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Poisson_Chart Command

The Poisson_Chart command analyzes the frequency of large moves in a time series and compares the observed occurrence rate with a Poisson probability model.

Example

Poisson_Chart(last(sp500,700),0.01)

This example examines the last 700 observations of the S&P 500 and studies the occurrence of daily moves greater than 1% in magnitude.

How It Works

The command first identifies observations whose percentage change exceeds a specified threshold. These events are then treated as arrivals in time and compared against a Poisson process.

If large market moves occur randomly and independently, the Poisson model often provides a reasonable approximation of their frequency. Deviations from the model may indicate volatility clustering, market stress, or prolonged periods of unusual calm.

Interpretation

• Low event frequency — Markets are relatively quiet, with few large moves.
• High event frequency — Markets are experiencing elevated volatility.
• Observed frequency near Poisson expectation — Large moves are occurring at a rate consistent with a random arrival process.
• Observed frequency above expectation — Volatility may be clustering, with large moves arriving in bursts.

The chart is particularly useful for identifying periods when investors become complacent or, conversely, when markets enter regimes characterized by persistent turbulence.

Typical Use Cases

• Volatility regime analysis
• Market stress monitoring
• Risk management studies
• Comparison of calm and turbulent market periods
• Frequency analysis of large price moves

Related Commands

• PoissonDist
• Vol_Study
• LogDiff