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Formulas

Formulas. Simple linear regressions, Multiple and correlation. Korelasi. Regresi Linear Berganda. Simple Linear Regression. Musiman dengan regresi dummy. Trend value at period 3, T 3. Step 1: Isolating the Trend Component. Smooth the time series to remove random effects and seasonality.

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Formulas

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  1. Formulas Simple linear regressions, Multiple and correlation

  2. Korelasi

  3. Regresi Linear Berganda

  4. Simple Linear Regression

  5. Musimandenganregresi dummy

  6. Trend value at period 3, T3 Step 1:Isolating the Trend Component • Smooth the time series to remove random effects and seasonality. Calculate moving averages. First moving average period is centered at quarter (1+4)/2 = 2.5 Average membership for the first 4 periods = [7130+6940+7354+7556]/4 = 7245.01 Second moving average period is centered at quarter (2+5)/2 = 3.5 Average membership for periods [2, 5]= [6940+7354+7556+7673]/4 = 7380.75 Centered moving average of the first two moving averages is [7245.01 + 7380.75]/2 = 7312.875 Centered location is t = 3

  7. =AVERAGE(C3:C6,C4:C7) Drag down to D16

  8. Step 2Determining the Period Factors • Determine “period factors” to isolate the (Seasonal)·(Random error) factor. Calculate the ratio yt/Tt. Since yt =TtStεt, then theperiod factor, Stεtis given by Stet = yt/Tt Example: In period 7 (3rd quarter of 1998):S7ε7= y7/T7 = 7662/7643.875 = 1.002371

  9. =C5/D5 Drag down to E16

  10. Step 3Unadjusted Seasonal Factors This eliminates the random factor from the period factors, Stεt This leaves us with only the seasonality component for each season. Example: Unadjusted Seasonal Factor for the third quarter. S3 = {S3,97e3,97+ S3,98e3,98 + S3,99e3,99}/3= {1.0056+1.0024+1.0079}/3 = 1.0053 • Determine the “unadjusted seasonal factors” to eliminate the random component from the period factors Average all the yt/Tt that correspond to the same season.

  11. =AVERAGE(E3,E7,E11,E15) Drag down to F6 Copy F3:F6 Paste Special(Values)

  12. Quarter 1 2 3 4 Adjusted Seasonal Factor 1.014325 .965252 1.004759 1.015663 Unadjusted Seasonal Factor 1.01490 .96580 1.00533 1.01624 Unadjusted Seasonal Factors/1.00057 Step 4Adjusted Seasonal Factors Calculate: Unadjusted seasonal factors Average seasonal factor • Determine the “adjusted seasonal factors” so that average adjusted factor is 1 Average seasonal factor = (1.01490+.96580+1.00533+1.01624)/4=1.00057

  13. F3/AVERAGE($F$3:$F$6) Drag down to G18

  14. Step 5The Deseasonalized Time Series Deseasonalized series value for Period 6 (2nd quarter, 1998) y6/(Quarter 2 Adjusted Seasonal Factor) = 7332/0.965252= 7595.94 • Determine “Deseasonalized data values”. Calculate: yt [Adjusted seasonal factors]t

  15. =C3/G3 Drag to cell H18

  16. Period (t) 17 18 19 20 Unadjusted Forecast (t) 8402.55 8480.95 8559.36 8637.76 Step 6The Time Series Trend Component • Regress on the Deseasonalized Time Series • Determine a deseasonalized forecast from the resulting regression equation (Unadjusted Forecast)t = 7069.6677 + 78.4046t

  17. Period 17 18 19 20 Unadjusted Forecast (t) 8402.55 8480.95 8559.36 8637.76 Adjusted Forecast (t) 8522.92 8186.26 8600.09 8773.06 Adjusted Seasonal Factor 1.014325 .965252 1.004759 1.015663 Step 7The Forecast Re-seasonalize the forecast by multiplying the unadjusted forecast by the adjusted seasonal factor for each period.

  18. Seasonally Adjusted Forecasts =I19*G3 Drag down to J22

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