Microsoft PowerPoint - Forecasting _with_Decomposition_2014x.pptx

Size: px

Start display at page:

Download "Microsoft PowerPoint - Forecasting _with_Decomposition_2014x.pptx"

案阳
5 years ago
Views:

1 Trend, Seasonality, Cycles Seasonality 是預測對象在各個週期都重複出現的變化型態週期 : 一年一月一週產品銷售量的 seasonality 通常是因氣候變化風俗習慣社會制度等因素而產生銷售通常同時受到 trend, seasonality, cycle 的影響評量長期發展趨勢時, 可忽略 seasonality 變化, 細部預測則必須納入所有因素影響 1 Seasonality 週期 : 年 (4,12) 月(30) 週(7) Simple Average Method week1 week2 week3 average seasonal factor Tues Wed Thur Fri Sat Sun Mon Overall Average =

2 Centered Moving Averages 以當期為基準, 將前後期併入平均值計算, 以抵銷季節性的影響 For weekly data: CMA t =(Y t-3 +Y t-2 +Y t-1 +Y t +Y t+1 +Y t+2 +Y t+3 )/7 For monthly data: MA t =(Y t-6 +Y t-5 + +Y t +Y t+1 + +Y t+5 )/12 Need adjustment if the number of periods is even. CMA t =(MA t +MA t+1 )/2 3 Seasonal Index Based on CMA Period Season Actual Centered MA Seasonal Factor 1 Tues 67 2 Wed 75 3 Thur 82 4 Fri Sat Sun Mon Tues Wed Thur Fri Sat Sun Mon Tues Wed Thur Fri Sat Sun Mon 50 98/71.857= seasonal index =1.2383/ =

I. Forecasting Trend and Seasonality Preparation: 由資料變化型態主觀判斷是否同時有 trend 與 seasonality 的影響 Approach 1: 運用可直接處理 seasonality 的預測方法 Multiple Regression, Holt-Winters Smoothing Approach 2: Time Series

3 I. Forecasting Trend and Seasonality Preparation: 由資料變化型態主觀判斷是否同時有 trend 與 seasonality 的影響 Approach 1: 運用可直接處理 seasonality 的預測方法 Multiple Regression, Holt-Winters Smoothing Approach 2: Time Series Decomposition 1. 根據數個週期的數據估算 seasonal factors 2. 將原始數據 deseaonalized 3. 以迴歸分析 deseaonalized 數據的趨勢並進行預測 4. 將預測再乘上 seasonal factors 的影響 5 Trend and Seasonal Factors Additive: trend+seasonal Multiplicative: trend seasonal 第 1 季第 2 季第 3 季第 4 季合計 / / / /250 次年預測 1100 第 1 季 =220 第 2 季 =385 第 3 季 =330 第 4 季 =

Decomposition Using Least Square Regression 1. Decomposition Calculate the seasonal factor. ( y )/3 1 y5 y9 SF y 1 0.816 SF 2 =1.098, SF 3 =0.972, SF 4 =1.115 Deseasonalize the demand.

4 Decomposition Using Least Square Regression 1. Decomposition Calculate the seasonal factor. ( y )/3 1 y5 y9 SF y SF 2 =1.098, SF 3 =0.972, SF 4 =1.115 Deseasonalize the demand. y i = y i / SF k Quarter (X) Sales (Y) Deseasonalized Develop a regression model from the deseasonalized data. Y = a + bx = x 2. Forecast Project the future using the regression model. Multiply the seasonal factor. Y = = Y=Y 0.816=

5 Decomposition Using Centered Moving Averages For quarterly data: MA t =(Y t-2 +Y t-1 +Y t +Y t+1 )/4 抵銷季節性的影響 For monthly data: MA t =(Y t-6 +Y t-5 + +Y t +Y t+1 + +Y t+5 )/12 Need adjustment if the number of periods is even. CMA t =(MA t +MA t+1 )/2 9 A Different Viewpoint of Decomposition 取平均值或中位數 Moving CMA Y/CMA Seasonal X Y Average Index Adjusted Deseasonalized 調整季節因素使平均值為

7000 6000 5000 4000 y = 395.55x + 263.63 R² = 0.9471 3000 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 y = 342.18x + 554.99 R² = 0.

