case 9-6 presentation

8/12/2019 Case 9-6 Presentation

1/19

Demand Analysis & Forecasting

Case 9-6

Presented by:

Firoz

Pooja

Sumeet


2/19

Problem Given

Question 1- Fit ARIMA(0,1,0)(0,1,1)12 Model.

Do we need constant??Question 2- Any other Model Fits??

Question 3 -Generate Forecast for next cycle

with chosen Model.

Question 4- Plot a Time Series Graph.


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Data Provided

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1989 16.2 16.7 18.7 18.8 20.6 22.5 23.3 23.8 22.3 22.3 22.1 23.6

1990 20.1 21.6 21.6 21.9 23.4 25.9 26 26.2 24.7 23.5 23.4 23.9

1991 20 20.4 20.9 21.6 23.2 25.6 26.6 26.3 23.7 22.2 22.7 23.6

1992 20.2 21.1 21.5 22.2 23.4 25.7 26.3 26.2 23.6 22.8 22.8 23.3

1993 21 21.7 22.2 23.1 24.8 26.6 27.4 27.1 25.3 23.6 23.5 24.7

1994 21.2 22.5 22.7 23.6 25.1 27.6 28.2 27.7 25.7 24.3 23.7 24.9

1995 21.8 21.9 23.1 23.2 24.2 27.2 28 27.6 25.2 24.1 23.6 24.1

1996 20.7 22 22.5 23.6 25.2 27.6 28.2 28 26.3 25.9 25.9 27.1

1997 22.9 23.8 24.8 25.4 27 29.9 31.2 30.7 28.3 28.3 28 29.1

1998 25.6 26.5 27.2 27.9 29.4 31.8 32.7 32.4 29.5 29.5 29.3 30.3


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Stationary Check on Sales

High

Probability.

Not

Stationary


5/19

Calculate D-1


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Stationary Test on D-1

Low

Probability.

Stationary!!!

We are lucky


7/19

Time Series Plot for D1

See the

seasonality

for

12,24,26!!


8/19

Calculated difference with Lag 12


9/19

Calculate ACF and PACF for D2

with default Lag-36


10/19

Calculated ACF & PACF for D2

Lag -12


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Question: Fit ARIMA(0,1,0)(0,1,1)12 Model.Do we need constant??

For Constant

Prob is

0.978!!


12/19

Decision- ARIMA(0,1,0)(0,1,1)12

Final Estimates of Parameters

Type Coef SE Coef T P

SMA 12 0.8622 0.0701 12.30 0.000

Constant 0.000273 0.009785 0.03 0.978--To be run without

constant because values are very small and probability of constant is very high

Differencing: 1 regular, 1 seasonal of order 12

Number of observations: Original series 120, after differencing 107

Residuals: SS = 18.7170 (backforecasts excluded)

MS = 0.1783 DF = 105

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48 Chi-Square 13.3 19.4 33.1 43.1

DF 10 22 34 46

P-Value 0.206 0.622 0.511 0.594


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QuestionAny other Model Fits??

Looking at the patternwe want to try

ARIMA(0,1,0)(0,1,1)12

Model without constant


14/19

Result- ARIMA(0,1,0)(0,1,1)12 ARIMA Model: Sales

Estimates at each iteration

Iteration SSE Parameters 0 33.1048 0.100

1 29.7097 0.250

2 27.1644 0.400

3 25.2427 0.550

4 24.6871 0.601

5 23.9300 0.676

6 22.6607 0.814

7 22.4309 0.862

8 22.4309 0.862

Relative change in each estimate less than 0.0010



SMA 12 0.8622 0.0686 12.57 0.000


Number of observations: Original series 120, after differencing 107 Residuals: SS = 18.7232 (backforecasts excluded)

MS = 0.1766 DF = 106


Lag 12 24 36 48

Chi-Square 13.3 19.4 33.1 43.1

DF 11 23 35 47

P-Value 0.274 0.680 0.561 0.636

Looks Good!!

MS=0.1766

Accepted


15/19

We also tried

ARIMA(0,1,1)(0,1,1)12 Model Final Estimates of Parameters


MA 1 0.1829 0.0963 1.90 0.060

SMA 12 0.8612 0.0680 12.66 0.000




MS = 0.1709 DF = 105


Lag 12 24 36 48

Chi-Square 9.2 16.0 26.4 34.7

DF 10 22 34 46

P-Value 0.512 0.818 0.819 0.889

MA prob is higher than 0.05!!

MS=0.1766

Rejected!!


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Now, ARIMA(1,1,0)(0,1,1)12 Model



AR 1 -0.1899 0.0956 -1.99 0.050

SMA 12 0.8600 0.0686 12.54 0.000




MS = 0.1714 DF = 105


Lag 12 24 36 48

Chi-Square 10.1 16.7 27.1 35.7

DF 10 22 34 46

P-Value 0.435 0.779 0.795 0.863

All Good!!

Accepted

MS=0.1714


17/19

ARIMA (1,1,0)(0,1,1)12 best fits

the Model


18/19

Question 3- Generate Forecast with

chosen Model

Model ARIMA(1,1,0)(0,1,1)12 Model w/o constant


19/19

Question 4-Time Series Plot again.

ForecastedPeriod from

121 to 130

case 9-6 presentation

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