Time Series



    Strong stationarity

    Consistent = same width (window) have the same distribution.

    If it is consistent => strong stationarity.

    Note: strong stationarity does not imply weak stationarity.

    Weak stationarity

    Don't require to be consistent, but mean, variance, and autocorrelation depends only on difference in time, not location in time.


    We can differentiate two categories:

    1. Statisticals based: - Exponential Smoothing (simple holt, winters-holt) - ARIMA - Seasonal ARIMA - Dynamic Linear Models - ARCH/GARCH (Volatility forecasting) - Vector AR (VAR)
    2. Machine learning based: - Autoregressive Neural Networks - Fourier Transforms - TBATS - Prophet - LSTM - Bootstrapping and Bagging - Time Series Clustering

    Stationary models

    • White noise
    • Autoregressive (AR)

    Non-stationary models

    • Moving average (MA), careful it's different than rolling mean (also called moving average)
    • ARIMA (-) asumption that it is stationary (no trend, no seasonal component)
    • SARIMA (-) limited to one seasonality effect, (-) SARIMAX is not well-suited to large seasonal patterns. setting S=365 would probably take a lot of memory and computation time, and would not necessarily even give good results. source
    • Prophet (+) handle piecewise trends, unexpected events (e.g. holiday)