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Time Series Analysis

Time Series Analysis. Whiteside. Pupose. To identify the components of variation in the time series Components Secular trend Cyclical variation Seasonal variation Residual or error variation. Secular trend. Over the long term, is the series changing on average

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Time Series Analysis

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  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

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