1 BIS APPLICATION 2002-2003 MANAGEMENT INFORMATION SYSTEM Advance forecasting Forecasting by...

1BIS APPLICATION 2002-2003 MANAGEMENT INFORMATION SYSTEM

Advance forecasting Forecasting by identifying patterns in the past data

Chapter outline:

1. Extrapolation from the past

• Cause and effect relationships

• Trend analysis

- Regression analysis

- Simple linear regression analysis

- Multiple linear regression analysis

- Quadratic regression analysis

3. Cyclical and seasonal issues

Seasonal decomposition of time series data

• Type of seasonal variation

• Computing Multiplication seasonal indices

• Using seasonal indices to forecast

• A caution regarding seasonal indices


Extrapolation from the pastCause-and-effect Relationships

- Causal forecasting seeks to identify specific cause-effect relationships that will influence the pattern of future data. Causes appear as independent variables, and effects as dependent , response variables in forecasting models.

Independent variable Dependent, response variable

Price demand

Decrease in population decrease in demand

Number of teenager demand for jeans

- Causal relationships exist even when there is no specific time series aspect involved.

- The most common technique used in causal modeling is least squares regression.


Extrapolation from the past Linear Trend analysis

45

55

65

75

85

0 1 2 3 4

D1

D3D2

45

55

65

75

85

0 1 2 3 4

D1D3

D2

P1=80

P2=68

Its noticed from this figure that there is a growth trend influencing the demand, which should be extrapolated into the future.


The linear trend model or sloping line rather than horizontal line. The forecasting equation for the linear trend model is

Y = +X or Y = a + bX

Where X is the time index (independent variable). The parameters alpha and beta ( a and b) (the “intercept” and “slope” of the trend line) are usually estimated via a simple regression in which Y is the dependent variable and the time index X is the independent variable.

Extrapolation from the pastLinear Trend analysis


Although linear trend models have their uses, they are often inappropriate for business and economic data.

Most naturally occurring business time series do not behave as though there are straight lines fixed in space that they are trying to follow: real trends change their slopes and/or their intercepts over time.

The linear trend model tries to find the slope and intercept that give the best average fit to all the past data, and unfortunately its deviation from the data is often greatest near the end of the time series, where the forecasting action is.

Extrapolation from the past Linear Trend analysis


Forecasting using three data items

Current Intercept: 42Current Slope: 8

Period DemandStraight Line

ForecastSquared

Deviaton1 50 50 02 60 58 43 64 66 4

Sums of Squares: 8MSE: 1.63

Table of MSESlope

1.632993 4 5 6 7 8 9 1038 12.33 10.23 8.16 6.16 4.32 2.94 2.8340 10.39 8.29 6.22 4.24 2.58 2.16 3.4642 8.49 6.38 4.32 2.45 1.63 2.94 4.90

Intercept 44 6.63 4.55 2.58 1.41 2.58 4.55 6.6346 4.90 2.94 1.63 2.45 4.32 6.38 8.4948 3.46 2.16 2.58 4.24 6.22 8.29 10.3950 2.83 2.94 4.32 6.16 8.16 10.23 12.3352 3.46 4.55 6.22 8.12 10.13 12.19 14.28


Using a data table (what if analysis ) to determine the best-fitting straight line with the lowest MSE



Simple linear Regression AnalysisRegression analysis is a statistical method of taking one or more variable called independent or predictor variable- and developing a mathematical equation that show how they relate to the value of a single variable- called the dependent variable.

Regression analysis applies least-squares analysis to find the best-fitting line, where best is defined as minimizing the mean square error (MSE) between the historical sample and the calculated forecast.

Regression analysis is one of the tools provided by Excel.


Simple linear Regression AnalysisQuarters Demand

1 1 3.472 4 3.123 9 3.974 16 4.505 25 4.066 36 6.907 49 3.608 64 6.479 81 4.27

10 100 5.2411 121 6.3912 144 5.4513 169 5.8814 196 8.9915 225 4.1216 256 6.6817 289 9.4418 324 7.7519 361 9.9120 400 9.1421 441 14.2522 484 14.8923 529 14.2224 576 15.56

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.866R Square 0.749Adjusted R Square 0.738Standard Error 1.986Observations 24

ANOVAdf SS MS F Significance F

Regression 1 259.031 259.031 65.691 0.000Residual 22 86.750 3.943Total 23 345.782

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 1.495 0.837 1.787 0.088 -0.240 3.231Quarters 0.475 0.059 8.105 0.000 0.353 0.596

