dec s 516 · web viewmgtop/stat 516dr. ahn analysis of tooth paste data for 1958 to 1963 crest and...

MgtOp/Stat 516 Dr. AhnAnalysis of Tooth Paste Data

For 1958 to 1963 Crest and Colgate engaged in a competition to establish a domination of the toothpaste market. Data (read across) consist of the market share differences (Crest minus Colgate share) for 276 consecutive weeks. At T=135, Crest introduced an innovative advertising campaign which emphasized the American Dental Association’s endorsement of Crest toothpaste. Let us access the effect of the advertising campaign and see if there is any “permanent” effects. The data and following SAS program may be accessed from https://faculty.business.wsu.edu/ahn/classes/.

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OPTIONS LINESIZE=72 NODATE; TITLE1 'MgtOp 516 TIME SERIES ANALYSIS'; TITLE2 'TOOTH PASTE DATA'; DATA ONE; INFILE 'C:\Users\ahn\My Documents\516\tooth.dat'; INPUT X @@; S=1; T+1; IF T < 135 THEN S=0;

PROC ARIMA DATA=ONE; IDENTIFY VAR=X ESACF MINIC STATIONARITY=(ADF=5) ;

DATA TWO; SET ONE; IF T >=135 THEN DELETE; PROC ARIMA DATA=TWO; IDENTIFY VAR=X ESACF MINIC STATIONARITY=(ADF=5) ;

PROC ARIMA DATA=TWO; IDENTIFY VAR=X NOPRINT; ESTIMATE P=1 Q=1 METHOD=ML PLOT;

PROC ARIMA DATA=ONE; IDENTIFY VAR=X CROSS=(S) NOPRINT; ESTIMATE Q=1 P=1 INPUT=(S) METHOD=ML PLOT; ESTIMATE Q=1 P=1 INPUT=(/(1)S) METHOD=ML PLOT; ESTIMATE Q=1 P=1 INPUT=(1$S) METHOD=ML PLOT; ESTIMATE Q=1 P=1 INPUT=(1$/(1)S) METHOD=ML PLOT;run;

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MgtOp 516 TIME SERIES ANALYSISTOOTH PASTE DATA

The ARIMA Procedure

Name of Variable = X

Mean of Working Series -0.05766

Standard Deviation 0.184845

Number of Observations 276

Autocorrelation Check for White Noise

To Lag Chi-Square DF Pr > ChiSq

Autocorrelations

6 1133.87 6 <.0001 0.858 0.844 0.827 0.796 0.801 0.788

12 2039.56 12 <.0001 0.763 0.755 0.730 0.712 0.699 0.684

18 2774.63 18 <.0001 0.663 0.655 0.655 0.638 0.624 0.634

24 3418.53 24 <.0001 0.618 0.597 0.586 0.590 0.593 0.596

Extended Sample Autocorrelation Function

Lags MA 0 MA 1 MA 2 MA 3 MA 4 MA 5

AR 0 0.8581 0.8439 0.8265 0.7960 0.8015 0.7878

AR 1 -0.4762

0.0159 0.0614 -0.1428

0.0900 0.0182

AR 2 -0.4559

0.0976 0.0220 -0.1345

0.0969 0.0307

AR 3 -0.2664

-0.2313 -0.2376 -0.0904

0.0200 0.0591

AR 4 -0.3346

-0.4620 -0.4246 -0.1717

0.0250 0.0296

AR 5 -0.4142

0.1774 -0.3308 0.1972 -0.0704 0.0377

ESACF Probability Values


AR 0

<.0001 <.0001 <.0001 <.0001

<.0001 <.0001

AR 1

<.0001 0.8263 0.3969 0.0500 0.2230 0.8058

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AR 2

<.0001 0.2150 0.7332 0.0409 0.2202 0.6490

AR 3

<.0001 0.0001 <.0001 0.2048 0.7695 0.4290

AR 4

<.0001 <.0001 <.0001 0.0170 0.7184 0.6881

AR 5

<.0001 0.0196 <.0001 0.0110 0.4278 0.6263

Minimum Information Criterion


AR 0

-3.40727 -3.41776

-3.43806 -3.45693

-3.4585 -3.47748

AR 1

-4.74779 -5.02578

-5.00998 -4.99021

-4.98631 -4.97978

AR 2

-4.94701 -5.01032

-4.99872 -4.97874

-4.97523 -4.9598

AR 3

-4.99372 -4.99218

-4.97924 -4.96732

-4.96058 -4.94187

AR 4

-4.9784 -4.97493

-4.97074 -4.96213

-4.94207 -4.92742

AR 5

-4.9935 -4.98109

-4.96077 -4.94364

-4.92668 -4.90707

Error series model: AR(6)

