Statistical

OpenAlgo Statistical Indicators Documentation

Statistical indicators analyze price data using mathematical and statistical methods to identify patterns, relationships, and forecast future price movements.

Import Statement

from openalgo import ta

Getting Market Data

from openalgo import api

client = api(api_key='your_api_key_here', host='http://127.0.0.1:5000')

# Fetch historical data
df = client.history(symbol="SBIN", 
                   exchange="NSE", 
                   interval="5m", 
                   start_date="2025-04-01", 
                   end_date="2025-04-08")

Available Statistical Indicators

---

Linear Regression (LINREG)

Linear Regression calculates the linear regression line for a given period using the least squares method to identify the underlying trend.

Usage

linreg_result = ta.linreg(data, period)

Parameters

• data (array-like): Price data (typically closing prices)

• period (int, default=14): Period for linear regression calculation

Returns

• array: Linear regression values in the same format as input

Example

# Calculate 20-period Linear Regression
linreg_20 = ta.linreg(df['close'], 20)

# Add to DataFrame
df['LINREG_20'] = linreg_20

print(df[['close', 'LINREG_20']].tail())

---

Linear Regression Slope (LRSLOPE)

Linear Regression Slope measures the rate of change of the linear regression line, indicating the strength and direction of the trend.

Usage

slope_result = ta.lrslope(data, period=100, interval=1)

Parameters

• data (array-like): Price data (typically closing prices)

• period (int, default=100): Period for linear regression calculation

• interval (int, default=1): Interval divisor for slope calculation

Returns

• array: Slope values in the same format as input

Example

# Calculate Linear Regression Slope
slope_50 = ta.lrslope(df['close'], period=50)

# Add to DataFrame
df['LR_SLOPE_50'] = slope_50

print(df[['close', 'LR_SLOPE_50']].tail())

---

Pearson Correlation Coefficient (CORREL)

Correlation measures the statistical relationship between two data series, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).

Usage

correlation_result = ta.correlation(data1, data2, period)

Parameters

• data1 (array-like): First data series

• data2 (array-like): Second data series

• period (int, default=20): Period for correlation calculation

Returns

• array: Correlation values in the same format as input

Example

# Calculate correlation between close and volume
correlation_20 = ta.correlation(df['close'], df['volume'], 20)

# Add to DataFrame
df['CORREL_CLOSE_VOLUME'] = correlation_20

print(df[['close', 'volume', 'CORREL_CLOSE_VOLUME']].tail())

# Calculate correlation between high and low
correlation_hl = ta.correlation(df['high'], df['low'], 15)
df['CORREL_HIGH_LOW'] = correlation_hl

---

Beta Coefficient (BETA)

Beta measures the volatility of a security relative to the market, indicating how much the security price moves relative to market movements.

Usage

beta_result = ta.beta(asset, market, period=252)

Parameters

• asset (array-like): Asset price data

• market (array-like): Market price data (benchmark)

• period (int, default=252): Period for beta calculation (typically 1 year = 252 trading days)

Returns

• array: Beta values in the same format as input

Example

# Assuming you have market index data
# For demonstration, we'll use another stock as market proxy
market_df = client.history(symbol="NIFTY", 
                          exchange="NSE_INDEX", 
                          interval="5m", 
                          start_date="2025-04-01", 
                          end_date="2025-04-08")

# Calculate 50-period Beta
beta_50 = ta.beta(df['close'], market_df['close'], 50)

# Add to DataFrame
df['BETA_50'] = beta_50

print(df[['close', 'BETA_50']].tail())

---

Variance (VAR)

Variance measures the dispersion of price data, supporting both logarithmic returns and price modes with smoothing and signal generation.

