Tsf

Time Series Forecast (TSF) — the rolling least-squares line projected one bar past the window, a trend-following one-step-ahead forecast.

Quick reference

Field	Value
Family	Price Statistics
Input type	f64 (single close)
Output type	f64
Output range	unbounded (price scale)
Default parameters	period is required
Warmup period	period
Interpretation	Where the recent linear trend projects the next bar to be.

Formula

Over the last period inputs, indexed x = 0, 1, …, period − 1, fit y = a + b·x by ordinary least squares and evaluate it one step beyond the most recent point (x = period):

b (slope)     = (n·Σxy − Σx·Σy) / (n·Σxx − (Σx)²)
a (intercept) = (Σy − b·Σx) / n
TSF           = a + b·period

Where LinearRegression evaluates the fit at the current bar (a + b·(period − 1)), TSF advances it one further bar. The result is a least-squares trend extrapolation — smoother and less laggy than a moving average on a trending series. Each update is O(1) over a sliding window. See crates/wickra-core/src/indicators/tsf.rs.

Parameters

Name	Type	Default	Valid range	Description	Source
period	usize	none	>= 2	Regression window length. period < 2 errors with Error::InvalidPeriod (a line needs at least two points).	tsf.rs:54

Inputs / Outputs

From crates/wickra-core/src/indicators/tsf.rs:

use wickra::{Indicator, Tsf};
// Tsf: Input = f64, Output = f64
const _: fn(&mut Tsf, f64) -> Option<f64> = <Tsf as Indicator>::update;

Python streams as float | None, batches as a 1-D numpy.ndarray (NaN for warmup). Node streams as number | null, batches as Array<number> with NaN placeholders.

Warmup

Tsf::new(period).warmup_period() == period. The first value is emitted once period points fill the window. The unit tests accessors_report_config and reference_value (which asserts out[0] and out[1] are None for period = 3) pin this.

Edge cases

• Exact extrapolation on a straight line. For collinear inputs the forecast lands exactly on the line's next point. The unit test forecasts_a_clean_line_one_step_ahead pins this (window [10, 12, 14] → y = 10 + 2x, forecast at x = 3 is 16).
• Short period. Tsf::new(1) returns Err(Error::InvalidPeriod). The unit test rejects_short_period pins this.
• Reset. tsf.reset() clears the window and the running sums. The unit test reset_clears_state pins this.

Examples

Rust

use wickra::{BatchExt, Indicator, Tsf};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut tsf = Tsf::new(3)?;
    let out: Vec<Option<f64>> = tsf.batch(&[1.0, 2.0, 9.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, Some(12.0)]

Period 3 over [1, 2, 9]: the least-squares fit is y = 0 + 4x, so the forecast at x = 3 is 0 + 4·3 = 12. This matches the reference_value unit test in crates/wickra-core/src/indicators/tsf.rs.

Python

import numpy as np
import wickra as ta

tsf = ta.Tsf(3)
print(tsf.batch(np.array([1.0, 2.0, 9.0])))

Output:

[nan nan 12.]

Node

const ta = require('wickra');
const tsf = new ta.Tsf(3);
for (const x of [1, 2, 9]) console.log(x, '->', tsf.update(x));

Output:

1 -> null
2 -> null
9 -> 12

Interpretation

TSF is a regression-based forecast: it assumes the recent linear trend continues for one more bar and reports where price would land. On a clean trend it leads a moving average of the same length (it extrapolates rather than averages), which makes TSF-vs-price and TSF-vs-SMA crossovers earlier signals. The trade-off is the usual one for extrapolation: it overshoots at turning points, where the linear assumption breaks.

TSF and LinearRegression differ only by one bar of projection (a + b·period vs a + b·(period − 1)); choose TSF when you explicitly want the next-bar forecast.

Common pitfalls

• Treating it as a guaranteed forecast. TSF is a linear extrapolation, not a prediction — it will overshoot through reversals and lag nothing, so it is most reliable inside an established trend.
• Period < 2. A regression line is undefined for a single point — the constructor rejects it.

References

The Time Series Forecast is TA-Lib's TSF function; it is the standard one-step-ahead ordinary-least-squares projection used by Tushar Chande's regression-based studies.

See also

• Indicator-LinearRegression — the fit at the current bar.
• Indicator-LinRegIntercept — the fit at the window start.
• Indicator-LinRegSlope — the per-bar slope.
• Indicators-Overview — the full taxonomy.