Data Handling and Visualization › Data Visualization
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Visualizations can make patterns and relationships easier to see than a table of raw observations.
Price Charts
A price chart is a common starting visualization for showing how a price series evolves over time.
In this simulated sample, AAPL and MSFT finish above their starting values while GOOGL finishes below. All three paths fluctuate and respond to the injected stress regime. Because the series begin at different price levels, indexing them to a common base is one useful way to compare relative price paths; returns or indexed total-wealth series are alternatives when their inputs are available.
The common baseline of 100 makes relative price changes easier to compare. All three simulated series dip during the injected stress period and then follow different paths. Indexing is useful here, but return charts, excess-return charts, and total-wealth series may be more appropriate for other comparisons.
Return Distributions
Return distribution visualizations reveal characteristics critical for quantitative models.
The simulated sample differs from its moment-matched normal reference. That behavior is expected because the generator uses Student-t common and idiosyncratic innovations. Many empirical financial return series also exhibit heavy tails, but this constructed example demonstrates the plotting method rather than establishing an empirical result for AAPL.
Scatter Plots and Correlations
Correlations between securities matter for portfolio construction and risk management. Scatter plots visualize pairwise relationships by plotting one variable against another.
The two simulated return series have positive sample correlation because the generator gives them a common factor as well as idiosyncratic terms. The regression line summarizes their linear association in this sample. Correlation of 1 places centered observations on a positive-slope line; zero correlation means no sample linear association, not necessarily an unstructured random cloud or independence. For multiple series, a correlation matrix summarizes pairwise linear relationships.
For these nonconstant sample series, the diagonal is 1.0; a constant or insufficiently observed series would have undefined self-correlation. Off-diagonal entries are sample correlations between the simulated series. All are positive in this seeded realization, consistent with its shared factor; the factor alone does not guarantee every finite-sample sign. In portfolio analysis, positive dependence can reduce diversification relative to otherwise comparable less-correlated assets, but this heatmap does not estimate market-wide or sector-wide dependence.
Rolling Statistics
Rolling correlations show how local sample estimates vary over time. That variation can arise from changing population relationships or simply from changing samples under constant parameters. Here the generator also includes a constructed stress regime.
The rolling estimates vary across this synthetic sample. The generator explicitly changes drift and log-shock scales during the stress interval and includes a common factor, so these plots illustrate information that a single full-sample correlation or volatility estimate would omit. They do not test a constant-parameter model against observed market data or show that every such model is inadequate.