6 y = x R² = y = x R² = Example: Light Truck Sales /3 87/3 88/3 89/3 90/3 91/3 92/3 93/3 94/3 95/3 96/3 97/3 98/3 99/3 00/3 March 1986 June 2000 銷售具有季節性與趨勢的變化, 每年第二季與第三季銷售最強勁 12 6

Deseasonalize the Demand seasonal factor= 計算各年分同一季 SF 的中位值, 除以整體平均值 March 86: 213.831/1.075=198.

7 Deseasonalize the Demand seasonal factor= 計算各年分同一季 SF 的中位值, 除以整體平均值 March 86: /1.075= Estimating Trend of Deseasonalized Data 2 次曲線的趨勢 Y= X+ 2 X y = x x R² =

64 Decomposition x=59 y = 0.1031x 2 + 1.235x + 219.19 = 652.

8 Forecasting Future Sales (Sep, 2000) Winters Triple Exponential Smoothing F=630.37, T=9.56, S=0.92 Forecast=(F+T) S= Decomposition x=59 y = x x = SF 3 =0.88 Forecast= Decomposition Using Minitab Note: Minitab 的分解法只能以線性趨勢分析 16 8

9 II. Modeling Cycles 銷售資料可能出現無法用趨勢或季節因素解釋的變化 Cycles 是指經濟景氣對銷售的影響, 沒有固定週期, 沒有固定的幅度, 影響遍及各種產品 Cycles 的轉折點是預測的難題 17 Time-Series Decomposition Model 假設銷售量受到下列因素影響 Y=T S C I Y: demand to be forecast T: long term trend S: seasonal indices C: cyclical factor I: irregularities or random variations ( 無法預測 ) 18 9

10 1. 季節因素影響顯著 2. 前半期受景氣影響 3. 後半期受景氣或趨勢影響 19 Centered Moving Averages Step 1: CMA removes short term fluctuations. For monthly data: MA t =(Y t-6 +Y t-5 + +Y t +Y t+1 + +Y t+5 )/12 Need adjustment if the number of periods is even. CMA t =(MA t +MA t+1 )/2 Jan-72 Feb-72 Mar-72 Apr-72 May-72 Jun-72 Jul-72 Aug-72 Sep-72 Oct-72 Nov-72 Dec-72 Jan MA 7 MA

11 21 去除季節因素與隨機波動後的銷售變化 22 11

12 Estimating Seasonal Indices 實際銷售抵銷季節性影響後的銷售 Step 2: Seasonal Factor SF t =Y t / CMA t Seasonal Index = average of SF t for the same month January: 071 April: 1.13 July: 1.13 October: 1.10 February: 0.74 May: 1.18 August: 1.11 November: 0.90 March: 1.00 June: 1.18 September: 1.06 December: 0.76 Deseasonalized demand=actual demand / seasonal index 23 Estimating the Long Term Trend Step 3: Regression: CMA t =a+b t + a=134.8, b= CMAT t = t 24 12

13 Estimating the Cyclical Factor Step 4: 針對過去資料計算 CF t =CMA t / CMAT t 抵銷季節性影響後的銷售, 再去除趨勢的影響

14 Overview of Business Cycles Business cycles 描述經濟活動強弱起伏, 景氣好的時候, 銷售會超過市場趨勢與季節性變化的預期幅度

15 Predicting the Cyclical Factor Step 1: 運用領先指標或時間數列方法預測未來的 CF t 29 Making Decomposition Forecast Step 2: Y=T S C I Y t =CMAT t SI t CF t (I=1) 30 15

估算 seasonal indexes 2. 針對去季節化的銷售數據, 估算 trend 3.

16 Forecast 31 Summary 繪圖觀察銷售量是否同時受到多種因素的影響 Time series decomposition 將數據分解以估算 trend, seasonality, cycles 的影響幅度 1. 估算 seasonal indexes 2. 針對去季節化的銷售數據, 估算 trend 3. 將去季節化的數據與 trend 估計值相除, 估算 Cycle Factors 需運用景氣領先指標或其他方法預測 cycles 的未來變化預測未來銷售時, 再將三者因素重組以進行預測 32 16

untitled

untitled 1 2 3 4 5 A 800 700 600 500 400 300 200 100 0-100 10000 9500 9000 8500 8000 7500 7000 6500 6000 2006.1-2007.5 A 1986.1-1991.12 6 7 6 27 WIND A 52.67 2007 44 8 60 55 50 45 40 35 30 25 20 15 10 2001-05 2002-02