# Weighted Moving Average

## Function Prototype

/* Weighted Moving Average */
/* Type: overlay */
/* Input arrays: 1    Options: 1    Output arrays: 1 */
/* Inputs: real */
/* Options: period */
/* Outputs: wma */
int ti_wma_start(TI_REAL const *options);
int ti_wma(int size,
TI_REAL const *const *inputs,
TI_REAL const *options,
TI_REAL *const *outputs);

## Description

This documentation is still a work in progress. It has omissions, and it probably has errors too. If you see any issues, or have any general feedback, please get in touch.

The Weighted Moving Average is similar to the Simple Moving Average but instead places more weight on more recent bars in the smoothing period and less weight on the oldest bars in the period.

It takes one parameter, the period n. Larger values for n will have a greater smoothing effect on the input data.

It is calculated for each bar as the weighted arithmetic mean of the previous n bars. For example, the weights w for an n of 4 are: 4, 3, 2, 1. The weights w for a n of 7 are: 7, 6, 5, 4, 3, 2, 1. So in that example, the most recent bar influences the average 7 times as much as the oldest bar.

Once the weights w are know, the calculation is as follows.

$$wma_{t} = \frac{1}{\sum w} \sum_{i=0}^{n-1} w_{i} in_{t-i}$$

Or, alternatively:

$$wma_{t} = \frac{1}{\sum_{i=1}^{n} i} \sum_{i=0}^{n-1} (n-i) in_{t-i}$$

## Example Usage

### Calling From C

/* Example usage of Weighted Moving Average */
/* Assuming that 'input' is a pre-loaded array of size 'in_size'. */
TI_REAL *inputs[] = {input};
TI_REAL options[] = {5}; /* period */
TI_REAL *outputs[1]; /* wma */

/* Determine how large the output size is for our options. */
const int out_size = in_size - ti_wma_start(options);

/* Allocate memory for output. */
outputs[0] = malloc(sizeof(TI_REAL) * out_size); assert(outputs[0] != 0); /* wma */

/* Run the actual calculation. */
const int ret = ti_wma(in_size, inputs, options, outputs);
assert(ret == TI_OKAY);


### Calling From Lua (with Tulip Chart bindings)

-- Example usage of Weighted Moving Average
wma = ti.wma(input, 5)


## Example Calculation

period = 5

dateinputwma
2005-11-0181.59
2005-11-0281.06
2005-11-0382.87
2005-11-0483.00
2005-11-0783.6182.83
2005-11-0883.1583.07
2005-11-0982.8483.10
2005-11-1083.9983.40
2005-11-1184.5583.81
2005-11-1484.3684.05
2005-11-1585.5384.64
2005-11-1686.5485.40
2005-11-1786.8986.03
2005-11-1887.7786.76
2005-11-2187.2987.12

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