Minimum Table Value: BIC(1,1) = -5.02578

ARMA(p+d,q) TentativeOrder Selection Tests

ESACF

p+d q BIC

1 3 -4.99021

3 3 -4.96732

5 4 -4.92668

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(5% Significance Level)

Augmented Dickey-Fuller Unit Root Tests

Type Lags

Rho Pr < Rho Tau Pr < Tau F Pr > F

Zero Mean 0 -34.5823 <.0001 -4.34 <.0001

1 -13.9595 0.0089 -2.71 0.0068

2 -8.5313 0.0423 -2.14 0.0317

3 -7.3803 0.0598 -1.98 0.0463

4 -4.9771 0.1245 -1.62 0.0990

5 -3.8158 0.1789 -1.38 0.1548

Single Mean 0 -37.1672 0.0015 -4.44 0.0004 9.93 0.0010

1 -14.4852 0.0431 -2.66 0.0821 3.71 0.1208

2 -8.4545 0.1920 -2.00 0.2846 2.28 0.4884

3 -7.1877 0.2603 -1.82 0.3686 1.96 0.5702

4 -4.5442 0.4784 -1.41 0.5795 1.39 0.7160

5 -3.3207 0.6163 -1.15 0.6979 1.08 0.7957

Trend 0 -148.488 0.0001 -10.03 <.0001 50.30 0.0010

1 -82.6949 0.0006 -6.38 <.0001 20.38 0.0010

2 -56.7732 0.0006 -5.03 0.0003 12.64 0.0010

3 -56.5166 0.0006 -4.79 0.0006 11.47 0.0010

4 -40.3651 0.0006 -4.03 0.0088 8.15 0.0050

5 -35.6146 0.0019 -3.78 0.0194 7.18 0.0257

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The ARIMA Procedure

Name of Variable = X

Mean of Working Series -0.224

Standard Deviation 0.080276

Number of Observations 134

Autocorrelation Check for White Noise

To Lag Chi-Square DF Pr > ChiSq

Autocorrelations

6 120.88 6 <.0001 0.458 0.376 0.358 0.373 0.340 0.364

12 164.84 12 <.0001 0.268 0.313 0.222 0.219 0.125 0.140

18 174.52 18 <.0001 0.101 0.109 0.115 0.057 0.045 0.150

24 184.97 24 <.0001 0.106 0.073 0.065 0.131 0.136 0.088

Extended Sample Autocorrelation Function


AR 0 0.4579 0.3763 0.3583 0.3732 0.3402 0.3640

AR 1 -0.3986

-0.0591 -0.0252 0.0514 -0.0420 0.1138

AR 2 -0.4963

0.0795 -0.0492 0.0237 0.0223 0.0264

AR 3 -0.5062

-0.2288 -0.2224 0.0310 0.0139 0.0363

AR 4 -0.4155

-0.4830 0.2208 -0.0158

-0.0141 0.0290

AR 5 -0.4810

-0.3049 0.2295 -0.0330

-0.0771 0.0338



AR 0

<.0001 0.0003 0.0015 0.0020

0.0085 0.0073

AR 1

<.0001 0.5591 0.8042 0.6116

0.6787 0.2446

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AR 2

<.0001 0.4810 0.6231 0.8248

0.8191 0.7996

AR 3

<.0001 0.0148 0.0381 0.7774

0.8984 0.7554

AR 4

<.0001 <.0001

0.0404 0.8876

0.9029 0.8008

AR 5

<.0001 0.0007 0.0334 0.7708

0.4422 0.7550

Minimum Information Criterion


AR 0

-5.07972 -5.09628

-5.09289 -5.08382

-5.08467 -5.07852

AR 1

-5.27973 -5.35251

-5.33207 -5.29679

-5.26543 -5.23022

