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Stat-TimeSeries.md

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Time Series Analysis

Overview

  • Univariate analysis: popular univariate methods

    • exponential smoothing
    • ARIMA (Autoregressive Integrated Moving Average)

  • Causal Modeling

    • assumption risk: future ~ past
    • causal (predictor) variables
      • improving accuracy
      • understanding which most influence
    • ROMI (Return on Marketing Investment): market response/marketing mix modeling
    • specialized regression procedures
      • transfer function models
      • ARMAX
      • dynamic regression

  • Multiple time series - frequently used approaches

    • Vector Autoregresion (VAR)
    • Vector error correction model (VECM)
    • State space framework

  • Other models

    • panel model
      • category - level analysis
      • handy when data are infrequent
    • longitudinal analysis
      • analysis of data w/ many time periods (e.g., > 25)
      • confusingly used term $\to$
        • panel modeling w/ a small number of periods
        • repeated measures, growth curve analysis or multilevel analysis
    • popular: structural equation modeling (SEM)
    • structural analysis
      • analyzing the expected length of time until one/more events happen
      • duration analysis in economics
      • event history analysis sociology
    • clusters of volatility
      • structural changes within the series and model parameters vary across time
      • models
        • breakpoint tests and models, e.g., state space, swithcing regression
        • GARCH (Generalized Autoregressive Conditional Heteroscedasticity) & ARCH
        • MGARCH (Multivariate GRACH): two or more series to analyze jointly
    • Non-parametric econometrics
      • time series and longitudinal data
      • feasible and useful
      • hard to interpret
    • machine learning
      • ANN, DL, ...
      • hard to interpret