InterceptSlope


Quarters DemandFitted

Demand Difference1 3.47 1.97 2.24 Intercept 1.4952 3.12 2.45 0.45 Slope 0.4753 3.97 2.92 1.11 MSE 1.9014 4.50 3.40 1.235 4.06 3.87 0.046 6.90 4.35 6.547 3.60 4.82 1.488 6.47 5.30 1.399 4.27 5.77 2.26

10 5.24 6.25 1.0111 6.39 6.72 0.1112 5.45 7.20 3.0313 5.88 7.67 3.2214 8.99 8.15 0.7115 4.12 8.62 20.2516 6.68 9.10 5.8317 9.44 9.57 0.0218 7.75 10.05 5.2619 9.91 10.52 0.3820 9.14 11.00 3.4521 14.25 11.47 7.7422 14.89 11.95 8.7023 14.22 12.42 3.2424 15.56 12.90 7.0925 13.3726 13.8527 14.3228 14.80

0.00

5.00

10.00

15.00

20.00

1 5 9 13 17 21 25



Multiple linear Regression AnalysisSimple linear regression analysis use one variable (quarter number) as the independent variable in order to predict the future value. In many situations, it is advantageous to use more than one independent variable in a forecast.


Hours Before

Breakdown Age

Number of Computer

Controls205 59 1236 48 1260 25 0176 39 0245 20 1123 66 2176 40 0150 62 0148 70 0265 20 0200 52 1

45 75 0110 75 0216 25 0176 63 1

90 75 0176 69 2112 65 0230 30 0280 23 1

Two factors that control the frequency of breakdown. So they are the independent variables.

Y = a + bX1 + cX2

Intercept Slope 1

Slope2

Multiple linear Regression Analysis


SUMMARY OUTPUT



Regression 2 62,920.044 31,460.022 38.325 0.000Residual 17 13,954.906 820.877Total 19 76,874.950

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 308.451 17.552 17.573 0.000 271.419 345.484Age -2.800 0.325 -8.622 0.000 -3.485 -2.115No of Computer Controls 25.232 9.631 2.620 0.018 4.912 45.551

Intercept Slope 1Slope 2

Multiple linear Regression Analysis


Hours Before

Breakdown Age

Number of Computer

ControlsHourse to

breakdown Difference

205 59 1 169 1332 Intercept 308.451236 48 1 199 1347 Age -2.800260 25 0 238 464 No of Computer Controls 25.232176 39 0 199 541 MSE 26.41487245 20 1 278 1069123 66 2 174 2616176 40 0 196 419150 62 0 135 229148 70 0 112 1261265 20 0 252 157200 52 1 188 14145 75 0 98 2861

110 75 0 98 133216 25 0 238 505176 63 1 157 34990 75 0 98 72

176 69 2 166 105112 65 0 126 210230 30 0 224 31280 23 1 269 115

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20



Quadratic Regression AnalysisQuadratic regression analysis fits a second-order curve of the form

Y = a + bX + cX2

Quadratic regression is prepared by adding the squared value of the time periods. The coefficients in the quadratic formula are calculated again using regression, where time periods and the squared time periods are the independent variables and the demand remains the dependent variable.


SUMMARY OUTPUT



Regression 2 297.037 148.518 63.984 0.000Residual 21 48.745 2.321Total 23 345.782

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Upper 95.0%Intercept 4.685 1.017 4.609 0.000 2.571 6.799 6.799Quarters -0.261 0.187 -1.395 0.178 -0.651 0.128 0.128Quarters Squared 0.029 0.007 4.046 0.001 0.014 0.045 0.045

Quadratic Regression Analysis


Quadratic Regression AnalysisQuarters

Quarters Squared Demand

Fitted Demand Difference

1 1 3.47 3.52 0.00 Intercept 3.5002 4 3.12 3.58 0.21 Slope 1 0.0003 9 3.97 3.67 0.09 Slope 2 0.0194 16 4.50 3.80 0.49 MSE 1.4945 25 4.06 3.98 0.016 36 6.90 4.18 7.397 49 3.60 4.43 0.698 64 6.47 4.72 3.099 81 4.27 5.04 0.60

10 100 5.24 5.40 0.0311 121 6.39 5.80 0.3512 144 5.45 6.24 0.6113 169 5.88 6.71 0.7014 196 8.99 7.22 3.1015 225 4.12 7.78 13.3616 256 6.68 8.36 2.8317 289 9.44 8.99 0.2018 324 7.75 9.66 3.6319 361 9.91 10.36 0.2020 400 9.14 11.10 3.8521 441 14.25 11.88 5.6322 484 14.89 12.70 4.8323 529 14.22 13.55 0.4524 576 15.56 14.44 1.2425 625 15.3826 676 16.3427 729 17.3528 784 18.40

