View
50
Download
2
Category
Tags:
Preview:
DESCRIPTION
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. - PowerPoint PPT Presentation
Citation preview
FormulasSimple linear regressions, Multiple and
correlation
Korelasi
Regresi Linear Berganda
Simple Linear Regression
Musiman dengan regresi dummy
First moving average period is centered at quarter (1+4)/ 2 = 2.5
Centered moving average of the first two moving averages is [7245.01 + 7380.75]/2 = 7312.875
• Smooth the time series to remove random effects and seasonality.
Calculate moving averages.
Step 1:Isolating the Trend Component
Average membership for the first 4 periods = [7130+6940+7354+7556]/4 = 7245.01
Second moving average periodis centered at quarter (2+5)/ 2 = 3.5
Average membership for periods [2, 5]= [6940+7354+7556+7673]/4 = 7380.75
Centered location is t = 3
Trend value at period 3, T3
=AVERAGE(C3:C6,C4:C7)Drag down to D16
Since yt =TtStεt, then the period factor, Stεt is given by
Stet = yt/Tt
Step 2Determining the Period Factors
• Determine “period factors” to isolate the (Seasonal)·(Random error) factor.
Calculate the ratio yt/Tt.
Example:In period 7 (3rd quarter of 1998):
S7ε7= y7/T7 = 7662/7643.875 = 1.002371
=C5/D5Drag down to E16
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 = {S3,97 e3,97 + S3,98 e3,98 + S3,99 e3,99}/3 =
{1.0056+1.0024+1.0079}/3 = 1.0053
Step 3Unadjusted Seasonal Factors
• 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.
=AVERAGE(E3,E7,E11,E15)Drag down to F6
Paste Special(Values)
Copy F3:F6
Average seasonal factor = (1.01490+.96580+1.00533+1.01624)/4=1.00057
Step 4Adjusted Seasonal Factors
• Determine the “adjusted seasonal factors” so that average adjusted factor is 1
Calculate:
Unadjusted seasonal factors Average seasonal factor
Quarter1234
UnadjustedSeasonal Factor
1.01490 .965801.005331.01624
AdjustedSeasonal Factor
1.014325 .9652521.0047591.015663
Unadjusted Seasonal Factors/1.00057
F3/AVERAGE($F$3:$F$6)Drag down to G18
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
=C3/G3Drag to cell H18
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
Period (t)17181920
Unadjusted Forecast (t)8402.558480.958559.368637.76
Step 7The ForecastRe-seasonalize the forecast by multiplying the
unadjusted forecast by the adjusted seasonal factor for each period.
UnadjustedForecast (t)
8402.558480.958559.368637.76
Period17181920
AdjustedForecast (t)
8522.928186.268600.098773.06
AdjustedSeasonal Factor
1.014325 .9652521.0047591.015663
=I19*G3Drag down to J22
SeasonallyAdjustedForecasts
Recommended