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Technical Indicators Reference Table

Complete List of 21 Technical Indicators

# Indicator Name Category Formula Parameters Purpose Interpretation
1 Open Price Raw OHLC data - Opening price of trading period Market opening sentiment
2 High Price Raw OHLC data - Highest price during period Intraday peak, resistance level
3 Low Price Raw OHLC data - Lowest price during period Intraday trough, support level
4 Close Price Raw OHLC data - Closing price of trading period Market closing sentiment, most important
5 Adj Close Price Close × Adjustment Factor - Price adjusted for splits/dividends Accurate historical price comparison
6 Volume Volume Raw trading volume - Number of shares traded Market activity, liquidity indicator
7 Return (1-day) Returns ret = (Close_t - Close_{t-1}) / Close_{t-1} window=1 Daily percentage change Short-term price momentum
8 Log Return (1-day) Returns log_ret = ln(Close_t / Close_{t-1}) window=1 Logarithmic daily return Statistical properties, compounding
9 SMA (10-day) Trend SMA = (1/n) × Σ(Close_i) for i=1 to n window=10 Simple Moving Average (10 days) Short-term trend direction
10 SMA (20-day) Trend SMA = (1/n) × Σ(Close_i) for i=1 to n window=20 Simple Moving Average (20 days) Medium-term trend direction
11 EMA (12-day) Trend EMA_t = α × Close_t + (1-α) × EMA_{t-1}
where α = 2/(n+1)		 window=12 Exponential Moving Average (12 days) Fast-reacting trend indicator
12 EMA (26-day) Trend EMA_t = α × Close_t + (1-α) × EMA_{t-1}
where α = 2/(n+1)		 window=26 Exponential Moving Average (26 days) Slow-reacting trend indicator
13 RSI (14-day) Momentum RSI = 100 - (100 / (1 + RS))
RS = Avg_Gain / Avg_Loss		 window=14 Relative Strength Index Overbought (>70) / Oversold (<30)
14 MACD Line Momentum MACD = EMA(12) - EMA(26) fast=12, slow=26 Moving Average Convergence Divergence Trend strength and direction
15 MACD Signal Momentum Signal = EMA(MACD, 9) signal=9 MACD signal line (9-day EMA of MACD) Buy/sell signal crossovers
16 MACD Histogram Momentum Histogram = MACD - Signal - Difference between MACD and signal Momentum strength, divergence
17 BB Middle Volatility BB_mid = SMA(Close, 20) window=20 Bollinger Band middle line Mean reversion reference
18 BB Upper Volatility BB_upper = BB_mid + (2 × σ) window=20, std=2 Bollinger Band upper boundary Overbought threshold, volatility expansion
19 BB Lower Volatility BB_lower = BB_mid - (2 × σ) window=20, std=2 Bollinger Band lower boundary Oversold threshold, volatility expansion
20 Stochastic %K Momentum %K = 100 × (Close - Low_n) / (High_n - Low_n) window=14 Stochastic oscillator %K line Current price vs. recent range
21 Stochastic %D Momentum %D = SMA(%K, 3) window=3 Stochastic oscillator %D line (signal) Smoothed %K, buy/sell signals

Detailed Formulas and Calculations

1-6. Price and Volume Features (Raw Data)

Basic OHLCV

Open:       Raw opening price
High:       Raw highest price  
Low:        Raw lowest price
Close:      Raw closing price
Adj_Close:  Close × (Adjustment for splits/dividends)
Volume:     Total shares traded

Purpose: Fundamental price action data; foundation for all technical indicators.

7-8. Return Features

Daily Return

ret_1d = (Close_t - Close_{t-1}) / Close_{t-1}
       = (Close_t / Close_{t-1}) - 1

Range: (-∞, +∞), typically [-10%, +10%] for stocks
Purpose: Measure daily percentage change; used in risk/return calculations

Log Return

log_ret_1d = ln(Close_t / Close_{t-1})
           = ln(Close_t) - ln(Close_{t-1})

Range: (-∞, +∞), approximately equal to ret_1d for small changes
Purpose:

  • Time-additive (can sum across periods)
  • Symmetric (±10% log returns are equal magnitude)
  • Better statistical properties (more normal distribution)

9-12. Moving Averages (Trend Indicators)

Simple Moving Average (SMA)

SMA_n = (1/n) × Σ(Close_i) for i=t-n+1 to t
      = (Close_{t-n+1} + Close_{t-n+2} + ... + Close_t) / n

SMA(10): Short-term trend (2 weeks)
SMA(20): Medium-term trend (1 month)

Interpretation:

  • Price > SMA → Uptrend
  • Price < SMA → Downtrend
  • SMA(10) crosses above SMA(20) → Golden Cross (bullish)
  • SMA(10) crosses below SMA(20) → Death Cross (bearish)

Exponential Moving Average (EMA)

EMA_t = α × Close_t + (1 - α) × EMA_{t-1}
where α = 2 / (n + 1)  # Smoothing factor

