# Time Series Forecast

## Technical Analysis Indicator: tsf ## Function Prototype

/* Time Series Forecast */
/* Type: overlay */
/* Input arrays: 1    Options: 1    Output arrays: 1 */
/* Inputs: real */
/* Options: period */
/* Outputs: tsf */
int ti_tsf_start(TI_REAL const *options);
int ti_tsf(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 Time Series Forecast is a smoothing functions that works by preforming linear least squares regression over a moving window. It then uses the linear model to predict the value for the next bar.

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

It is calculated as:

$$\overline{x} = \frac{1}{n} \sum_{i=1}^{n} i$$
$$\overline{y}_{t} = \frac{1}{n} \sum_{i=0}^{n-1} in_{t-i}$$
$$\widehat{\beta}_{t} = \frac {\sum_{i=1}^{n}(i-\overline{x})(in_{(t-n+i)}-\overline{y}_{t})} {\sum_{i=1}^{n}(i-\overline{x})^{2}}$$
$$\widehat{\alpha}_{t} = \overline{y}_{t} - \widehat{\beta}_{t}\overline{x}$$
$$tsf_{t} = \widehat{\alpha}_{t} + \widehat{\beta}_{t} (n+1)$$

## Example Usage

### Calling From C

/* Example usage of Time Series Forecast */
/* Assuming that 'input' is a pre-loaded array of size 'in_size'. */
TI_REAL *inputs[] = {input};
TI_REAL options[] = {5}; /* period */
TI_REAL *outputs; /* tsf */

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

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

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


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

-- Example usage of Time Series Forecast
tsf = ti.tsf(input, 5)


## Example Calculation

period = 5

dateinputtsf
2005-11-0181.59
2005-11-0281.06
2005-11-0382.87
2005-11-0483.00
2005-11-0783.6184.22
2005-11-0883.1584.21
2005-11-0982.8483.12
2005-11-1083.9983.68
2005-11-1184.5584.44
2005-11-1484.3685.02
2005-11-1585.5385.98
2005-11-1686.5486.82
2005-11-1786.8987.63
2005-11-1887.7788.67
2005-11-2187.2988.23

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