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Time Series Analysis Whiteside

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Pupose zTo identify the components of variation in the time series zComponents ySecular trend yCyclical variation ySeasonal variation yResidual or error variation

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Secular trend zOver the long term, is the series changing on average ylong term is relative to the time period considered zHow? yIncrease vs. decrease yLinear? Faster? Slower? xexponential xother

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Cyclical variation zUndulating, wave-like change around the trend zIn business data, cyclical variation is tied to cycles of the economy as a whole zEconomic and financial data is usually cyclical zCycles can be several months to several years in length zPeaks and troughs are unpredictable

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Seasonal variation zRepeating patterns within a year zSeasonal variation is predictable zSeasonal variation is measured by seasonal index numbers zA season can be a month, a quarter, a week, etc.

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Erratic or residual variation zRemaining variation after other components zUnpredictable, usually unexplainable

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Identifying components - superimpose zRaw data zTrend equation zMoving average

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Analysis zTrend - Recognized by the plot of expected model values zCycle - Recognized by the difference between the trend and the moving average zSeasonality - Recognized by the difference between the raw data and the seasonality

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Summary zSeries may have none to all of components zPredictable series are dominated by trend and/or seasonality zUnpredictable series are dominated by cycle and/or erratic variation

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Using NCSS decompositon zTrend - linear is the only choice, zSeasonality - seasonal index numbers are plotted and provided numerically zCycle - optional, must be input for true forecasts, plots available

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