Section 8 – Chapter 1 – Inferential Statistics

Chapter 1 – Inferential Statistics
Section 8 - Statistics for Technicians
Presented By :
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Agenda
 Define hypothesis testing
 Describe the steps in hypothesis testing
 Compare the possible errors in hypothesis
testing
 Demonstrate the use of hypothesis testing
to frame statistical tests

📊 Hypothesis Testing in Trading & Market Analysis
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 Hypothesis testing is a mathematical tool for confirming a financial or business claim
or idea.
 Hypothesis testing is useful for investors trying to decide what to invest in and
whether the instrument is likely to provide a satisfactory return.
 Despite the existence of different methodologies of hypothesis testing, the same four
steps are used: define the hypothesis, set the criteria, calculate the statistic, and reach
a conclusion.
 This mathematical model, like most statistical tools and models, has limitations and is
prone to certain errors, necessitating investors also considering other models in
conjunction with this one

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✅ Objective Decision-Making: Helps traders validate strategies using data instead of
intuition.
✅ Risk Management: Determines if a market pattern is statistically significant or
random noise.
✅ Backtesting Validation: Used to test the profitability of trading signals before live
execution.
✅ Market Efficiency: Helps detect mispricing opportunities in stocks, options, and
forex markets.
✅ Application in Quantitative Finance: Used for factor-based investing, arbitrage,
and risk models.

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Concept Definition Trading Application
Null Hypothesis (H )
₀ No significant relationship exists
"A Moving Average Crossover does NOT
impact returns"
Alternative Hypothesis (H )
₁ A significant relationship exists
"A Moving Average Crossover DOES impact
returns"
P-Value
Probability of observing results under
H₀
p < 0.05 → Reject H (Statistically significant)
₀
Confidence Level Degree of certainty in results 95% or 99% is common in trading tests
Type I Error (False Positive) Incorrectly rejecting a true H₀ Believing a strategy works when it doesn’t
Type II Error (False Negative) Failing to reject a false H₀ Ignoring a profitable strategy
T-Test / Z-Test Compares means of datasets
Tests if a strategy's returns are different from
zero
Chi-Square Test
Measures categorical variable
relationships
Tests correlation between news events &
price jumps
Regression Analysis
Identifies relationships between
variables
Measures impact of interest rates on stock
returns

📊 Trading Strategy Using Hypothesis Testing
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📌 Step 1: Define the Hypothesis
🔹 H₀ (Null Hypothesis): "The Moving Average Crossover strategy does not generate excess
returns."
🔹 H₁ (Alternative Hypothesis): "The Moving Average Crossover strategy generates excess
returns."
📌 Step 2: Collect Data
🔹 Historical stock prices for S&P 500 stocks over 10 years
🔹 Apply 50-day & 200-day Moving Average Crossover strategy
🔹 Record daily returns after crossover signals

📊 Trading Strategy Using Hypothesis Testing
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📌 Step 3: Perform Hypothesis Testing
Use a T-Test to compare crossover returns vs. normal market returns.
Compute P-Value:
p < 0.05 → Reject H (Strategy is significant).
₀
p > 0.05 → Fail to reject H (No significant effect).
₀
📌 Step 4: Implement Trading Strategy Based on Results
If H is rejected
₀ → Use the crossover strategy in trading.
If H is not rejected
₀ → The strategy lacks edge, refine parameters or discard it.

📊 Conclusion: Why Hypothesis Testing Matters in Trading
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📌 Conclusion: Why Hypothesis Testing Matters in Trading
✅ Eliminates Bias: Prevents traders from relying on intuition alone.
✅ Improves Strategy Development: Helps refine and optimize trading models.
✅ Reduces Risk: Avoids using strategies based on random patterns.
✅ Enhances Portfolio Performance: Ensures strategies have statistical
significance before deployment.

📊 Significance & Interpretation in Market Analysis
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Significance & Interpretation in Market Analysis
📌 Fundamental Analysis: Test if earnings growth impacts stock prices significantly.
📌 Technical Analysis: Verify if chart patterns lead to consistent profits.
📌 Options Trading: Check if implied volatility changes predict price swings.
📌 Algo Trading: Validate algorithmic signals using statistical tests.

📌
📊 Case Study: Hypothesis Testing on a Trading Strategy
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🔹 Hypothesis Setup
• H₀ (Null Hypothesis): The Moving Average Crossover strategy does not generate excess returns
(mean return = 0).
• H₁ (Alternative Hypothesis): The Moving Average Crossover strategy generates excess returns
(mean return ≠ 0).
🔹 Strategy:
• Buy Signal: When the 50-day Moving Average crosses above the 200-day Moving Average.
• Sell Signal: When the 50-day MA crosses below the 200-day MA.
• Holding Period: 10 trading days after the crossover signal.
• Dataset: Historical daily price data of S&P 500 or a specific stock (e.g., AAPL).

