Time Series Analysis

1. Time Series Analysis Whiteside

2. Pupose • To identify the components of variation in the time series • Components • Secular trend • Cyclical variation • Seasonal variation • Residual or error variation

3. Secular trend • Over the long term, is the series changing on average • “long term” is relative to the time period considered • How? • Increase vs. decrease • Linear? Faster? Slower? • exponential • other

4. Cyclical variation • Undulating, wave-like change around the trend • In business data, cyclical variation is tied to cycles of the economy as a whole • Economic and financial data is usually cyclical • Cycles can be several months to several years in length • Peaks and troughs are unpredictable

5. Seasonal variation • Repeating patterns within a year • Seasonal variation is predictable • Seasonal variation is measured by seasonal index numbers • A season can be a month, a quarter, a week, etc.

6. Erratic or residual variation • Remaining variation after other components • Unpredictable, usually unexplainable

7. Identifying components - superimpose • Raw data • Trend equation • Moving average

8. Analysis • Trend - Recognized by the plot of “expected” model values • Cycle - Recognized by the difference between the trend and the moving average • Seasonality - Recognized by the difference between the raw data and the seasonality

9. Summary • Series may have none to all of components • Predictable series are dominated by trend and/or seasonality • Unpredictable series are dominated by cycle and/or erratic variation

10. Using NCSS decompositon • Trend - linear is the only choice, • Seasonality - seasonal index numbers are plotted and provided numerically • Cycle - optional, must be input for true forecasts, plots available