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trend fitting noteshells

# trend fitting noteshells - Time Series 2 Trend Fitting...

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1 Time Series 2 -- Trends 1 Time Series 2: Trend Fitting Sections 16.2-16.4 Time Series 2 -- Trends 2 16.2 Component models head2right Many forecasting techniques assume that behavior observed in the past will be repeated in the future. head2right A decomposition approach assumes the series has several components of behavior that can be estimated separately, then combined together for forecasting. head2right These components were usually assumed to be trend, seasonality and the (business) cycle.

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2 Time Series 2 -- Trends 3 The three major components 1. Trend (TR): a long-term pattern of upward or downward movement 2. Seasonality (S): a regular pattern of fluctuations that occurs within each year of data 3. Cycle (C): a medium-term pattern of up and down swings consisting of prosperity, recession, depression and recovery Time Series 2 -- Trends 4 Additive or Multiplicative? An additive approach assumes the series is a sum of its components Y t = TR t + S t + C t + E t A multiplicative model assumes the series is a product of the components Y t = TR t S t C t E t E t is the error or irregular component
3 Time Series 2 -- Trends 5 Cycles in unemployment rates Apr-06 Dec-97 Aug-89 Apr-81 Dec-72 Aug-64 Apr-56 12 10 8 6 4 2 0 Month Percent Oct-09 Jun-03 Jun-92 Dec-82 May-75 Aug-71 May-61 Jul-58 Sep-54 Oct-49 US Unemployment rates since 1948 Time Series 2 -- Trends 6 A common simplification head2right In order to estimate the Cycle, we need to see several periods of peak-trough-peak behavior. head2right Since a cycle often lasts 7-10 years, this requires a long series, which we may not have. head2right We often find that the length of the cycle is quite variable, which adds further difficulty. head2right You often see Cycle and Error combined, yielding a simpler model.

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4 Time Series 2 -- Trends 7 Further simplification head2right If a series is not seasonal, perhaps because it is annual, the only components of behavior it would have is trend and "other". head2right To see what type of underlying pattern is present, we often use a smoother to filter out irregularities.
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trend fitting noteshells - Time Series 2 Trend Fitting...

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