Empirical Characteristics of HFT Data

When we look at millions of data points, certain "Stylized Facts" (patterns) emerge universally across markets (Stocks, Forex, Crypto).

1. Intraday "U-Shape" Pattern (Diurnal Pattern)

Volatility and Volume are NOT constant throughout the day. They follow a U-Shape.

• Morning (Open): High Volume, High Volatility. (Price discovery happening).
• Lunch (Mid-day): Low Volume, Low Volatility. (Traders take a break).
• Closing (Close): High Volume, High Volatility. (Mutual funds rebalancing, portfolio closing).

2. Negative First-Order Autocorrelation

In daily returns, autocorrelation is often zero. In tick returns, it is strongly Negative.

• Reason: The Bid-Ask Bounce.
• If a trade hits the Ask (high), the next trade is likely to hit the Bid (low).
• Using formula: Price(t) - Price(t-1) creates a "zig-zag" pattern.

3. Discrete Price Changes

Prices are not continuous. They move in Ticks (e.g., 0.05 increments).

• This "Discreteness" creates issues for standard calculus-based models (like Black-Scholes) which assume continuous movement.

4. Heavy Tails (Kurtosis)

HF returns have extremely "Fat Tails".

• Extreme moves (jumps) happen FAR more often than a Normal Distribution predicts.