Statistical Functions

Statistical and regression-based indicators for analyzing price distributions, correlations, and trends.

STDDEV - Standard Deviation

The Standard Deviation measures the dispersion of prices around their mean over a specified period.

Formula

\[\mu = \frac{1}{n}\sum_{i=0}^{n-1} price_i\]

\[\sigma = nbdev \times \sqrt{\frac{1}{n}\sum_{i=0}^{n-1}(price_i - \mu)^2}\]

where \(nbdev\) is the number of standard deviations multiplier (default: 1.0).

Parameters

Parameter	Type	Default	Range	Description
period	int	5	1-100000	Number of periods
nbdev	double	1.0	> 0	Standard deviation multiplier

Characteristics

Property	Value
Input	Close price
Output	Single value (standard deviation)
Lookback	period - 1
Memory	O(period)

API Usage

Python

from techkit import STDDEV

stddev = STDDEV(period=20, nbdev=1.0)
result = stddev.update(close_price)
if result.valid:
    print(f"Std Dev: {result.value:.2f}")

Node.js

const stddev = tk.stddev(20, 1.0);
const result = stddev.update(close);

C++

techkit::STDDEV stddev(20, 1.0);
auto result = stddev.update(close);

C

tk_indicator stddev = tk_stddev_new(20, 1.0);
tk_result r = tk_update(stddev, close);

Trading Usage

Volatility Measure: Higher stddev = higher volatility
Bollinger Bands: Used in BBANDS calculation (stddev × multiplier)
Risk Assessment: Higher stddev = higher risk
Mean Reversion: Prices far from mean (multiple stddevs) may revert

VAR - Variance

The Variance is the square of standard deviation, measuring price dispersion.

Formula

\[\mu = \frac{1}{n}\sum_{i=0}^{n-1} price_i\]

\[VAR = \frac{1}{n}\sum_{i=0}^{n-1}(price_i - \mu)^2\]

Note: Uses population variance (divide by n, not n-1).

Parameters

Parameter	Type	Default	Range	Description
period	int	5	1-100000	Number of periods

Characteristics

Property	Value
Input	Close price
Output	Single value (variance)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import VAR

var = VAR(period=20)
result = var.update(close_price)
if result.valid:
    print(f"Variance: {result.value:.4f}")
    # Standard deviation = sqrt(variance)
    stddev = result.value ** 0.5

Trading Usage

Volatility Proxy: Variance is a measure of volatility
Risk Models: Used in portfolio risk calculations
Relationship: STDDEV = sqrt(VAR)

Linear Regression Functions

Linear regression fits a straight line to price data over a period using least squares method.

General Formula

For a linear regression line \(y = a + bx\):

\(a\) = intercept (LINEARREG_INTERCEPT)
\(b\) = slope (LINEARREG_SLOPE)
\(y\) at end = predicted value (LINEARREG)
Angle = atan(b) × 180/π (LINEARREG_ANGLE)

LINEARREG - Linear Regression

Returns the predicted value at the end of the regression period.

Formula

\[LINEARREG = a + b \times (period - 1)\]

where \(a\) and \(b\) are calculated from least squares regression.

Parameters

Parameter	Type	Default	Range	Description
period	int	14	2-100000	Number of periods

Characteristics

Property	Value
Input	Close price
Output	Single value (predicted price)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import LINEARREG

linearreg = LINEARREG(period=14)
result = linearreg.update(close_price)
if result.valid:
    print(f"Predicted value: {result.value:.2f}")

Trading Usage

Trend Projection: Projects trend forward
Support/Resistance: Can act as dynamic S/R level
Entry Signals: Price crossing regression line = trend change

LINEARREG_SLOPE - Linear Regression Slope

Returns the slope coefficient (b) of the regression line, indicating trend direction and strength.

Formula

\[b = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}\]

where \(x\) = bar index (0 to period-1), \(y\) = price.

Parameters

Parameter	Type	Default	Range	Description
period	int	14	2-100000	Number of periods

Characteristics

Property	Value
Input	Close price
Output	Single value (slope per bar)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import LINEARREG_SLOPE

slope = LINEARREG_SLOPE(period=14)
result = slope.update(close_price)
if result.valid:
    if result.value > 0:
        print("Uptrend")
    elif result.value < 0:
        print("Downtrend")
    else:
        print("Sideways")

Trading Usage

Trend Direction:
- Positive slope = uptrend
- Negative slope = downtrend
- Near zero = sideways
Trend Strength: Larger absolute value = stronger trend
Entry Signals: Slope crossing zero = trend reversal

LINEARREG_INTERCEPT - Linear Regression Intercept

Returns the intercept coefficient (a) of the regression line.

Formula

\[a = \bar{y} - b \times \bar{x}\]

where \(\bar{x}\) and \(\bar{y}\) are the means.

