# Variance Over Period

## Function Prototype

/* Variance Over Period */
/* Type: math */
/* Input arrays: 1    Options: 1    Output arrays: 1 */
/* Inputs: real */
/* Options: period */
/* Outputs: var */
int ti_var_start(TI_REAL const *options);
int ti_var(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 Variance Over Period indicator calculates the variance of the input over a moving window.

It takes one parameters: the period n.

$$ma_{t} = \frac{1}{n} \sum_{i=0}^{n-1} in_{t-i}$$
$$var_{t} = {\frac{1}{n} \sum_{i=0}^{n-1} (in_{t-i}-ma_{t})^{2}}$$

## Example Usage

### Calling From C

/* Example usage of Variance Over Period */
/* 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]; /* var */

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

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

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


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

-- Example usage of Variance Over Period
var = ti.var(input, 5)


## Example Calculation

period = 5

dateinputvar
2005-11-0181.59
2005-11-0281.06
2005-11-0382.87
2005-11-0483.00
2005-11-0783.610.90
2005-11-0883.150.77
2005-11-0982.840.08
2005-11-1083.990.18
2005-11-1184.550.37
2005-11-1484.360.45
2005-11-1585.530.76
2005-11-1686.540.86
2005-11-1786.891.04
2005-11-1887.771.38
2005-11-2187.290.57

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