Interactive Tools

Time Series Analysis

Interactive time series visualizations revealing patterns, trends, and forecasts across temporal data from various industries and research domains.

Random Walk Visualizer

An interactive exploration of random walks and their statistical properties. This visualization demonstrates how random walks behave over time, showing multiple realizations, statistical distributions, and key properties like variance scaling and the central limit theorem in action. Includes controls for step size, number of walks, and time horizon to explore different scenarios.

Time Series Stationarity Visualizer

An interactive exploration of stationarity in time series data. This visualization demonstrates the key concept that a time series is stationary when its statistical properties (mean, variance, autocovariance) remain constant over time, including examples of trending, seasonal, and white noise processes to illustrate the differences between ensemble and time means.

Exponential Smoothing Methods

Interactive exploration of exponential smoothing techniques that progressively handle level, trend, and seasonal patterns in time series data.

Simple Exponential Smoothing (SES)

Master the fundamentals of exponential smoothing by exploring how the α parameter controls the trade-off between stability and responsiveness. Watch the weighted averaging process in action as SES creates flat forecasts, and discover why high α values (approaching 1) signal model inadequacy when data contains trends or seasonal patterns.

Holt's Linear Trend Method

Advance beyond flat forecasts by decomposing time series into level and trend components. Experiment with dual smoothing parameters α and β* to understand how each component adapts independently, creating dynamic sloped forecasts that naturally extend trending patterns into the future.

Holt-Winters Seasonal Method

Experience the complete forecasting framework with three-component decomposition of level, trend, and seasonality. Observe how the triple smoothing parameters α, β*, and γ work together to capture complex data patterns, producing sophisticated forecasts that maintain both trending behavior and cyclical seasonal patterns.

ARIMA Models

Interactive exploration of Autoregressive Integrated Moving Average (ARIMA) models, the foundation of modern time series forecasting that combines AR and MA components.

AR(1) & MA(1) Models Visualization

Understand the fundamental building blocks of ARIMA models through interactive AR(1) and MA(1) visualizations. Compare how autoregressive models use past values versus moving average models using past errors for forecasting. Experiment with parameters to observe stationarity conditions, autocorrelation patterns, and the distinct forecasting behaviors of each model type.

SARIMA Model Visualization (Airline Passengers)

Explore Seasonal ARIMA models using the classic airline passenger dataset (1949-1960). Interactively adjust both non-seasonal (p,d,q) and seasonal (P,D,Q)ₘ parameters to understand how SARIMA captures trend and seasonality. Observe how the optimal model SARIMA(2,1,0)(1,1,1)₁₂ handles monthly patterns and forecast future passenger numbers with confidence intervals.

Machine Learning & AI

Explore interactive visualizations showcasing machine learning algorithms, neural networks, and artificial intelligence applications across various domains.

Decision Tree Regression for Time Series

Discover how Decision Trees partition feature space for time series forecasting using lagged features. Interactively adjust tree depth and forecast horizon to visualize the tree structure, decision boundaries in 2D lag space, and multi-step ahead forecasts. Understand why tree-based models struggle with trend and seasonality through recursive forecasting demonstrations.

Deep Neural Networks for Time Series

Experience how Deep Neural Networks learn complex nonlinear patterns in time series using the airline passenger dataset. Interactively configure network architecture (1-4 hidden layers), adjust neurons per layer, choose activation functions (ReLU, tanh), and control the number of lagged features (1-12 lags). Watch the model train in real-time with live loss curves, explore feature importance from learned weights, and compare DNN performance against Linear Regression benchmarks to understand when added complexity provides value.

Stock Market & Trading

Financial market visualizations including price movements, trading patterns, portfolio analysis, and risk management tools for informed investment decisions.

Miscellaneous