Time Series Analysis:Classical Approach
What is Time Series
A time series is a set of observed values, such as production or sales data, for a sequentially ordered series of time periods. A time series is portrayed graphically by a line graph, with the time periods represented on the horizontal axis and time series values represented on the vertical axis. Time series analysis is the procedure by which the time-related factors that influence the values observed in the time series are identified and segregated. Once identified, they can be used to aid in the interpretation of historical time series values and to forecast future time series values.
The classical approach
The classical approach to time series analysis identifies four such influences, or components:
1. Trend (T ): The general long-term movement in the time series values over an extended period of years.
2. Cyclical fluctuations (C): Recurring up and down movements with respect to trend that have a duration of several years.
3. Seasonal variations (S): Up and down movements with respect to trend that are completed within a year and recur annually.
4. Irregular variations (I ): The erratic variations from trend that cannot be ascribed to the cyclical or seasonal influences.
The model underlying classical time series analysis is based on the assumption that for any designated period in the time series the value of the variable is determined by the four components defined above, and, furthermore, that the components have a multiplicative relationship. Thus, where Y represents the observed time series value,
Y = T × C × S × I
The model represented is used as the basis for separating the influences of the various components that affect time series values.