Parameters

Parameter	Type	Default	Range	Description
period	int	14	2-100000	Number of periods

Characteristics

Property	Value
Input	Close price
Output	Single value (intercept)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import LINEARREG_INTERCEPT

intercept = LINEARREG_INTERCEPT(period=14)
result = intercept.update(close_price)
if result.valid:
    print(f"Intercept: {result.value:.2f}")

Trading Usage

Base Level: Starting point of regression line
Combined Use: Use with slope to reconstruct full regression line
Analysis: Intercept + slope × index = predicted value

LINEARREG_ANGLE - Linear Regression Angle

Returns the angle of the regression line in degrees, providing an intuitive measure of trend steepness.

Formula

\[\text{angle} = \arctan(b) \times \frac{180}{\pi}\]

where \(b\) is the slope.

Parameters

Parameter	Type	Default	Range	Description
period	int	14	2-100000	Number of periods

Characteristics

Property	Value
Input	Close price
Output	Single value (angle in degrees, -90 to +90)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import LINEARREG_ANGLE

angle = LINEARREG_ANGLE(period=14)
result = angle.update(close_price)
if result.valid:
    if result.value > 45:
        print("Very steep uptrend")
    elif result.value > 0:
        print("Moderate uptrend")
    elif result.value < -45:
        print("Very steep downtrend")
    elif result.value < 0:
        print("Moderate downtrend")

Trading Usage

Trend Steepness:
- 45°: Very steep uptrend
- 0-45°: Moderate uptrend
- -45° to 0°: Moderate downtrend
- < -45°: Very steep downtrend
Entry Timing: Steeper angles = stronger trends
Visualization: Easier to interpret than raw slope

TSF - Time Series Forecast

The Time Series Forecast extrapolates the linear regression one period ahead, providing a forecasted price.

Formula

\[TSF = LINEARREG + LINEARREG\_SLOPE\]

Essentially: \(TSF = a + b \times period\) (one step ahead of LINEARREG).

Parameters

Parameter	Type	Default	Range	Description
period	int	14	2-100000	Number of periods

Characteristics

Property	Value
Input	Close price
Output	Single value (forecasted price)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import TSF

tsf = TSF(period=14)
result = tsf.update(close_price)
if result.valid:
    print(f"Forecast: {result.value:.2f}")
    # Compare with actual
    if close_price > result.value:
        print("Price above forecast (stronger than expected)")

Trading Usage

Price Forecast: Predicts next period’s price
Expectation vs. Reality: Compare forecast to actual price
Entry Signals: Price crossing forecast = momentum shift
Trend Continuation: Forecast above price = uptrend expected

BETA - Beta Coefficient

The Beta coefficient measures the sensitivity of one asset’s returns to another asset’s returns (typically a benchmark).

Formula

\[\beta = \frac{\text{Cov}(X, Y)}{\text{Var}(Y)} = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(y_i - \bar{y})^2}\]

where:

\(X\) = asset returns
\(Y\) = benchmark returns

Parameters

Parameter	Type	Default	Range	Description
period	int	5	2-100000	Number of periods

Characteristics

Property	Value
Input	Two close price arrays (asset, benchmark)
Output	Single value (beta coefficient)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import BETA

beta = BETA(period=20)
result = beta.update(asset_price, benchmark_price)
if result.valid:
    beta_value = result.value
    if beta_value > 1:
        print(f"Asset is {beta_value:.2f}x more volatile than benchmark")
    elif beta_value < 1:
        print(f"Asset is {beta_value:.2f}x less volatile than benchmark")
    else:
        print("Asset moves with benchmark")

Trading Usage

Risk Assessment:
- β > 1: More volatile than benchmark
- β = 1: Moves with benchmark
- β < 1: Less volatile than benchmark
- β < 0: Moves opposite to benchmark (rare)
Portfolio Analysis: Measure systematic risk
Hedging: Use beta to calculate hedge ratios

CORREL - Pearson Correlation

The Pearson Correlation measures the linear relationship between two price series, ranging from -1 to +1.

Formula

\[r = \frac{\text{Cov}(X, Y)}{\sigma_X \times \sigma_Y} = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum(x_i - \bar{x})^2 \sum(y_i - \bar{y})^2}}\]

Parameters

Parameter	Type	Default	Range	Description
period	int	30	2-100000	Number of periods

Characteristics

Property	Value
Input	Two close price arrays
Output	Single value (correlation, -1 to +1)
Lookback	period - 1
Memory	O(period)

API Usage

from techkit import CORREL

correl = CORREL(period=30)
result = correl.update(price1, price2)
if result.valid:
    r = result.value
    if r > 0.7:
        print("Strong positive correlation")
    elif r > 0.3:
        print("Moderate positive correlation")
    elif r > -0.3:
        print("Weak correlation")
    elif r > -0.7:
        print("Moderate negative correlation")
    else:
        print("Strong negative correlation")

Trading Usage

Correlation Strength:
- |r| > 0.7: Strong correlation
- 0.3 < |r| < 0.7: Moderate correlation
- |r| < 0.3: Weak correlation
Direction:
- r > 0: Positive (move together)
- r < 0: Negative (move opposite)
Pairs Trading: Find highly correlated pairs
Diversification: Low correlation = better diversification