AR 2

-5.30664 -5.32797

-5.31341 -5.28322

-5.25074 -5.22217

AR 3

-5.30386 -5.29494

-5.2835 -5.24695

-5.2196 -5.1885

AR 4

-5.29796 -5.26802

-5.25257 -5.22132

-5.18525 -5.15205

AR 5

-5.27007 -5.2344 -5.22017 -5.18745

-5.1509 -5.11848

Error series model: AR(6)

Minimum Table Value: BIC(1,1) = -5.35251

ARMA(p+d,q) TentativeOrder Selection Tests

ESACF

p+d q BIC

1 1 -5.35251

4 3 -5.22132

5 3 -5.18745

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(5% Significance Level)

Augmented Dickey-Fuller Unit Root Tests

Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F

Zero Mean 0 -8.3407 0.0439 -2.09 0.0358

1 -3.6829 0.1857 -1.39 0.1513

2 -2.1270 0.3151 -1.08 0.2542

3 -1.3444 0.4164 -0.87 0.3376

4 -0.9340 0.4830 -0.70 0.4121

5 -0.5365 0.5608 -0.49 0.5031

Single Mean 0 -71.8218 0.0011 -6.98 <.0001 24.39 0.0010

1 -46.7277 0.0011 -4.83 0.0002 11.67 0.0010

2 -31.6809 0.0011 -3.76 0.0042 7.08 0.0010

3 -21.0567 0.0070 -3.01 0.0365 4.55 0.0549

4 -16.3079 0.0248 -2.59 0.0984 3.35 0.2177

5 -11.0592 0.0976 -2.11 0.2414 2.22 0.5040

Trend 0 -82.6236 0.0004 -7.58 <.0001 28.81 0.0010

1 -58.1352 0.0004 -5.24 0.0002 13.80 0.0010

2 -40.9192 0.0004 -4.03 0.0100 8.25 0.0046

3 -27.1906 0.0112 -3.16 0.0971 5.16 0.1454

4 -21.6474 0.0408 -2.72 0.2288 3.84 0.4098

5 -15.2662 0.1595 -2.28 0.4408 2.66 0.6458

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The ARIMA Procedure

Maximum Likelihood Estimation

Parameter Estimate Standard Error t Value ApproxPr > |t|

Lag

MU -0.23138 0.02424 -9.55 <.0001 0

MA1,1 0.69297 0.09336 7.42 <.0001 1

AR1,1 0.93134 0.04556 20.44 <.0001 1

Constant Estimate -0.01589

Variance Estimate 0.004609

Std Error Estimate 0.06789

AIC -337.041

SBC -328.347

Number of Residuals

134

Correlations of Parameter Estimates

Parameter MU MA1,1 AR1,1

MU 1.000 -0.030 -0.036

MA1,1 -0.030 1.000 0.749

AR1,1 -0.036 0.749 1.000

Autocorrelation Check of Residuals

To Lag Chi-Square

DF Pr > ChiSq Autocorrelations

6 2.14 4 0.7103 0.028 -0.061 -0.039

0.032 0.009 0.090

12 5.58 10 0.8491 -0.037

0.100 -0.016

0.028 -0.102

-0.024

18 10.40 16 0.8449 -0.061

-0.026 0.006 -0.083 -0.097

0.101

24 12.51 22 0.9459 0.021 -0.031 -0.044

0.069 0.068 -0.015

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Model for variable X

Estimated Mean -0.23138

Autoregressive Factors

Factor 1: 1 - 0.93134 B**(1)

Moving Average Factors

Factor 1: 1 - 0.69297 B**(1)


