# Trend adjusted exponential smoothing forecasting metho ds

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Published on January 15, 2014

Author: kiranhanjar

Source: slideshare.net

## Description

A method that uses measurable, historical data observations, to make forecasts by calculating the weighted average of the current period’s actual value and forecast, with a trend adjustment added in

Quantitative Techniques in Decision Making TREND ADJUSTED EXPONENTIAL SMOOTHING FORECASTING METHOD

Defining the Method A Forecasting Model: • Predicts future levels of a variable • Can be either quantitative or qualitative There are two types of quantitative models: Time series and Causal. • Time series models see the future level of a variable as a function of time. (exponential smoothing, weighted moving average models) • Causal models, on the other hand, see the future level of a variable as a function of something other than time. (regression models)

Exponential Smoothing • Quantitative forecasting method • Most widely practiced method of time series forecasting • Weighted average of two variables Ft+1 = α Dt + (1 – α )Ft Where… Ft +1 = Dt = Ft = α = forecast for next period actual value for present period previously determined forecast for present period weighting factor (between 0 and 1)

Adjusted Exponential Smoothing Forecasting Method • A method that uses measurable, historical data observations, to make forecasts by calculating the weighted average of the current period’s actual value and forecast, with a trend adjustment added in. When to Use the Method • Preferred Scenario: – When a trend is present • Good Scenario: – When there’s a cyclical or seasonal pattern

Adjusted Exponential Smoothing: Where… Tt +1 = = Tt = β = AFt+1 = Ft+1 + Tt+1 β (Ft+1 – Ft ) + (1 - β ) Tt trend factor for the next period trend factor for the current period smoothing constant for the adjustment factor (just add a trend adjustment factor) Points to Consider: • To start, pick an unadjusted forecast • In period 1, trend equals 0

Problem: 2005 U.S. Housing Starts (monthly) Given the following data for 9 months, compute trend adjusted smoothing average. Use α = 0.3 (weighting factor), β = 0.6 (smoothing constant for the trend adjustment factor) Period Month Actual Demand Unadjusted forecast Trend Adjusted forecast 1 Jan 2188 2100 0 2 Feb 2228 2126 16 2142 3 Mar 1833 2157 25 2182 4 Apr 2027 2060 -48 2011 5 May 2041 2050 -25 2025 6 Jun 2065 2047 -12 2036 7 Jul 2062 2053 -1 2051 8 Aug 2038 2055 1 2056 9 Sep 2108 2050 -3 2047

Calculations: Feb : unadjusted forecast: Ft+1 = α Dt + (1 – α )Ft = 0.3*2188 + 0.7*2100 = 2126 Trend factor for the next period: Tt +1 = β(Ft+1 – Ft ) + (1 - β)Tt = 0.6*(2126 – 2100) – 0.4*0 = 16 Trend Adjusted Exponential Smoothing: AFt+1 = Ft+1 + Tt+1 = 2126 + 16 = 2142

Housing starts 2200 Actual demand Unadjusted forecast 2100 Adjusted forecast 2000 1900 1800 Jan Feb Mar Apr May Jun Months Jul Aug Sep

• Problem :2 Intel quarterly sales revenue. Given the following data for 4 months, compute trend adjusted smoothing average. Use α = 0.3 (weighting factor), β = 0.6 (smoothing constant for the trend adjustment factor) Quarter Month ending Sales revenue (actual) in \$ Unadjusted forecast(α=o.4) in \$ Trend (β=0.7) 1 Dec-04 110,448 105,000 0 2 Mar-05 105,707 3 Jun-05 115,552 4 Sep-05 111,396 5 Dec-05 Adjusted forecast (AFt) in \$

Solution Quarter Month ending Sales revenue (actual) in \$ Unadjusted forecast(α=o.4) in \$ Trend (β=0.7) in \$ Adjusted forecast (AFt) in \$ 1 Dec-04 110,448 105,000 0 2 Mar-05 105,707 107,179 1525 108,705 3 Jun-05 115,552 106,590 45 106,636 4 Sep-05 111,396 110,175 2523 112,698 5 Dec-05 110,663 1099 111,762

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