In partnership with
You Can't Automate Good Judgement
AI promises speed and efficiency, but it’s leaving many leaders feeling more overwhelmed than ever.
The real problem isn’t technology.
It’s the pressure to do more with less — without losing what makes your leadership effective.
BELAY created the free resource 5 Traits AI Can’t Replace & Why They Matter More Than Ever to help leaders pinpoint where AI can help and where human judgment is still essential.
At BELAY, we help leaders accomplish more by matching them with top-tier, U.S.-based Executive Assistants who bring the discernment, foresight, and relational intelligence that AI can’t replicate.
That way, you can focus on vision. Not systems.
🔔 Limited-Time Deal: 20% Off Our Complete 2026 Playbook! 🔔
Level up before the year ends!
AlgoEdge Insights: 30+ Python-Powered Trading Strategies – The Complete 2026 Playbook
30+ battle-tested algorithmic trading strategies from the AlgoEdge Insights newsletter – fully coded in Python, backtested, and ready to deploy. Your full arsenal for dominating 2026 markets.
Special Promo: Use code SPRING2026 for 20% off
Valid only until March 20, 2026 — act fast!
👇 Buy Now & Save 👇
Instant access to every strategy we've shared, plus exclusive extras.
— AlgoEdge Insights Team
🔔 Flash Launch Alert: AlgoEdge Colab Vault – Your 2026 Trading Edge! 🔔
The $79 book gives you ideas on paper.
This gives you 20 ready-to-run money machines in Google Colab.
I've turned my 20 must-have, battle-tested Python strategies into fully executable Google Colab notebooks – ready to run in your browser with one click.
One-click notebooks • Real-time data • Bias-free backtests • Interactive charts • OOS tests • CSV exports • Pro metrics
Test on any ticker instantly (SPY, BTC, PLTR, TSLA, etc.).
Launch Deal (ends Feb 28, 2026):
$129 one-time (save $40 – regular $169 after)
Lifetime access + free 2026 updates.
Inside the Vault (20 powerhouses):
Bias-Free Cubic Poly Trend
3-State HMM Volatility Filter
MACD-RSI Momentum
Bollinger Squeeze Breakout
Supertrend ATR Rider
Ichimoku Cloud
VWAP Scalper
Donchian Breakout
Keltner Reversion
RSI Divergence
MA Ribbon Filter
Kalman Adaptive Trend
ARIMA-GARCH Vol Forecast
LSTM Predictor
Random Forest Regime Classifier
Pairs Cointegration
Monte Carlo Simulator
FinBERT Sentiment
Straddle IV Crush
Fibonacci Retracement
👇 Grab It Before Price Jumps 👇
Buy Now – $129
P.S. Run code today → test live tomorrow → outperform the book readers.
Reply “VAULT” for direct link or questions.
Premium Members – Your Full Notebook Is Ready
The complete Google Colab notebook from today’s article (with live data, full Hidden Markov Model, interactive charts, statistics, and one-click CSV export) is waiting for you.
Preview of what you’ll get:
Inside:
Automatic PLTR (or any ticker) daily data download from 2021 → today via free yfinance
Full polynomial regression demo (degrees 1–4) with R², MAE, RMSE, MAPE metrics & beautiful comparison plots
Bias-free expanding-window cubic (deg=3) regression – no lookahead bias, real walk-forward style
Clear trading signals: long when price > cubic fit and slope > 0, with entry/exit markers
Interactive-style plots: price + trend filter + green/red signals + in-position highlights
Complete backtest vs Buy & Hold: daily/ cumulative returns, 0.1% transaction costs applied
Detailed performance metrics: Total Return, CAGR, Ann. Volatility, Sharpe (rf=0), Max Drawdown
Trade statistics: number of trades, win rate, average trade return
Realistic Out-of-Sample (OOS) test on last ~10% of data + separate metrics & chart
Bonus: change one line to test any symbol (e.g. TSLA, BTC-USD, AAPL, GLD) or adjust degree/window/costs
Free readers – you already got the full breakdown and visuals in the article. Paid members – you get the actual tool.
Not upgraded yet? Fix that in 10 seconds here👇
Google Collab Notebook With Full Code Is Available In the End Of The Article Behind The Paywall 👇 (For Paid Subs Only)
1. Introduction
Stocks rise and fall, creating patterns and movements that can feel as unpredictable as ocean waves. Yet, much like how scientists predict the movement of the waves by understanding the currents below, we too can decipher some of the patterns of the stock market with similar tools.
By tapping into the power of the Wavelet Transform, we look beneath the surface, seeking to uncover the deep currents that drive stock prices. This journey is not just about numbers and data; it’s about translating the abstract into the tangible, taking the seemingly erratic behavior of stocks and finding rhythm and reason.
