Data Science Tutorials

An autoregressive model predicts future values of a time series from its own past. Learn how to fit one in Python with statsmodels, choose the lag order with PACF and AIC/BIC, and compare it to MA and ARIMA.

Learn how SARIMAX combines seasonal time series modeling with external predictors. Understand its parameters, see how it differs from ARIMA and SARIMA, and build a forecasting model in Python.

Learn how ARIMAX extends ARIMA with external predictors, understand its parameters and assumptions, and build a forecasting model in Python with statsmodels.

Learn what quadrature is, how numerical integration approximates definite integrals, and how methods such as the trapezoidal rule, Simpson's rule, and Gaussian quadrature work.

Learn how the Box-Cox transformation works, how to choose the lambda parameter, and when to use it to stabilize variance, reduce skewness, and improve statistical models.

A likelihood ratio compares how well two hypotheses or models explain the same data, and this article covers the formula, a worked coin-flip example, the likelihood ratio test for nested regression models in Python and R, and diagnostic likelihood ratios.

Stepwise regression automates predictor selection with forward, backward, and bidirectional search, but its simplicity comes with trade-offs in stability and overfitting.

Learn what statistical arbitrage is, how quantitative traders identify temporary pricing relationships, and how strategies such as pairs trading and mean reversion work in practice.

Learn how state space models represent dynamic systems using hidden states and observations, including the state and observation equations, Kalman filtering, and time-series applications.

Learn what a residual plot is, how to interpret common patterns, and how residual plots help identify nonlinearity, heteroscedasticity, outliers, and other regression problems.

A practical, math-first look at saddle points - what makes them different from local minima and maxima, how to spot one using gradients and the Hessian, and why they show up so often in high-dimensional optimization and neural network training.

Learn what an augmented matrix is, how it represents systems of equations, and how to use row operations to solve them.