Usage

variance_result = ta.variance(data, lookback=20, mode="PR", ema_period=20, 
                             filter_lookback=20, ema_length=14, return_components=False)

Parameters

• data (array-like): Price data (close prices)

• lookback (int, default=20): Variance lookback period

• mode (str, default="PR"): Variance mode ("LR" for Logarithmic Returns, "PR" for Price)

• ema_period (int, default=20): EMA period for variance smoothing

• filter_lookback (int, default=20): Lookback period for variance filter

• ema_length (int, default=14): EMA length for z-score smoothing

• return_components (bool, default=False): If True, returns all components

Returns

• array or tuple: Variance values or (variance, ema_variance, zscore, ema_zscore, stdev) if return_components=True

Example

# Calculate basic variance
variance_20 = ta.variance(df['close'], lookback=20)
df['VARIANCE_20'] = variance_20

# Calculate variance with all components
var_components = ta.variance(df['close'], lookback=20, return_components=True)
variance, ema_var, zscore, ema_zscore, stdev = var_components

df['VARIANCE'] = variance
df['EMA_VARIANCE'] = ema_var
df['VAR_ZSCORE'] = zscore

print(df[['close', 'VARIANCE', 'EMA_VARIANCE', 'VAR_ZSCORE']].tail())

---

Time Series Forecast (TSF)

Time Series Forecast predicts the next value using linear regression analysis.

Usage

tsf_result = ta.tsf(data, period=14)

Parameters

• data (array-like): Price data

• period (int, default=14): Period for forecast calculation

Returns

• array: Time Series Forecast values in the same format as input

Example

# Calculate 14-period Time Series Forecast
tsf_14 = ta.tsf(df['close'], 14)

# Add to DataFrame
df['TSF_14'] = tsf_14

print(df[['close', 'TSF_14']].tail())

# Compare actual vs forecast
df['TSF_DIFF'] = df['close'] - df['TSF_14']
print("Forecast accuracy (last 10 periods):")
print(df[['close', 'TSF_14', 'TSF_DIFF']].tail(10))

---

Rolling Median (MEDIAN)

Rolling Median calculates the median value over a rolling window, which is less sensitive to outliers than mean-based indicators.

Usage

median_result = ta.median(data, period=3)

Parameters

• data (array-like): Price data (default hl2 in Pine Script)

• period (int, default=3): Period for median calculation

Returns

• array: Median values in the same format as input

Example

# Calculate 5-period Rolling Median
median_5 = ta.median(df['close'], 5)

# Calculate median of typical price
typical_price = (df['high'] + df['low'] + df['close']) / 3
median_typical = ta.median(typical_price, 7)

# Add to DataFrame
df['MEDIAN_5'] = median_5
df['MEDIAN_TYPICAL'] = median_typical

print(df[['close', 'MEDIAN_5', 'MEDIAN_TYPICAL']].tail())

---

Median Bands (MEDIAN_BANDS)

Median Bands combine median calculation with ATR-based bands and EMA smoothing for comprehensive analysis.

Usage

median, upper_band, lower_band, median_ema = ta.median_bands.calculate_with_bands(
    high, low, close, source=None, median_length=3, atr_length=14, atr_mult=2.0
)

Parameters

• high (array-like): High prices

• low (array-like): Low prices

• close (array-like): Close prices

• source (array-like, optional): Source data for median (default: hl2)

• median_length (int, default=3): Period for median calculation

• atr_length (int, default=14): Period for ATR calculation

• atr_mult (float, default=2.0): ATR multiplier for bands

Returns

• tuple: (median, upper_band, lower_band, median_ema) arrays

Example

# Calculate Median Bands
median, upper, lower, median_ema = ta.median_bands.calculate_with_bands(
    df['high'], df['low'], df['close']
)

# Add to DataFrame
df['MEDIAN'] = median
df['MEDIAN_UPPER'] = upper
df['MEDIAN_LOWER'] = lower
df['MEDIAN_EMA'] = median_ema

print(df[['close', 'MEDIAN', 'MEDIAN_UPPER', 'MEDIAN_LOWER']].tail())

---

Rolling Mode (MODE)

Rolling Mode calculates the most frequent value over a rolling window using discretization.