2. Wavelet Transform Theory
At its core, a wavelet is a brief oscillation that has its energy concentrated in time, ensuring it’s both short-lived and limited in duration. Imagine striking a drum: the sound produced is intense but fades quickly. This ephemeral characteristic of wavelets makes them immensely suitable to analyze financial signals that are non-stationary (i.e., their statistical properties change over time). Wavelet Transform is akin to providing a microscope to view the intricate details of stock data, capturing both its large trends and minute fluctuations.
2.1 Why Not Fourier Transform?
Many might think, why not just use the Fourier Transform, which is a very popular tool to analyze signals? Fourier Transform breaks down a signal into its constituent sinusoids. However, its Achilles’ heel is its inability to provide both time and frequency information simultaneously. While it can tell us the frequencies present, it’s often oblivious to when they occur. Unlike its Fourier counterpart, Wavelet Transform captures both the frequency and the time, providing a time-frequency representation of the signal.
How Will You Generate Retirement Income?
Most people with $1,000,000 or more saved have a number. Fewer have a plan for turning it into reliable income. Fisher Investments' Definitive Guide to Retirement Income helps you calculate future costs and build a portfolio strategy around them.
2.2 The Essence of Wavelet Transform
Mathematically, the Wavelet Transform can be represented as:
Where:
W is the result of our comparison, giving us a measure of similarity.
f (t) represents our stock data.
ψ (t) is the chosen wavelet pattern.
In essence, we’re moving our wavelet ψ across the stock data f(t), looking for places where they align well. This gives us the wavelet coefficients W(b) which tell us how strongly the stock data matches the wavelet at each point in time. Put simply, the better the match at any given point, the higher the value of W.
On the left, the Continuous Wavelet Transform (CWT) visualizes stock data at different scales, capturing varied time durations. On the right, a Ricker wavelet moves through the stock signal, with its correlation shown below. Together, they spotlight how wavelets localize patterns in stock data, distinguishing short-term fluctuations from long-term trends.
In the presented visualizations, we see the mechanism of the Wavelet Transform as applied to time series data, such as stock prices. On the left, we see a vivid portrayal of the Continuous Wavelet Transform (CWT) applied to stock data. Each frame of the animation displays wavelet coefficients at a different scale, capturing patterns that exist at varying time durations. Wider wavelets detect longer-term trends, while narrower ones focus on short-term fluctuations.
Beside it, on the right, is a depiction of how a wavelet, in this case, a Ricker wavelet, traverses through the stock signal. As the wavelet slides across, it gets multiplied point-by-point with the stock data, and the resultant values are summed up to produce a single coefficient. This ‘correlation’ is plotted below, with the red dot marking the current coefficient value as the wavelet moves. High peaks in the correlation plot indicate locations where the wavelet aligns well with the stock data, capturing specific patterns. In essence, this process is a systematic approach to unearth local patterns within vast time series data, offering a granular perspective that Fourier Transform might miss.
Go from AI overwhelmed to AI savvy professional
AI will eliminate 300 million jobs in the next 5 years.
Yours doesn't have to be one of them.
Here's how to future-proof your career:
Join the Superhuman AI newsletter - read by 1M+ professionals
Learn AI skills in 3 mins a day
Become the AI expert on your team
3. Python Implementation
We’ll now delve into the Python implementation of the Wavelet Transform for deriving buy/sell signals from stock data which is what might be of interest to traders and Data Scientist. The code employs the Continuous Wavelet Transform to extract features that can indicate potential buy or sell moments in the stock’s historical data.
3.1 Setting up the Environment
Ensure you have the required Python libraries. If not, they can be installed via pip:
pip install numpy pandas matplotlib yfinance scipy3.2 Fetching the Stock Data
Using the yfinance library, we can easily fetch stock data for analysis:
import yfinance as yf
ticker = "SIE.DE"
stock_data = yf.download(ticker, start="2018-01-01", end="2023-12-30")3.3 Applying the Continuous Wavelet Transform (CWT)
The scipy library provides the required functions to compute the CWT using the Ricker wavelet:
from scipy import signal
widths = np.arange(1, 15)
cwt_result = signal.cwt(stock_data['Close'].values, signal.ricker, widths)3.4 Extracting Buy and Sell Signals
From the computed CWT, positive and negative coefficients can be extracted, indicating upward and downward movements in stock price, respectively.
cwt_positive = np.where(cwt_result > 0, cwt_result, 0)
cwt_negative = np.where(cwt_result < 0, cwt_result, 0)
buy_signal = pd.Series(np.sum(cwt_positive, axis=0), index=stock_data.index)
sell_signal = pd.Series(-np.sum(cwt_negative, axis=0), index=stock_data.index)3.5 Identifying Signal Crossovers
Crossovers between buy and sell signals can potentially indicate trading opportunities.