The ARIMA Procedure


Parameter

Estimate Standard Error t Value Approx

Pr > |t|

Lag Variable Shift

MU -0.21255 0.02751 -7.73 <.0001 0 X 0

MA1,1 0.70559 0.06440 10.96 <.0001 1 X 0

AR1,1 0.93784 0.03231 29.02 <.0001 1 X 0

NUM1 0.30367 0.03383 8.98 <.0001 0 S 0




AIC -630.862

SBC -616.381

Number of Residuals

276


VariableParameter

XMU

XMA1,1

XAR1,

1

SNUM1

X MU 1.000 0.087 0.149 -0.639

X MA1,1 0.087 1.000 0.749 -0.025

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VariableParameter

XMU

XMA1,1

XAR1,

1

SNUM1

X AR1,1 0.149 0.749 1.000 -0.065

S NUM1 -0.639 -0.025 -0.065 1.000


To Lag Chi-Square


6 4.56 4 0.3352 -0.004

0.021 0.001 -0.108 0.059 0.025

12 8.15 10 0.6139 -0.015

0.088 0.006 -0.019 -0.063

-0.011

18 13.20 16 0.6584 -0.057

-0.055 0.048 -0.006 -0.052

0.077

24 17.76 22 0.7199 0.013 -0.072 -0.060

-0.008 0.014 0.077

30 24.54 28 0.6525 -0.023

-0.031 0.033 0.025 -0.047

0.128

36 27.83 34 0.7632 0.011 0.003 0.037 0.045 0.036 0.075

42 31.45 40 0.8311 0.030 -0.022 -0.021

0.032 -0.078

0.048

48 33.70 46 0.9111 -0.011

-0.025 0.047 -0.052 -0.007

0.032

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Estimated Intercept -0.21255


Factor 1: 1 - 0.93784 B**(1)


Factor 1: 1 - 0.70559 B**(1)

Input Number 1

Input Variable S

Overall Regression Factor 0.303669


Parameter


Pr > |t|

Lag Variable Shift

MU -0.22768 0.02608 -8.73 <.0001 0 X 0

MA1,1 0.70302 0.06673 10.53 <.0001 1 X 0

AR1,1 0.93232 0.03456 26.97 <.0001 1 X 0

NUM1 0.15356 0.05143 2.99 0.0028 0 S 0

DEN1,1 0.54411 0.15633 3.48 0.0005 1 S 0




AIC -633.224

SBC -615.14

Number of Residuals

275


VariableParameter

XMU

XMA1,1

XAR1,1

SNUM1

SDEN1,1

X MU 1.000 -0.006 -0.002 -0.079 -0.126

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VariableParameter

XMU

XMA1,1

XAR1,1

SNUM1

SDEN1,1

X MA1,1 -0.006 1.000 0.764 -0.009 0.036

X AR1,1 -0.002 0.764 1.000 0.006 0.034

S NUM1 -0.079 -0.009 0.006 1.000 -0.953

S DEN1,1 -0.126 0.036 0.034 -0.953 1.000


To Lag Chi-Square


6 5.03 4 0.2843 -0.013

0.017 0.015 -0.099 0.074 0.043

12 8.21 10 0.6086 -0.012

0.083 0.005 -0.016 -0.056

-0.027

18 13.81 16 0.6126 -0.069

-0.053 0.044 -0.023 -0.054

0.078

24 19.91 22 0.5887 0.020 -0.064 -0.074

0.006 0.038 0.093

30 25.39 28 0.6063 -0.019

-0.022 0.031 0.039 -0.045

0.111

36 29.26 34 0.6991 -0.011

-0.023 0.078 0.052 0.020 0.049

42 32.14 40 0.8072 0.007 -0.036 -0.024

0.025 -0.057

0.056

48 35.05 46 0.8802 -0.007

-0.033 0.028 -0.079 -0.007

0.021

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Factor 1: 1 - 0.93232 B**(1)


Factor 1: 1 - 0.70302 B**(1)

Input Number 1

Input Variable S


Denominator Factors

Factor 1: 1 - 0.54411 B**(1)