Usage

mode_result = ta.mode(data, period=20, bins=10)

Parameters

• data (array-like): Price data

• period (int, default=20): Period for mode calculation

• bins (int, default=10): Number of bins for discretization

Returns

• array: Mode values in the same format as input

Example

# Calculate 15-period Rolling Mode
mode_15 = ta.mode(df['close'], period=15, bins=8)

# Add to DataFrame
df['MODE_15'] = mode_15

print(df[['close', 'MODE_15']].tail())

# Calculate mode for volume (often useful for volume analysis)
volume_mode = ta.mode(df['volume'], period=20, bins=12)
df['VOLUME_MODE'] = volume_mode

---

Complete Example: Statistical Analysis Dashboard

import pandas as pd
from openalgo import api, ta

# Get market data
client = api(api_key='your_api_key_here', host='http://127.0.0.1:5000')

df = client.history(symbol="SBIN", 
                   exchange="NSE", 
                   interval="5m", 
                   start_date="2025-04-01", 
                   end_date="2025-04-08")

# Calculate comprehensive statistical indicators
print("Calculating Statistical Indicators...")

# Trend Analysis
df['LINREG_20'] = ta.linreg(df['close'], 20)
df['LR_SLOPE_20'] = ta.lrslope(df['close'], 20)
df['TSF_14'] = ta.tsf(df['close'], 14)

# Central Tendency
df['MEDIAN_5'] = ta.median(df['close'], 5)
df['MODE_15'] = ta.mode(df['close'], 15)

# Variability Analysis
df['VARIANCE_20'] = ta.variance(df['close'], 20)

# Get variance components for detailed analysis
var_components = ta.variance(df['close'], lookback=20, return_components=True)
variance, ema_var, zscore, ema_zscore, stdev = var_components

df['VARIANCE'] = variance
df['EMA_VARIANCE'] = ema_var
df['VAR_ZSCORE'] = zscore
df['STDEV'] = stdev

# Correlation Analysis
df['CORREL_CLOSE_VOLUME'] = ta.correlation(df['close'], df['volume'], 20)
df['CORREL_HIGH_LOW'] = ta.correlation(df['high'], df['low'], 15)

# Median Bands Analysis
median, upper, lower, median_ema = ta.median_bands.calculate_with_bands(
    df['high'], df['low'], df['close'], median_length=5, atr_length=14
)

df['MEDIAN_BANDS'] = median
df['MEDIAN_UPPER'] = upper
df['MEDIAN_LOWER'] = lower
df['MEDIAN_EMA'] = median_ema

# Create analysis summary
analysis_cols = [
    'close', 'LINREG_20', 'LR_SLOPE_20', 'TSF_14', 
    'MEDIAN_5', 'VARIANCE_20', 'VAR_ZSCORE', 
    'CORREL_CLOSE_VOLUME', 'MEDIAN_BANDS'
]

print("\nStatistical Analysis Summary (Last 10 periods):")
print(df[analysis_cols].tail(10))

# Generate trading signals based on statistical indicators
print("\nGenerating Statistical Trading Signals...")

# Trend Strength Signal (based on Linear Regression Slope)
df['TREND_SIGNAL'] = 'NEUTRAL'
df.loc[df['LR_SLOPE_20'] > 0.5, 'TREND_SIGNAL'] = 'BULLISH'
df.loc[df['LR_SLOPE_20'] < -0.5, 'TREND_SIGNAL'] = 'BEARISH'

# Variance-based Volatility Signal
df['VOLATILITY_SIGNAL'] = 'NORMAL'
df.loc[df['VAR_ZSCORE'] > 1.5, 'VOLATILITY_SIGNAL'] = 'HIGH'
df.loc[df['VAR_ZSCORE'] < -1.5, 'VOLATILITY_SIGNAL'] = 'LOW'

# Price Position relative to Statistical Measures
df['PRICE_VS_LINREG'] = (df['close'] - df['LINREG_20']) / df['LINREG_20'] * 100
df['PRICE_VS_MEDIAN'] = (df['close'] - df['MEDIAN_5']) / df['MEDIAN_5'] * 100

