CTA Statistical & Quantitative Methods 1 — Questions and Answers
Question 1: What does a Pearson correlation coefficient of -1.0 between two assets indicate?
- No linear relationship exists between the assets
- A perfect positive linear relationship between the assets
- A perfect negative linear relationship between the assets (Correct answer)
- A moderate inverse relationship between the assets
Correct answer: A perfect negative linear relationship between the assets
A correlation coefficient of -1.0 indicates a perfect negative linear relationship, meaning the two assets move in exactly opposite directions.
Question 2: Which statistical measure is used to construct Bollinger Bands around a moving average?
- Mean absolute deviation
- Variance
- Standard deviation (Correct answer)
- Standard error of the mean
Correct answer: Standard deviation
Bollinger Bands are constructed by adding and subtracting a specified multiple of the standard deviation from a simple moving average.
Question 3: In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?
- 68%
- 99.7%
- 90%
- 95% (Correct answer)
Correct answer: 95%
By the empirical rule, approximately 95% of data in a normal distribution falls within two standard deviations of the mean.
Question 4: What does R-squared (R²) measure when linear regression is applied to price data?
- The slope of the regression line
- The standard error of the estimate
- The time-price correlation coefficient
- The proportion of price variance explained by the regression model (Correct answer)
Correct answer: The proportion of price variance explained by the regression model
R-squared, the coefficient of determination, measures the proportion of variance in the dependent variable (price) that is explained by the independent variable(s) in the model.
Question 5: What does a Z-score tell a technical analyst about a data point?
- The absolute dollar change of the data point from the prior period
- The momentum of the data point relative to its trend
- How many standard deviations the data point lies above or below the mean (Correct answer)
- The trend direction implied by the data point
Correct answer: How many standard deviations the data point lies above or below the mean
A Z-score measures how many standard deviations a data point is from the mean, allowing analysts to identify statistically unusual price levels.
Question 6: What is the primary purpose of applying a moving average to price data?
- To predict exact future price reversal points
- To smooth price fluctuations and identify the underlying trend direction (Correct answer)
- To precisely measure current market volatility
- To calculate total trading volume over a period
Correct answer: To smooth price fluctuations and identify the underlying trend direction
Moving averages smooth short-term price fluctuations to reveal the underlying trend direction of a security over the chosen period.
Question 7: In time series analysis of price data, what does autocorrelation measure?
- The relationship between price changes and volume changes
- The variance of returns over a specific time window
- The probability of future price movements based on current momentum
- The correlation between a time series and a lagged version of itself (Correct answer)
Correct answer: The correlation between a time series and a lagged version of itself
Autocorrelation measures the correlation between a time series and its own past values at specified lag intervals, helping analysts assess price persistence.
CTA Statistical & Quantitative Methods 1
What does a Pearson correlation coefficient of -1.0 between two assets indicate?