints argument applies to all type specifications except for the 'exponential' and 'modified' options.

Data Types: char | string

Output Arguments

ma — Moving average series

matrix | table | timetable

Moving average series, returned with the same number of rows (M) and the same type (matrix, table, or timetable) as the input Data.

References

[1] Achelis, S. B. Technical Analysis from A to Z. Second Edition. McGraw-Hill, 1995, pp. 184–192.

Version History

Introduced before R2006a

R2023a: fints support removed for Data input argument

fints object support for the Data input argument is removed.

R2018a: Lead and Lag input arguments not supported

The syntax for movavg has changed. There is no longer support for the input arguments Lead and Lag, only a single windowSize is supported, and there is only one output argument (ma). If you want to compute the leading and lagging moving averages, you need to run movavg twice and adjust the windowSize.