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)