modeling seasonal series

modeling seasonal series - Time Series 4 Modeling Seasonal...

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1 Seasonal series 1 Time Series 4: Modeling Seasonal Series Section 16.7 and elsewhere Seasonal series 2 Decomposition A long-popular method for modeling time series. Assumption: the series has components of behavior that can be estimated separately. We already discussed trend fitting, now we take on seasonality.

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2 Seasonal series 3 Decomposition Models An additive approach assumes the series is a sum of its components Y t = TR t + S t + E t A multiplicative model assumes the series is a product of the components Y t = TR t S t E t E t is the error or irregular component Seasonal series 4 The Seasonal Component The seasonal factors are a set of numbers that reflect the upswings and downswings in a series that tend to repeat over and over Called “seasonals” because the pattern usually follows the calendar (months, quarters, weeks or days)
3 Seasonal series 5 Example Series NAICS series 4411 from Economagic; monthly sales at all US automobile dealers, in millions of \$. January 1992: \$25.8 billion Peak: July 2005 ( \$75.4 billion ). Dropped to \$40 billion in 2008. Seasonal series 6 US Auto Dealer Sales 20000 40000 60000 80000 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Month Sales (Million\$) March Car Sales: NAICS 4411

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4 Seasonal series 7 Additive or Multiplicative? Additive: seasonal effect is a constant amount . March was often \$4 billion higher than monthly average for the year. Multiplicative: seasonal is a percentage . March sales were usually 8% higher than the typical month. Multiplicative approach used most often. Seasonal series 8 Seasonal adjustment h For monthly data, we have S 1 , S 2 , …, S 12 h S t = S 1 if January, = S 2 if February h In a multiplicative model, adjust by Y t / S t h In an additive model, adjust by Y t - S t
5 Seasonal series 9 Seasonals for car sales From a multiplicative model. Low: S 1 = 0.892 means High: S 8 = 1.083 means Closest to 1.00 = Month Factor January 0.892 February 0.931 March 1.079 April 1.024 May 1.073 June 1.070 July 1.066 August 1.083 September 0.979 October 0.982 November 0.899 December 0.923 Seasonal series 10 Adjustment example Comparing August to September: Month Sales Factor Adjusted Aug-04 65267 1.083 60250.4 Sep-04 63586 0.979

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6 Seasonal series 11 Estimating seasonal factors Will illustrate with quarterly data (need only four factors) since too much detail with
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modeling seasonal series - Time Series 4 Modeling Seasonal...

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