cross_above = (buy_signal >= sell_signal) & (buy_signal.shift(1) < sell_signal.shift(1))
cross_below = (buy_signal <= sell_signal) & (buy_signal.shift(1) > sell_signal.shift(1))3.6 Visualization
A visual representation can provide a clearer perspective on the buy/sell moments against the stock’s historical data:
import matplotlib.pyplot as plt
plt.figure(figsize=(30, 6))
plt.plot(stock_data.index, stock_data['Close'], label='Close Prices', alpha=0.5)
plt.scatter(stock_data.index[cross_above], stock_data['Close'][cross_above], label='Buy Signal', marker='^', color='g')
plt.scatter(stock_data.index[cross_below], stock_data['Close'][cross_below], label='Sell Signal', marker='v', color='r')
plt.title(f'{ticker} Historical Close Prices with Wavelet Transform Buy and Sell Signals')
plt.legend()
plt.show()3.7 Complete Python Code
Putting all the code together we get
import numpy as npimport pandas as pdimport matplotlib.pyplot as pltimport yfinance as yffrom scipy import signal
# Download ASML.AS historical stock data
ticker = "SIE.DE"
stock_data = yf.download(ticker, start="2018-01-01", end="2023-12-30")
# Compute the Continuous Wavelet Transform (CWT) using the Ricker wavelet
widths = np.arange(1, 15)
cwt_result = signal.cwt(stock_data['Close'].values, signal.ricker, widths)
# Extract the relevant CWT coefficients for analysis
cwt_positive = np.where(cwt_result > 0, cwt_result, 0)
cwt_negative = np.where(cwt_result < 0, cwt_result, 0)
# Calculate the buy and sell signals from the CWT coefficients
buy_signal = pd.Series(np.sum(cwt_positive, axis=0), index=stock_data.index)
sell_signal = pd.Series(-np.sum(cwt_negative, axis=0), index=stock_data.index)
# Identify buy and sell signal crossovers
cross_above = (buy_signal >= sell_signal) & (buy_signal.shift(1) < sell_signal.shift(1))
cross_below = (buy_signal <= sell_signal) & (buy_signal.shift(1) > sell_signal.shift(1))
# Plot the stock prices and buy/sell signals
plt.figure(figsize=(30, 6))
plt.plot(stock_data.index, stock_data['Close'], label='Close Prices', alpha=0.5)
plt.scatter(stock_data.index[cross_above], stock_data['Close'][cross_above], label='Buy Signal', marker='^', color='g')
plt.scatter(stock_data.index[cross_below], stock_data['Close'][cross_below], label='Sell Signal', marker='v', color='r')
plt.title(f'{ticker} Historical Close Prices with Wavelet Transform Buy and Sell Signals')
plt.legend()
plt.show()
Visualization of historical close prices for SIE.DE from 2018 to 2023, with Wavelet Transform-derived buy (green upward-pointing triangles) and sell (red downward-pointing triangles) signals using a basic CWT approach.
3.7 Bonus — Optimized Parameters
While the wavelet transform offers an innovative approach to analyzing stock data and generating buy/sell signals, its effectiveness hinges largely on the choice of parameters: the width of the wavelets and the threshold values. These parameters influence the sensitivity and specificity of our strategy.
With the code below, you can implement an optimization technique to systematically select the best parameters. Leveraging a backtesting function, we’ll simulate our strategy’s past performance for various parameter combinations. By the end, we aim to fine-tune our strategy to maximize historical performance, keeping in mind the adage: past performance isn’t necessarily indicative of future results.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import yfinance as yf
from scipy import signal
# Download ASML.AS historical stock data
ticker = "ASML.AS"
stock_data = yf.download(ticker, start="2018-01-01", end="2023-12-30")
# Define parameter ranges
widths_range = np.arange(1, 15)
threshold_range = np.arange(0.1, 1.0, 0.1)
# Store the best parameters and their performance
best_widths = None
best_threshold = None
best_performance = -np.inf
def backtest(stock_data, cross_above, cross_below):
# We'll start with one "unit" of cash
cash = 1.0
stock = 0.0
position = "out"
# Go through each day in our data
for i in range(len(stock_data)):
# If we have a buy signal and we're not already holding the stock
if cross_above[i] and position == "out":
# Buy the stock
stock += cash / stock_data['Close'][i]
cash = 0.0
position = "in"
# If we have a sell signal and we're holding the stock
elif cross_below[i] and position == "in":
# Sell the stock
cash += stock * stock_data['Close'][i]
stock = 0.0
position = "out"
# Return our final portfolio value
if position == "in":
return cash + stock * stock_data['Close'][-1]
else:
return cash
# Go through each combination of parameters
for widths in widths_range:
for threshold in threshold_range:
# Compute the CWT
cwt_result = signal.cwt(stock_data['Close'].values, signal.ricker, [widths])
# Extract relevant coefficients
cwt_positive = np.where(cwt_result > threshold, cwt_result, 0)
