Time Series Basics

Time series can have three components

  • Trend
  • Seasonality
  • Random fluctuations (noise)

Stationary Time series

  • Mean, Variance, Covariance remains constant over time (needs to remove trend, seasonal components) from time series as certain model works on Stationary time series
  • To make series stationary , take log, differencing (or both), square root, log transformation

Model that requires Time series has to be stationary

  • AR(p) — p is number of last lag’s data value taken in account for predicting
  • MA(q) — q is number last lag’s error taken into account predicting
  • ARIMA (p,d,q) — d for differencing to remove trend and seasonal effect
  • SARIMA (p,d,q)(P,D,Q)s — s is frequency for seasonality

Model requires to know value of p and q that is determined by plotting

  • ACF — Auto Correlation Plot (used for MA model to decide for q value, the number from which correlation cuts-off to very insignificant value)
  • PCF — Partial Correlation Plot (used for AR model to decide for p value, the number from which correlation cuts-off to very insignificant value)

Models that Doesn’t assume that time series stationary

  • Holt models (models around level (mean) alpha, trend (beta)) — when time series has no seasonal component
  • Holt Winters model (same as above + Seasonal component (gamma)
  • ARCH model (based on Variance)

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