TIME SERIES
Time series are sequences of data points collected or recorded at specific time intervals, typically ordered chronologically. Time series analysis focuses on understanding patterns, trends, seasonality, and other temporal dynamics within the data, allowing for forecasting and decision-making based on historical behavior
Introduction
What is a time series?
A time series is a sequence of observations recorded over time. Learn its components, how to decompose it, and why standard statistical methods are not directly applicable.
Stationarity in time series
Stationarity is the key assumption behind most time series models. Learn how to detect and fix non-stationarity using formal tests and transformations.
ACF and PACF
The ACF and PACF are the primary tools for identifying the order of AR and MA components in time series models.
Time series models
Autoregressive model (AR)
Explore the Autoregressive (AR) model, a key concept in time series analysis used for modeling and forecasting data by regressing the variable onto its own lagged values.
Moving average model (MA)
Learn about the Moving Average (MA) model, a fundamental concept in time series analysis used to capture the impact of past error terms on current values.
Autoregressive moving average model (ARMA)
Explore the ARMA model, which integrates both autoregressive and moving average components to model and forecast stationary time series data.
ARIMA model
ARIMA extends ARMA to non-stationary series by differencing the data d times before fitting an ARMA(p,q) model.
SARIMA model
SARIMA adds seasonal AR, differencing and MA terms to ARIMA, making it the standard model for time series with repeating seasonal patterns.
Exponential smoothing
Exponential smoothing is a family of forecasting methods that assign exponentially decreasing weights to past observations, balancing recency with history.
Holt-Winters method
Explore the Holt-Winters method, a triple exponential smoothing technique that models level, trend and seasonality for accurate seasonal forecasting.
ARIMAX model
ARIMAX extends ARIMA by including external (exogenous) variables as regressors, combining the autocorrelation structure of ARIMA with the explanatory power of regression.
Kalman filter
The Kalman filter estimates unobservable states from noisy measurements by alternating between prediction and update steps, optimal under Gaussian assumptions.
GARCH model
GARCH models time-varying conditional variance (volatility clustering) in financial returns, extending ARCH with a more parsimonious parameterization.
EGARCH model
EGARCH extends GARCH to capture asymmetric volatility: negative shocks increase variance more than positive shocks of the same size, a key feature of equity markets.
VAR model
VAR (Vector Autoregression) extends AR to multiple time series simultaneously, capturing cross-variable dynamics and enabling impulse response analysis.