Time Series Analysis

Trend, seasonality, cyclicity and noise; additive versus multiplicative models.

Strict and weak stationarity, why it matters for modelling, and differencing and transformation to achieve it.

Assumes: Components of a Time Series

ADF, KPSS and Phillips–Perron tests, their opposite null hypotheses, and interpreting conflicting results.

Assumes: Stationarity · The Hypothesis Testing Framework

Autocorrelation and partial autocorrelation computed by hand, and reading order off the plots.

Assumes: Stationarity

AR(p) structure, the Yule–Walker equations, stationarity conditions and parameter estimation.

Assumes: ACF and PACF

MA(q) structure, invertibility, and the duality between AR and MA representations.

Assumes: Autoregressive Models

Combining AR and MA, integrating for non-stationarity, and the Box–Jenkins model selection procedure.

Assumes: Moving Average Models

SARIMA notation, seasonal differencing, and SARIMAX with external drivers.

Assumes: ARMA and ARIMA

Simple exponential smoothing, the smoothing constant, and worked forecast recursions.

Assumes: Components of a Time Series

Adding trend and seasonal components, the ETS taxonomy, and damped trends.

Assumes: Exponential Smoothing

Classical decomposition, X-11, STL and their robustness to outliers.

Assumes: Holt and Holt–Winters

MAE, RMSE, MAPE, sMAPE and MASE; rolling-origin cross-validation and why random k-fold is invalid here.

Assumes: ARMA and ARIMA

Vector autoregression, testing predictive causality, and the limits of the Granger notion.

Assumes: Forecast Evaluation and Backtesting

The state-space formulation, the Kalman filter update derived, and a full numeric filtering pass.

Assumes: Granger Causality and VAR · Hidden Markov Models

Windowing for supervised learning, LSTM and TCN forecasters, N-BEATS, and transformer-based models.

Assumes: Forecast Evaluation and Backtesting · Long Short-Term Memory