# Fisher Transform

## Technical Analysis Indicator: fisher ## Function Prototype

/* Fisher Transform */
/* Type: indicator */
/* Input arrays: 2    Options: 1    Output arrays: 2 */
/* Inputs: high, low */
/* Options: period */
/* Outputs: fisher, fisher_signal */
int ti_fisher_start(TI_REAL const *options);
int ti_fisher(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 Fisher Transform helps identify price reversals.

It takes one parameter, the period n.

It is calculated as follows:

$$hl_{t} = \frac{high_{t} + low_{t}}{2}$$
$$max_{t} = maximum(hl_{t}, hl_{t-1}, ..., hl_{t-n+1})$$
$$min_{t} = minimum(hl_{t}, hl_{t-1}, ..., hl_{t-n+1})$$
$$val_{t} = 0.33 \cdot 2 (\frac{hl_{t}-min_{t}}{max_{t}-min_{t}} - 0.5) + .67 \cdot val_{t-1}$$
$$\text{fisher}_{t} = 0.5 \cdot \log (\frac{1 + val_{t}}{1-val_{t}}) + 0.5 \cdot \text{fisher}_{t-1}$$
$$\text{fisher_signal}_{t} = \text{fisher}_{t-1}$$

## Example Usage

### Calling From C

/* Example usage of Fisher Transform */
/* Assuming that 'high' and 'low' are pre-loaded arrays of size 'in_size'. */
TI_REAL *inputs[] = {high, low};
TI_REAL options[] = {5}; /* period */
TI_REAL *outputs; /* fisher, fisher_signal */

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

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

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


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

-- Example usage of Fisher Transform
fisher, fisher_signal = ti.fisher(high, low, 5)


## Example Calculation

period = 5

datehighlowfisherfisher_signal
2005-11-0182.1581.29
2005-11-0281.8980.64
2005-11-0383.0381.31
2005-11-0483.3082.65
2005-11-0783.8583.070.340.00
2005-11-0883.9083.110.790.34
2005-11-0983.3382.490.830.79
2005-11-1084.3082.300.810.83
2005-11-1184.8484.151.070.81
2005-11-1485.0084.111.441.07
2005-11-1585.9084.031.851.44
2005-11-1686.5885.392.281.85
2005-11-1786.9885.762.702.28
2005-11-1888.0087.173.122.70
2005-11-2187.8787.013.193.12

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