For n=12: α = 2/13 = 0.1538
For n=26: α = 2/27 = 0.0741

EMA(12): Fast-reacting, more weight on recent prices
EMA(26): Slow-reacting, more weight on historical prices

Advantages over SMA:

  • More responsive to recent price changes
  • Weights decrease exponentially (not equally)
  • Used in MACD calculation

13. Relative Strength Index (RSI)

Full Calculation

# Step 1: Calculate price changes
Gain_t = max(Close_t - Close_{t-1}, 0)
Loss_t = max(Close_{t-1} - Close_t, 0)

# Step 2: Calculate average gains and losses (14-day)
Avg_Gain = EMA(Gain, 14)
Avg_Loss = EMA(Loss, 14)

# Step 3: Calculate Relative Strength
RS = Avg_Gain / Avg_Loss

# Step 4: Calculate RSI
RSI = 100 - (100 / (1 + RS))
    = 100 × (Avg_Gain / (Avg_Gain + Avg_Loss))

Range: 0 to 100
Interpretation:

  • RSI > 70 → Overbought (potential sell signal)
  • RSI < 30 → Oversold (potential buy signal)
  • RSI = 50 → Neutral (equal buying/selling pressure)

Divergences:

  • Bullish: Price makes lower low, RSI makes higher low
  • Bearish: Price makes higher high, RSI makes lower high

14-16. MACD (Moving Average Convergence Divergence)

MACD Line

MACD = EMA(Close, 12) - EMA(Close, 26)

Purpose: Shows difference between fast and slow trend
Positive MACD: Uptrend (fast EMA > slow EMA)
Negative MACD: Downtrend (fast EMA < slow EMA)

MACD Signal Line

Signal = EMA(MACD, 9)

Purpose: Smoothed version of MACD for crossover signals

MACD Histogram

Histogram = MACD - Signal

Purpose: Visual representation of MACD-Signal difference
Interpretation:

  • Histogram > 0 → Bullish momentum
  • Histogram < 0 → Bearish momentum
  • Histogram increasing → Momentum strengthening
  • Histogram decreasing → Momentum weakening

Trading Signals:

  • MACD crosses above Signal → Buy signal
  • MACD crosses below Signal → Sell signal
  • Histogram crosses zero line → Trend change

17-19. Bollinger Bands

BB Middle (SMA)

BB_mid = SMA(Close, 20)

BB Upper Band

BB_upper = BB_mid + (k × σ)
where σ = StdDev(Close, 20)
      k = 2 (standard multiplier)

BB Lower Band

BB_lower = BB_mid - (k × σ)

Full Calculation:

# 1. Calculate 20-day SMA
BB_mid = (1/20) × Σ(Close_i)

# 2. Calculate 20-day standard deviation
σ = sqrt((1/20) × Σ(Close_i - BB_mid)²)

# 3. Calculate bands
BB_upper = BB_mid + 2σ
BB_lower = BB_mid - 2σ

# 4. Calculate bandwidth
BB_width = (BB_upper - BB_lower) / BB_mid

Interpretation:

  • Price touches upper band: Overbought, potential reversal
  • Price touches lower band: Oversold, potential reversal
  • Bands narrow (squeeze): Low volatility, breakout likely
  • Bands widen (expansion): High volatility, trend continuation
  • Price consistently above mid: Uptrend
  • Price consistently below mid: Downtrend

Statistical Meaning:

  • ~68% of prices fall within ±1σ
  • ~95% of prices fall within ±2σ
  • ~99.7% of prices fall within ±3σ

20-21. Stochastic Oscillator

Stochastic %K

%K = 100 × (Close - Low_n) / (High_n - Low_n)

where:
Low_n = Lowest low over past n periods (typically 14)
High_n = Highest high over past n periods (typically 14)

Range: 0 to 100
Interpretation:

  • Measures where current close is relative to recent range
  • %K = 100 → Close at highest high
  • %K = 0 → Close at lowest low
  • %K = 50 → Close at midpoint

Stochastic %D (Signal Line)

%D = SMA(%K, 3)
   = (%K_{t-2} + %K_{t-1} + %K_t) / 3

Purpose: Smoothed version of %K to reduce noise

Trading Signals:

  • %K > 80 → Overbought
  • %K < 20 → Oversold
  • %K crosses above %D → Buy signal
  • %K crosses below %D → Sell signal

Divergences:

  • Bullish: Price makes lower low, %K makes higher low
  • Bearish: Price makes higher high, %K makes lower high

Indicator Categories

By Purpose

Category Count Indicators Primary Use
Price 5 Open, High, Low, Close, Adj Close Raw price data
Volume 1 Volume Market activity
Returns 2 ret_1d, log_ret_1d Price changes
Trend 4 SMA(10), SMA(20), EMA(12), EMA(26) Trend direction
Momentum 6 RSI, MACD, MACD Signal, MACD Hist, %K, %D Price momentum
Volatility 3 BB Upper, BB Mid, BB Lower Price volatility

By Time Sensitivity

Speed Indicators Responsiveness
Instant OHLC, Volume, Returns Real-time
Fast EMA(12), %K 1-2 weeks
Medium SMA(10), RSI(14), Stochastic 2-3 weeks
Slow SMA(20), EMA(26), Bollinger(20) 3-4 weeks