📌
📊 Case Study: Hypothesis Testing on a Trading Strategy
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🔹 Steps for Hypothesis Testing
1. Collect Historical Data (Stock prices over several years).
2. Calculate Moving Averages (50-day & 200-day).
3. Identify Trade Signals (Buy/Sell based on crossovers).
4. Compute Returns (10-day returns after signals).
5. Conduct a T-Test (Compare returns vs. market returns).
6. Interpret Results (Check statistical significance).

📊 Errors in Hypothesis Testing (Type I vs. Type II Errors in Trading)
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Type I Error (False Positive)
🔹 Definition: Rejecting a true null hypothesis (H₀), meaning we incorrectly
conclude that a strategy works when it does not.
🔹 Impact in Trading: A trader thinks a strategy is profitable based on
sample data, but in reality, it's just random noise.
🔹 Example:
• A trader tests a Moving Average Crossover strategy.
• Reality: The strategy does not consistently generate excess returns.

📊 Errors in Hypothesis Testing (Type I vs. Type II Errors in Trading)
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• Mistake: The test incorrectly shows significance (p-value < 0.05), and the
trader starts using a bad strategy.
• Consequence: Leads to financial losses due to trading based on false signals.
🔹 How to Reduce It?
✅ Set a lower significance level (α = 0.01 instead of 0.05) for stricter testing.
✅ Use out-of-sample data to verify results.
✅ Perform multiple tests on different stocks and timeframes.

📊 Type II Error (False Negative)
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🔹 Definition: Failing to reject a false null hypothesis (H₀), meaning we incorrectly
conclude that a strategy does not work when it actually does.
🔹 Impact in Trading: A trader ignores a profitable strategy because the test fails
to detect its significance.
🔹 Example:
• A trader tests a seasonal trading strategy (e.g., "Sell in May and Go Away").
• Reality: The strategy actually has an edge over the long term.

📊 Type II Error (False Negative)
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• Mistake: The test fails to detect significance (p-value > 0.05) due to insufficient
sample size.
• Consequence: The trader misses a profitable opportunity.
🔹 How to Reduce It?
✅ Increase sample size (Use more historical data).
✅ Choose a higher confidence level (90% instead of 95%) to avoid missing
potential opportunities.
✅ Use Bayesian analysis to refine probability-based trading decisions.

📊 Comparison Table: Type I vs. Type II Errors in Trading
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Error Type Definition Trading Impact Example How to Reduce It?
Type I Error (False
Positive)
Rejecting a true H₀
Believing a bad
strategy works
Using a random
price pattern as a
valid strategy
Lower α (e.g., 0.01),
Out-of-sample
testing
Type II Error (False
Negative)
Failing to reject a
false H₀
Ignoring a working
strategy
Dismissing a
profitable breakout
strategy
Increase sample
size, Bayesian
analysis

📌
📊 Case Study: Type I vs. Type II Errors in Trading
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We will test a Breakout Trading Strategy on a stock (e.g., AAPL) and analyze the impact of
Type I and Type II errors in hypothesis testing.
Hypothesis Setup
• H₀ (Null Hypothesis): The breakout strategy does NOT generate excess returns.
• H₁ (Alternative Hypothesis): The breakout strategy generates excess returns.
Strategy Details
• Entry Condition: Buy when the stock price closes above its 20-day high.
• Exit Condition: Sell after 10 days.
• Dataset: Historical stock price data (AAPL).

📊 Expected Errors in Hypothesis Testing
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🔴 Type I Error (False Positive) - Trading a Bad Strategy
📌 Scenario: The test wrongly shows that breakouts generate profits when they actually don’t.
📌 Reason: Small sample size, random market movements, or data overfitting.
📌 Consequence: A trader wastes capital on an ineffective breakout system.
🔵 Type II Error (False Negative) - Ignoring a Good Strategy
📌 Scenario: The test fails to show statistical significance, so the trader ignores the strategy.
📌 Reason: The sample size is too small, or the chosen confidence level (p-value) is too strict.
📌 Consequence: A trader misses out on a profitable strategy.

Next Chapter 1 - Momentum And Indicator
Interpretation Part 1
Next Section 9 – Technical Indicators
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Section 8 – Chapter 1 – Inferential Statistics

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