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 h Many forecasting techniques assume that behavior observed in the past will be repeated in the future. h A decomposition approach assumes the series has several components of behavior that can be estimated separately, then combined together for forecasting. h 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
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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 h In order to estimate the Cycle, we need to see several periods of peak-trough-peak behavior. h Since a cycle often lasts 7-10 years, this requires a long series, which we may not have. h We often find that the length of the cycle is quite variable, which adds further difficulty. h You often see Cycle and Error combined, yielding a simpler model.
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4 Time Series 2 -- Trends 7 Further simplification h If a series is not seasonal, perhaps because it is annual, the only components of behavior it would have is trend and "other". h To see what type of underlying pattern is present, we often use a smoother to filter out irregularities. h
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This note was uploaded on 02/14/2011 for the course QMB 3250 taught by Professor Thompson during the Spring '08 term at University of Florida.

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

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