# Forecast Accuracy
df['FORECAST_ERROR'] = abs(df['close'] - df['TSF_14'].shift(1))
df['FORECAST_ACCURACY'] = (1 - df['FORECAST_ERROR'] / df['close']) * 100

print("\nTrading Signals Summary:")
signal_summary = df[['TREND_SIGNAL', 'VOLATILITY_SIGNAL', 'PRICE_VS_LINREG', 
                    'PRICE_VS_MEDIAN', 'FORECAST_ACCURACY']].tail(5)
print(signal_summary)

# Statistical Summary
print("\nStatistical Metrics Summary:")
print(f"Average Correlation (Close vs Volume): {df['CORREL_CLOSE_VOLUME'].mean():.4f}")
print(f"Average Variance: {df['VARIANCE_20'].mean():.4f}")
print(f"Average Forecast Accuracy: {df['FORECAST_ACCURACY'].mean():.2f}%")
print(f"Current Trend Slope: {df['LR_SLOPE_20'].iloc[-1]:.4f}")

# Volatility Analysis
recent_volatility = df['VAR_ZSCORE'].tail(20)
print(f"Recent Volatility Z-Score: {recent_volatility.mean():.2f}")
print(f"Volatility Regime: {df['VOLATILITY_SIGNAL'].iloc[-1]}")

Advanced Statistical Analysis

# Advanced correlation matrix
def calculate_correlation_matrix(df, period=20):
    """Calculate correlation matrix for OHLCV data"""
    correlations = {}
    
    price_cols = ['open', 'high', 'low', 'close', 'volume']
    
    for i, col1 in enumerate(price_cols):
        for col2 in price_cols[i+1:]:
            corr_name = f"CORR_{col1.upper()}_{col2.upper()}"
            correlations[corr_name] = ta.correlation(df[col1], df[col2], period)
    
    return correlations

# Calculate all correlations
correlations = calculate_correlation_matrix(df, 20)
for name, values in correlations.items():
    df[name] = values

print("\nCorrelation Matrix (Latest Values):")
corr_cols = [col for col in df.columns if col.startswith('CORR_')]
latest_corr = df[corr_cols].iloc[-1]
print(latest_corr)

# Statistical anomaly detection
def detect_statistical_anomalies(df, z_threshold=2.0):
    """Detect statistical anomalies in price data"""
    
    # Price anomalies based on variance z-score
    df['PRICE_ANOMALY'] = abs(df['VAR_ZSCORE']) > z_threshold
    
    # Volume anomalies
    volume_zscore = (df['volume'] - df['volume'].rolling(20).mean()) / df['volume'].rolling(20).std()
    df['VOLUME_ANOMALY'] = abs(volume_zscore) > z_threshold
    
    # Return anomalies
    returns = df['close'].pct_change()
    returns_zscore = (returns - returns.rolling(20).mean()) / returns.rolling(20).std()
    df['RETURN_ANOMALY'] = abs(returns_zscore) > z_threshold
    
    return df

# Detect anomalies
df = detect_statistical_anomalies(df)

# Summary of anomalies
anomaly_summary = df[['PRICE_ANOMALY', 'VOLUME_ANOMALY', 'RETURN_ANOMALY']].sum()
print(f"\nAnomaly Detection Summary:")
print(f"Price Anomalies: {anomaly_summary['PRICE_ANOMALY']}")
print(f"Volume Anomalies: {anomaly_summary['VOLUME_ANOMALY']}")
print(f"Return Anomalies: {anomaly_summary['RETURN_ANOMALY']}")

Performance Tips

1. Period Selection: Choose appropriate periods based on your analysis timeframe

2. Data Quality: Ensure clean data for accurate statistical calculations

3. Correlation Interpretation: Remember correlation doesn't imply causation

4. Statistical Significance: Consider sample size when interpreting results

5. Regime Changes: Monitor for changes in statistical relationships over time

Common Use Cases

1. Trend Analysis: Use Linear Regression and slopes for trend identification

2. Risk Management: Apply variance and correlation for portfolio risk assessment

3. Anomaly Detection: Use statistical z-scores to identify unusual market behavior

4. Forecasting: Combine TSF with other indicators for price prediction

5. Market Relationships: Analyze correlations between different assets or timeframes