Time Series

Description:

• Discrete Stochastic Process
• Has:
  • $Y$ is the actual time series
  • $T$ is the trend series
  • $S$ is the seasonal component
  • $R$ is the random component (can be assumed to be negligible)

Time Series Models:

• A time series model can be expressed as some combination of these four components.

Types of models:

• 2 models that are commonly associated with time series:
  • Additive Model
  • Multiplicative Model
• The multiplicative model is better than the additive model for forecasting when the Time Series Trend is increasing or decreasing over time
• The additive model suffers from the somewhat unrealistic assumption that the components are independent of each other.
• In most instances, movements in one component will have an impact on other components.
• The multiplicative model is often preferred.
  • It assumes that the components interact with each other and do not move independently.
• Since extrapolation is based on historical data alone, and does not include effects of developments, it can be used for short-term forecasts only for specific areas, where no untypical developments are expected.

Components

• Time Series Trend
• Seasonal Variation
• Cyclical Variation
  • Many variables often exhibit a tendency to fluctuate above and below the long-term trend over a long period of time.
  • They cover much longer time periods than do seasonal variations.
• Random Variation
  • Caused by unusual and unexpected occurences producing movements which have no discernible pattern.
  • These movements are unique and unlikely to reoccur in similar fashion.
  • They can be caused by events such as wars, floods, earthquakes, political elections, or oil embargoes.

Deseasonalization