Parameter


Pr > |t|

Lag Variable Shift

MU -0.21382 0.02647 -8.08 <.0001 0 X 0

MA1,1 0.71069 0.06515 10.91 <.0001 1 X 0

AR1,1 0.93648 0.03323 28.19 <.0001 1 X 0

NUM1 0.30948 0.03290 9.41 <.0001 0 S 1




AIC -631.012

SBC -616.545

Number of Residuals

275

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VariableParameter

XMU

XMA1,1

XAR1,

1

SNUM1

X MU 1.000 0.048 0.129 -0.641

X MA1,1 0.048 1.000 0.757 0.032

X AR1,1 0.129 0.757 1.000 -0.036

S NUM1 -0.641 0.032 -0.036 1.000


To Lag Chi-Square


6 4.41 4 0.3538 -0.012

0.006 0.022 -0.090 0.067 0.049

12 6.88 10 0.7369 -0.016

0.068 0.003 -0.019 -0.033

-0.047

18 11.84 16 0.7549 -0.073

-0.036 0.033 -0.039 -0.053

0.070

24 18.86 22 0.6538 0.027 -0.060 -0.095

0.009 0.050 0.086

30 22.97 28 0.7345 -0.026

-0.006 0.013 0.048 -0.039

0.093

36 30.39 34 0.6455 0.001 -0.053 0.125 0.053 0.007 0.048

42 32.23 40 0.8040 0.019 -0.040 -0.008

0.007 -0.033

0.050

48 35.89 46 0.8581 0.003 -0.023 0.027 -0.097 0.019 0.007

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Factor 1: 1 - 0.93648 B**(1)


Factor 1: 1 - 0.71069 B**(1)

Input Number 1

Input Variable S

Shift 1



Parameter


Pr > |t|

Lag Variable Shift

MU -0.21947 0.02551 -8.60 <.0001 0 X 0

MA1,1 0.70222 0.06803 10.32 <.0001 1 X 0

AR1,1 0.93027 0.03565 26.09 <.0001 1 X 0

NUM1 0.20786 0.06601 3.15 0.0016 0 S 1

DEN1,1 0.35654 0.20753 1.72 0.0858 1 S 1




AIC -627.659

SBC -609.593

Number of Residuals

274

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VariableParameter

XMU

XMA1,1

XAR1,1

SNUM1

SDEN1,1

X MU 1.000 0.021 0.064 -0.091 -0.124

X MA1,1 0.021 1.000 0.771 0.091 -0.073

X AR1,1 0.064 0.771 1.000 0.052 -0.040

S NUM1 -0.091 0.091 0.052 1.000 -0.948

S DEN1,1 -0.124 -0.073 -0.040 -0.948 1.000


To Lag Chi-Square


6 4.60 4 0.3312 -0.015

0.009 0.025 -0.087 0.072 0.052

12 7.13 10 0.7131 -0.012

0.072 0.006 -0.021 -0.039

-0.041

18 12.45 16 0.7124 -0.079

-0.041 0.034 -0.039 -0.054

0.068

24 19.55 22 0.6110 0.030 -0.060 -0.086

0.008 0.056 0.092

30 23.56 28 0.7046 -0.020

-0.007 0.021 0.053 -0.038

0.089

36 30.92 34 0.6191 -0.024

-0.047 0.125 0.063 0.006 0.032

42 33.18 40 0.7687 -0.001

-0.045 -0.016

0.013 -0.021

0.064

48 37.11 46 0.8222 -0.009

-0.024 0.019 -0.103 0.007 0.013

24




Factor 1: 1 - 0.93027 B**(1)


Factor 1: 1 - 0.70222 B**(1)

Input Number 1

Input Variable S

Shift 1


Denominator Factors

Factor 1: 1 - 0.35654 B**(1)

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Intervention Insignificant Significant Residual

Model σ̂ 2AIC SBC Coefficients ACF PACF

ω0S t(135 )

0.00586 630.86 616.38

ω0

1−δBSt

(135 )

0.00574 633.22 615.14

ω0BSt(135)

0.00580 613.012 616.54

ω0

1−δBBSt

(135 )

0.00581 627.66 609.59 δ̂

For these intervention models, ARMA(1,1) model are used for the noise term.

The final model:

X t=−0 .22768+ 0. 153561−0.54411B

St(135 )+ 1−0 .70302B

1−0.93232Bat

, σ̂2=0. 00574

The market share difference X t was increased by 0.15356 and each week it was increased by

(0 .54411)t−135(0 .15356 ) , and the eventual increase is

0 .153561−0 . 54411

=0 .3368

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