Characteristics of Financial Time Series Data

Financial time series data is unique. It behaves differently from data in physics or biology. It is messy, noisy, and driven by human psychology.

1. Non-Stationarity

Most financial prices are Non-Stationary.

• Stationary: Mean and variance are constant over time.
• Non-Stationary: Mean and variance change over time.
• Implication: You cannot directly predict stock prices ($P_t$) using simple statistics because the average price 10 years ago has no relevance to the average price today. We typically convert prices to returns to make them stationary.

2. Autocorrelation (Serial Correlation)

Do past values influence future values?

• In efficient markets, asset returns should NOT have significant autocorrelation (Random Walk Hypothesis). Past returns shouldn't predict future returns.
• However, volatility often has high autocorrelation (if returns were wild yesterday, they likely will be wild today).

3. Volatility Clustering

This is a famous stylized fact (Mandelbrot).

• "Large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes."
• This means markets go through "calm" periods and "turbulent" periods. Volatility is not constant; it comes in clusters.

4. Fat Tails (Leptokurtic)

Financial returns do not follow a perfect Normal Distribution (Bell Curve).

• Fat Tails: Extreme events (market crashes or booms) happen far more often than a Normal Distribution predicts.
• Black Swan Events: These "tail events" carry the most risk.

5. Leverage Effect

Volatility tends to increase more when prices fall (bad news) than when prices rise (good news) by the same amount.

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