APSY6423/MESA6420 – Intermediate Statistics Fall 2025

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APSY6423/MESA6420 – Intermediate Statistics Fall 2025

ARIMA stands for AutoRegressive Integrated Moving Average, a class of statistical models used for analyzing and forecasting time series data. The model has three key components represented by the notation ARIMA(p,d,q): the autoregressive term (p) uses past values to predict future values, the integrated term (d) represents the number of times the data needs to be differenced to achieve stationarity, and the moving average term (q) uses past forecast errors to improve predictions. ARIMA models are particularly effective for non-stationary time series data that exhibit trends or patterns over time. The autoregressive component captures the relationship between an observation and a lagged observation, while the moving average component models the dependency between an observation and residual errors from past predictions. Differencing removes trends and seasonal patterns, transforming the data into a stationary series where statistical properties remain constant over time. Model selection typically involves examining ACF and PACF plots, comparing information criteria like AIC or BIC, and validating that residuals resemble white noise. ARIMA models are widely used in economics, finance, and forecasting applications because they balance flexibility with interpretability and can capture complex temporal dependencies in data.

APSY6423/MESA6420 – Intermediate Statistics Fall 2025

Samuel Alberto Mateo Bonilla Franco Nicolas Zapata Clavijo