0.00

5.00

10.00

15.00

20.00

1 4 7 10

13

16

19

22

25

28

Demand

Forecast


Extrapolation from the pastCyclical and Seasonal Issues

The fundamental approach to including cyclical or seasonal factors is to break the forecast into two components:

(1) The underlying growth component

(2) The seasonal variations

To prepare a forecast model:

- Use a method to fit a growth curve to the historical record

- Determine the pattern of the seasonal variability

In general, two sets of parameters to be estimated:

( the coefficients in the trend line, and the percents in the seasonal patterns )


Extrapolation from the pastCyclical and Seasonal Issues

Basically two things must be done:

1- determine the trend line

2- take the trend line out ( calculate deviations from the trend)

3- create a pie, radar, or polar chart of the average period value

0

500

1,000

1,500

2,000

2,500

3,0001

23

4

1

2

3

4

1

2

34

12

3

4

1

2

3

4

1

2

34 1 2

3

4

1

2

3

4

1

2

3

41

23

41

2

3

4

1

2

3

4


Cyclical and Seasonal Issues Seasonal Decomposition of Time Series Data

Time series data are usually considered to consist of six component :

1. Average demand: is simply the long-term mean demand

2. Trend component : is how rapidly demand is growing or shrinking

3. Autocorrelation: is simply a statement that demand next period is related to demand this period

4. Seasonal component: is that portion of demand that follows a short-term pattern

5. Cyclical component: is much like the seasonal component, only its period is much longer.

6. Random component is the unpredictable component of demand


Cyclical and Seasonal Issues Type of Seasonal Variation

There are two types of seasonal variation:

Additive seasonal variation :

Occurs when the seasonal effects are the same regardless of the trend.

Multiplication seasonal variation :

Occurs when the seasonal effects vary with the trend effects. It’s the most common type of seasonal variation


Cyclical and Seasonal Issues Computing Multiplicative Seasonal Indices

Steps of Multiplicative Time Series Model:

1. Decide that the data is seasonal in nature.

2. Then realized that the seasonal variation is quarterly

3. If the variation of the data is larger to the right, then that seasonal variation is multiplicative.

4. Seasonal indices is needed to produce the seasonal forecast model.


1. Computing seasonal indices requires data that match the seasonal period. If the seasonal period is monthly, then monthly data are required. A quarterly seasonal period requires quarterly data.

2. Calculate the centered moving averages (CMAs) whose length matches the seasonal cycle. The seasonal cycle is the time required for one cycle to be completed. Quarterly seasonality requires a 4-period moving average, monthly seasonality requires a 12-period moving average and so on.

3. Determine the Seasonal-Irregular Factors or components. This can be done by dividing the raw data by the corresponding depersonalized value.

4. Determine the average seasonal factors. In this step the random and cyclical components will be eliminated by averaging them.




Quarter DataFour Period

Moving Average

Seasonal Irregular

ComponentSeasonal

Index1 5602 990 1,100 0.90000 0.873643 1,740 1,120 1.55357 1.640724 1,110 1,088 1.02069 0.908931 640 1,133 0.56512 0.538252 860 1,080 0.796303 1,920 1,090 1.761474 900 1,150 0.782611 680 1,163 0.584952 1,100 1,190 0.924373 1,970 1,198 1.645094 1,010 1,198 0.843421 710 1,263 0.562382 1,100 1,313 0.838103 2,230 1,275 1.749024 1,210 1,363 0.888071 560 1,393 0.402152 1,450 1,475 0.983053 2,350 1,573 1.494444 1,540 1,525 1.009841 950 1,648 0.576632 1,260 1,575 0.800003 2,8404 1,250

=AVERAGE(D3,D7,D11,D15,D19,D23)=AVERAGE(D4,D8,D12,D16,D20)=AVERAGE(D5,D9,D13,D17,D21)=AVERAGE(D6,D10,D14,D18,D22)

Step 2

= AVERAGE(B2:B5)

Step 3

= B3/C3

Step 1

Step 4


Cyclical and Seasonal Issues Using Seasonal Indices to Forecast

To forecast using seasonal indices

1- Compute the forecast using an annual values. Any forecasting techniques can be used.

2- Use the seasonal indices to share out the annual forecast by periods

Year Data

Forecast Including

Trend Forecast Trend MAD1 4,400 4,125 4,000 125 275 Alpha 0.62 4,320 4,498 4,290 208 178 Delta 0.53 4,760 4,545 4,391 154 215 MAD 2694 5,250 4,893 4,674 219 3575 5,900 5,433 5,107 326 4676 6,300 6,179 5,713 466 1217 6,754 6,252 5027 6,754 1 912 Q1 0.54

2 1469 Q2 0.873 2769 Q3 1.644 1537 Q4 0.91

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