Correlation Analysis

Expected High Correlations (|r| > 0.9)

Indicator Pair Correlation Reason
Open ↔ Close ~1.00 Same day prices
Close ↔ Adj Close 1.00 Adjustment factor only
SMA(20) ↔ EMA(12) ~0.99 Similar timeframes
BB_mid ↔ SMA(20) 1.00 BB_mid IS SMA(20)
BB_upper ↔ BB_lower ~0.99 Parallel bands
%K ↔ %D ~0.92 %D is smoothed %K
ret_1d ↔ log_ret_1d ~1.00 Approximation for small changes

Expected Low Correlations (|r| < 0.3)

Indicator Pair Correlation Reason
Volume ↔ Close ~0.1-0.3 Independent factors
RSI ↔ Volume ~0.1 Different dimensions
MACD ↔ Volume ~0.2 Price vs. activity

Implementation Code Reference

Python Calculation Example

import pandas as pd
import numpy as np

def add_technical_indicators(df):
    """Add all 21 technical indicators to dataframe."""
    
    # 1-6: Raw OHLCV (already present)
    
    # 7-8: Returns
    df['ret_1d'] = df['close'].pct_change()
    df['log_ret_1d'] = np.log(df['close'] / df['close'].shift(1))
    
    # 9-10: Simple Moving Averages
    df['sma_10'] = df['close'].rolling(window=10).mean()
    df['sma_20'] = df['close'].rolling(window=20).mean()
    
    # 11-12: Exponential Moving Averages
    df['ema_12'] = df['close'].ewm(span=12, adjust=False).mean()
    df['ema_26'] = df['close'].ewm(span=26, adjust=False).mean()
    
    # 13: RSI
    delta = df['close'].diff()
    gain = (delta.where(delta > 0, 0)).rolling(window=14).mean()
    loss = (-delta.where(delta < 0, 0)).rolling(window=14).mean()
    rs = gain / loss
    df['rsi_14'] = 100 - (100 / (1 + rs))
    
    # 14-16: MACD
    df['macd'] = df['ema_12'] - df['ema_26']
    df['macd_signal'] = df['macd'].ewm(span=9, adjust=False).mean()
    df['macd_hist'] = df['macd'] - df['macd_signal']
    
    # 17-19: Bollinger Bands
    df['bb_mid'] = df['close'].rolling(window=20).mean()
    bb_std = df['close'].rolling(window=20).std()
    df['bb_upper'] = df['bb_mid'] + (2 * bb_std)
    df['bb_lower'] = df['bb_mid'] - (2 * bb_std)
    
    # 20-21: Stochastic Oscillator
    low_14 = df['low'].rolling(window=14).min()
    high_14 = df['high'].rolling(window=14).max()
    df['stoch_k'] = 100 * ((df['close'] - low_14) / (high_14 - low_14))
    df['stoch_d'] = df['stoch_k'].rolling(window=3).mean()
    
    return df

Trading Strategy Combinations

Common Indicator Combinations

Strategy Indicators Used Logic
Trend Following SMA(10), SMA(20), MACD Buy when SMA(10) > SMA(20) and MACD > 0
Mean Reversion RSI, Bollinger Bands Buy when RSI < 30 and Close < BB_lower
Momentum RSI, MACD, Stochastic Buy when all three show bullish signals
Breakout Bollinger Bands, Volume Buy when Close breaks BB_upper with high volume
Multi-Timeframe SMA(10), SMA(20), EMA(26) Align short, medium, long-term trends

Key Insights for ML Models

Feature Engineering Considerations

  1. Multicollinearity:

    • Many indicators highly correlated (SMA/EMA variations)
    • Consider regularization (L1/L2) or feature selection
    • Principal Component Analysis (PCA) may help

  2. Scaling Requirements:

    • Price features: Large values ($100-300)
    • RSI/Stochastic: Already bounded [0, 100]
    • Returns: Small values (-0.1 to 0.1)
    • Recommend: StandardScaler or MinMaxScaler

  3. Temporal Dependencies:

    • All indicators use historical windows
    • Already capture past information
    • LSTM benefits from sequential nature

  4. Missing Values:

    • First n days will have NaN (e.g., SMA(20) needs 20 days)
    • Use forward-fill or drop initial rows
    • Affects train/valid/test split

References

  1. Bollinger Bands: Bollinger, J. (2001). "Bollinger on Bollinger Bands"
  2. MACD: Appel, G. (2005). "Technical Analysis: Power Tools for Active Investors"
  3. RSI: Wilder, J. W. (1978). "New Concepts in Technical Trading Systems"
  4. Stochastic: Lane, G. (1950s). Stochastic Oscillator
  5. Moving Averages: Murphy, J. J. (1999). "Technical Analysis of Financial Markets"

Document Version: 1.0
Last Updated: October 14, 2025
Source Code: src/data/indicators.py
Feature Engineering: src/data/preprocess.py