cwt_negative = np.where(cwt_result < -threshold, cwt_result, 0)
# Calculate signals
buy_signal = pd.Series(np.sum(cwt_positive, axis=0), index=stock_data.index)
sell_signal = pd.Series(-np.sum(cwt_negative, axis=0), index=stock_data.index)
cross_above = (buy_signal >= sell_signal) & (buy_signal.shift(1) < sell_signal.shift(1))
cross_below = (buy_signal <= sell_signal) & (buy_signal.shift(1) > sell_signal.shift(1))
# Calculate performance based on trading signals
performance = backtest(stock_data, cross_above, cross_below)
# Update best parameters if this performance is better
if performance > best_performance:
best_performance = performance
best_widths = widths
best_threshold = threshold
# Print the best parameters
print(f"Best widths: {best_widths}")
print(f"Best threshold: {best_threshold}")
print(f"Best performance: {best_performance * 100}%")
# Recalculate the CWT and buy/sell signals using the best parameters
cwt_result = signal.cwt(stock_data['Close'].values, signal.ricker, [best_widths])
cwt_positive = np.where(cwt_result > best_threshold, cwt_result, 0)
cwt_negative = np.where(cwt_result < -best_threshold, cwt_result, 0)
buy_signal = pd.Series(np.sum(cwt_positive, axis=0), index=stock_data.index)
sell_signal = pd.Series(-np.sum(cwt_negative, axis=0), index=stock_data.index)
cross_above = (buy_signal >= sell_signal) & (buy_signal.shift(1) < sell_signal.shift(1))
cross_below = (buy_signal <= sell_signal) & (buy_signal.shift(1) > sell_signal.shift(1))
# Plot the stock prices and buy/sell signals
plt.figure(figsize=(30, 6))
plt.plot(stock_data.index, stock_data['Close'], label='Close Prices', alpha=0.5)
plt.scatter(stock_data.index[cross_above], stock_data['Close'][cross_above], label='Buy Signal', marker='^', color='g')
plt.scatter(stock_data.index[cross_below], stock_data['Close'][cross_below], label='Sell Signal', marker='v', color='r')
plt.title(f'{ticker} Historical Close Prices with Wavelet Transform Buy and Sell Signals')
plt.legend()
plt.show()
Enhanced visualization of historical close prices for ASML.AS from 2018 to 2023, highlighting buy and sell signals obtained after optimizing the Wavelet Transform parameters for improved trading performance.
4. Interpretation and Analysis
After implementing the wavelet transform on stock data and refining it with optimized parameters, we arrive at a series of buy and sell signals. Upon a closer look:
Sensitivity to Market Noise: Just like other technical indicators, the wavelet transform isn’t immune to market noise. However, its multi-scale nature provides a degree of resilience, allowing it to highlight genuine patterns while potentially filtering out short-term fluctuations.
Periodic Patterns: Stocks often exhibit cyclical behaviors — quarterly financial reports, yearly market trends, etc. The wavelet’s ability to capture such behaviors at different scales can be a significant advantage in predicting future movements.
Performance Metrics: While our optimization boosted historical performance, it’s essential to validate the strategy on out-of-sample data. Performance on historical data doesn’t guarantee similar results in the future. It’s crucial to be aware of potential overfitting.
5. Potential Improvements and Extensions
Alternative Wavelets: We utilized the Ricker wavelet, but several other wavelet families, such as Daubechies or Haar, might offer different insights. Exploring these can be an exciting avenue.
Incorporating Other Indicators: While the wavelet transform provides a unique perspective, combining it with other technical indicators might strengthen the decision-making process.
Machine Learning Integration: Leveraging machine learning algorithms can help in predicting buy/sell signals more accurately. The wavelet coefficients can serve as features for models like decision trees, neural networks, etc.
Adaptive Thresholding: Instead of a static threshold, dynamic thresholding methods that adapt to changing market conditions might improve signal reliability.
6. Conclusion
Wavelet transform provides a unique lens to analyze stock market data, balancing both time and frequency insights. While it offers a fresh perspective, the technique isn’t foolproof — choosing the right parameters is crucial. This approach is just one tool among many in understanding market movements. Traders should combine wavelet analysis with other methods for even sharper insights. Our journey through wavelet analysis emphasizes the continuous innovation in financial research, always seeking clearer understanding and predictive power.
Subscribe to our premium content to read the rest.
Become a paying subscriber to get access to this post and other subscriber-only content.
Upgrade