Statistical Data Analysis and Inference › Statistical Data Analysis and Inference

A positive average return is not enough to establish that a strategy's modeled mean differs from zero. The estimate may be small relative to its sampling uncertainty. Before interpreting a historical return series, you need to separate what the sample shows from what the sampling model lets you infer.

We'll summarize historical returns, then estimate uncertainty about a mean under a specified sampling model. Mean and volatility describe center and dispersion. Skewness records a third standardized moment, while kurtosis records a fourth; neither statistic alone determines tail probabilities. The Central Limit Theorem explains when a normal approximation is justified, and hypothesis tests and confidence intervals put that approximation to work. Using a historical estimate to forecast returns requires an additional assumption that the historical process is informative about the forecast horizon.

Statistical analysis informs many quantitative decisions in finance. These techniques support systematic analysis in portfolio optimization, risk management, and strategy evaluation.