Using a Centered Moving Average to Extract the Seasonal ...

Using a Centered Moving Average to Extract the Seasonal ...

Using a Centered Moving Average to Extract the Seasonal Component of a Time Series If we are forecasting with say, quarterly time series data, a 4-period moving average should be free of seasonality since it always includes one observation for each quarter of the year Suppose we have a quarterly time series X1, X2, X3, . . . , Xn The first value that can be calculated for this series by a 4-period MA process would use observations X1, X2, X3, and X4. Notice that our first 4-period average has a center between quarter 2 and quarter 3. Hence we will designate it X*2.5. Thus we have: X1 X 2 X 3 X 4 X * 2 .5 4 The next value is: X2 X3 X4 X5 X * 3 .5

4 For the series X1, X2, X3, . . . , Xn, the formula is1 : Xt 1 Xt Xt 1 Xt 2 X * t .5 4 This algorithm gives us a series that is free of seasonality. Alas, the location of the values of this series do not correspond to the original series. (1) We can correct this problem with a centered moving average If we average adjacent pairs of X*ts, we obtain a series that is free of seasonality and is aligned correctly with our original series To get a 4-period moving average that is

centered at quarter 3 (designated by X3**), take the average of X2* and X3*: X 3 ** X 2.5 * X 3.5 * 2 The general formula is: Xt * * Xt .5 * Xt .5 * 2 (2) Combining equations (2) and (3), the series Xt** can be expressed by a weighted moving average: Xt 2 2 Xt 1 2 Xt 1 Xt 2 Xt * * 8

The seasonal index (St) can be computed by dividing Xt by Xt**. That is: Xt St Xt * * Example: Quarterly product sales t 1 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5

9 10 11 Xt 897 476 Xt* Xt** St 573.35 0.656 588.625 0.865 599.125 1.614

585.75 0.903 558.125 0.729 532.5 0.697 505.125 1.75 564.2 376 582 509 595.25 967 603 529

568.5 407 547.75 371 517.25 884 407 310 Notice we lose 2 data points at the beginning of the series, and 2 at the end. For monthly data, we would lose a total of 12 data points.

Recently Viewed Presentations

  • SPINAL CORD INJURY - Weebly

    SPINAL CORD INJURY - Weebly

    Spinal shock is a sudden depression of reflexes below the spinal cord injury. This happens because the spinal cord below the level if injury is damaged and neurologic messages cannot be transmitted down the spinal cord. T.W.'s lower half cannot...
  • Bearings, Seals, and Greases - Cengage

    Bearings, Seals, and Greases - Cengage

    Bearings, Seals, and Greases Chapter 60 Objectives Understand terms that relate to wheel bearings Select the correct grease to use for a particular application Describe the various wheel and axle bearing arrangements Service wheel bearings on front and rear axles...
  • Poetry Unit

    Poetry Unit

    What are Haiku Poems? Topic 2 - $200 Answer. Click to return to Jeopardy Board. Poetry that represents meaning not only by the way the words sound but how they look. The print of the poem itself takes shape as...
  • Ch 29 The Rise of Modernism! Art of

    Ch 29 The Rise of Modernism! Art of

    Impressionism! It was a shifting and nebulous movement; exhibited together in the 1870s and 1880s. A hostile critic labeled the movement "Impressionism" in response to the painting "Impression: Sunrise" by Claude Monet. The term Impressionism had been used before to...
  • MLA 8th Edition Formatting and Style Guide Purdue

    MLA 8th Edition Formatting and Style Guide Purdue

    Quoting more than four lines of prose. In-text example: Nelly Dean treats Heathcliff poorly and dehumanizes him throughout her narration: They entirely refused to have it in bed with them, or even in their room, and I had no more...
  • Setup Instructions - Monroe Library, Loyola University New ...

    Setup Instructions - Monroe Library, Loyola University New ...

    Register your clicker by tapping the . Add a Clicker . option on your . Profile. screen and entering your 8-character clicker ID. TIP: Use your registered clicker or REEF Polling to respond to questions. Either way, if you have...
  • Risk assessment and control of risks

    Risk assessment and control of risks

    Mandatory risk assessments for Secondary and Primary School science experiments: Let RiskAssess help you! Phillip Crisp and Eva Crisp * * * * CURRENT LAW Occupational Health & Safety Act 2004 Persons who control or manage matters that give rise...
  • Welcome Year 9 - STEM

    Welcome Year 9 - STEM

    A basic cake design with no reference to brief of adapting a traditional cake using healthy or local ingredients. Reference to cake making method. A medium skilled cake design, some adaptations to traditional recipes. Theme of cake relates to brief....