PPT12 Time Series Decomposition F2010

PPT12 Time Series Decomposition F2010 - McGill University...

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McGill University Advanced Business Statistics MGSC-272
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Time Series Decomposition
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Decomposition Models Y t = data at time t T t = Trend C t = Cyclical component S t = Seasonal Component R t or I t = Random (Irregular) Component Multiplicative Model Y t = T t x C t x S t x Rt Additive Model Y t = T t + C t + S t + R t
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Multiplicative Model
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Example: Classical Time Series Components
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Data USA Clothing Store Sales ($1,000,000) 1997-2001
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The trend line: Scatter Diagram
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Time Series with Linear Trend: Line Plot
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Table showing Y t and T t
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T = 1642.92 + 40.31t Detrended Series
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Original vs Detrended Series Y = T x C x S x R Y/T = C x S x R
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Moving Averages 1373 1676 1714 2461 1545 1902 1935 2673 1569 1888 2045 2751 1674 1939 2188 2864 1780 2061 2205 3081 7224 7396 7622 Problem: The data are not “centered”. This means that the 4-quarter totals do not correspond to the same time scale as the original data. Thus, for example, the first total of 7224 falls halfway between the values of 1676 and 1714. If each original data value corresponds to the median point in time of the corresponding quarter, then 1373 corresponds to Feb 14, 1676 corresponds to May 15, 1714, corresponds to Aug 15, etc.
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PPT12 Time Series Decomposition F2010 - McGill University...

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