Financial Risk Manager Part 1

Explanation:

A time series is said to be stationary (specifically, covariance stationary or weakly stationary) if it satisfies three conditions:

1. Constant Mean: The expected value (mean) of the series is constant over time
2. Constant Variance: The variance of the series is finite and constant over time
3. Constant Covariance: The covariance between values at different time lags depends only on the lag length, not on the actual time period

Option A correctly captures this definition by stating that "statistical properties including the mean and variance do not change over time."

Why other options are incorrect:

• Option B: Incorrect because stationary time series require constant mean, variance, and covariances
• Option C: Incorrect because both mean AND variance must be constant for stationarity
• Option D: Incorrect because both mean AND variance must be constant, not variable

Importance in Financial Risk Management: Stationarity is crucial in time series analysis because:

1. Many statistical models (like ARIMA) assume stationarity
2. Non-stationary series can lead to spurious regression results
3. Stationarity allows for meaningful forecasting and inference
4. In risk management, understanding whether financial time series (like returns) are stationary helps in modeling volatility and correlations accurately