Time Series Analysis

AR, MA, ARIMA models, forecasting, stationarity, and seasonal decomposition.

Key Concepts

• •Stationarity: definition, tests (ADF), and differencing to achieve stationarity
• •Autoregressive (AR) models: AR(p) with autocorrelation structure
• •Moving average (MA) models: MA(q) with partial autocorrelation properties
• •ARMA and ARIMA models: combining AR and MA with differencing
• •ACF and PACF: using correlograms for model identification
• •Model estimation: MLE and least squares for time series parameters
• •Forecasting: point forecasts and prediction intervals
• •Exponential smoothing: simple, double, and Holt-Winters methods
• •Seasonal models: SARIMA for data with periodic patterns
• •Model selection: AIC, BIC, and out-of-sample forecast evaluation

Study Tips

• 1.Learn to read ACF and PACF plots for model identification before diving into estimation.
• 2.Practice differencing non-stationary series and verifying stationarity.
• 3.Work through ARIMA(p,d,q) identification examples step by step.
• 4.Compare exponential smoothing with ARIMA forecasts on practice data.
• 5.Understand the theory behind each model before focusing on calculations.

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