# Hull Moving Average

## Technical Analysis Indicator: hma ## Function Prototype

/* Hull Moving Average */
/* Type: overlay */
/* Input arrays: 1    Options: 1    Output arrays: 1 */
/* Inputs: real */
/* Options: period */
/* Outputs: hma */
int ti_hma_start(TI_REAL const *options);
int ti_hma(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.

Hull Moving Average modifies Weighted Moving Average to greatly reduce lag.

It takes one parameter, the period n.

It is calculated for each bar as follows:

$$m = \lfloor \frac{n}{2} \rfloor$$
$$s = \lfloor \sqrt n \rfloor$$
$$\text{first}_{t} = \frac{1}{\sum_{i=1}^{m} i} \sum_{i=0}^{m-1} (m-i) in_{t-i}$$
$$\text{second}_{t} = \frac{1}{\sum_{i=1}^{n} i} \sum_{i=0}^{n-1} (n-i) in_{t-i}$$
$$\text{diff}_{t} = 2 \cdot \text{first}_{t} - \text{second}_{t}$$
$$\text{hma}_{t} = \frac{1}{\sum_{i=1}^{s} i} \sum_{i=0}^{s-1} (s-i) (\text{diff}_{t-i})$$

It can also be expressed as a combination of Weighted Moving Average:

$$\text{hma} = wma( 2 \cdot wma(in, m) - wma(in, n), s)$$

## Example Usage

### Calling From C

/* Example usage of Hull 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; /* hma */

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

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

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


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

-- Example usage of Hull Moving Average
hma = ti.hma(input, 5)


## Example Calculation

period = 5

dateinputhma
2005-11-0181.59
2005-11-0281.06
2005-11-0382.87
2005-11-0483.00
2005-11-0783.61
2005-11-0883.1583.69
2005-11-0982.8483.04
2005-11-1083.9983.47
2005-11-1184.5584.55
2005-11-1484.3684.84
2005-11-1585.5385.36
2005-11-1686.5486.55
2005-11-1786.8987.35
2005-11-1887.7787.97
2005-11-2187.2987.92

## Other Indicators

Previous indicator: Forecast Oscillator

Next indicator: Kaufman Adaptive Moving Average

Random indicator: Accumulation/Distribution Oscillator