# Exponential Moving Average

## Function Prototype

/* Exponential Moving Average */
/* Type: overlay */
/* Input arrays: 1    Options: 1    Output arrays: 1 */
/* Inputs: real */
/* Options: period */
/* Outputs: ema */
int ti_ema_start(TI_REAL const *options);
int ti_ema(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 exponential moving average, or exponential smoothing function, works by calculating each bar as a portion of the current input and a portion of the previous exponential moving average.

It takes one parameter, the period n, a positive integer. Larger values for n will have a greater smoothing effect on the input data but will also create more lag.

First a scaling factor, a, is calculated:

$$a = \frac{2}{n+1}$$

This will satisfy the relation:

$$0 \lt a \leq 1$$

Then the exponential moving average is calculated for each bar as:

$$ema_{t} = (1-a)ema_{t-1} + (a)in_{t}$$

The calculation is started by simply setting the first ema output to the first input.

## Example Usage

### Calling From C

/* Example usage of Exponential 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]; /* ema */

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

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

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


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

-- Example usage of Exponential Moving Average
ema = ti.ema(input, 5)


## Example Calculation

period = 5

dateinputema
2005-11-0181.5981.59
2005-11-0281.0681.41
2005-11-0382.8781.90
2005-11-0483.0082.27
2005-11-0783.6182.71
2005-11-0883.1582.86
2005-11-0982.8482.85
2005-11-1083.9983.23
2005-11-1184.5583.67
2005-11-1484.3683.90
2005-11-1585.5384.44
2005-11-1686.5485.14
2005-11-1786.8985.73
2005-11-1887.7786.41
2005-11-2187.2986.70

## Other Indicators

Previous indicator: Exponential Decay

Next indicator: Ease of Movement

Random indicator: Standard Deviation Over Period
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