# Statistics & QR Szymon Kopyciński · 23 September 2026 ## Statistics and quantitative research ### Quant Short for **quantitative**. Depending on context, _a quant_ may be a quantitative researcher, trader, developer, analyst or another mathematically oriented role. ### Model A simplified mathematical or statistical representation of some aspect of reality. ### Feature An input variable used by a model. Examples include recent returns, volatility, order book imbalance and macroeconomic data. ### Target The quantity a model is trying to predict. For example, the return over the next five minutes. ### Observation One data point or sample in a dataset. ### Time series Data indexed through time. Asset prices and returns are classic examples. ### Cross-sectional data Data describing many different entities at one point or period in time. For example, comparing valuation ratios across 500 stocks today. ### Mean The arithmetic average. ### Median The middle value after observations are ordered. ### Variance A measure of how dispersed values are around their mean. ### Standard deviation The square root of variance. It is the standard measure of volatility. ### Covariance A measure of how two variables move together. ### Correlation A normalised measure of how strongly two variables move together. Correlation ranges from −1 to +1. ### Autocorrelation Correlation between a time series and lagged versions of itself. For example, whether today's return is related to yesterday's return. ### Regression A statistical method for modelling the relationship between variables. A simple linear regression is written: $$ y = \alpha + \beta x + \epsilon $$ ### Alpha In regression, the intercept term. In finance, _alpha_ also means excess return or trading edge (see Alpha in section 7). ### Beta A coefficient describing sensitivity to another variable. In asset pricing, market beta describes how strongly an asset moves relative to the market. ### Residual The difference between a model's prediction and the observed value. ### Factor A variable used to explain common variation in asset returns. Examples include market, value, momentum, size and sector exposure. ### Stationarity The property that a time series' statistical properties, such as its mean and variance, remain stable over time. Many statistical methods assume stationarity. Prices are typically non-stationary, whereas returns are much closer to stationary, which is one reason research is usually done on returns. ### Distribution A mathematical description of the possible values a random variable can take and how likely each is. ### Normal distribution The familiar bell-shaped probability distribution. Simple models often assume normally distributed returns, but real returns have heavier tails and other deviations. ### Fat tails / Heavy tails A distribution with extreme outcomes more frequent than a normal distribution would predict. Financial returns typically display fat tails. ### Skewness A measure of asymmetry in a distribution. ### Kurtosis A measure of the tail heaviness of a distribution. Financial returns typically show excess kurtosis relative to a normal distribution. ### Expected value The probability-weighted average outcome of a random variable. A strategy needs positive expected value after costs to be profitable over time. ### Hypothesis test A statistical procedure for assessing evidence against a specified null hypothesis. ### P-value The probability, assuming the null hypothesis is true, of observing a result at least as extreme as the one actually observed. It is not the probability that the null hypothesis is true, nor the probability that your hypothesis is correct. ### Statistical significance A statement that an observed result passes a predefined statistical threshold. Statistical significance does not imply economic significance or tradability: a statistically significant effect may be too small to survive costs. Part of [Glossary Index](/blog/glossary-index) · Previous: [Positions, PnL & Risk](/blog/glossary-index/glossary-positions-pnl-risk) · Next: [Backtesting & Validation](/blog/glossary-index/glossary-backtesting-and-validation)