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FORECASTING OF TATA STEEL SALES Primer on estimation model 11/30/2010 Vinod Krishnan
Table of Contents INTRODUCTION ..................................................................................................................................3
Methodology......................................................................................................................................3
Regression......................................................................................................................................3
ARIMA............................................................................................................................................3
PRELIMINARY ANALYSIS ......................................................................................................................4
ARIMA METHOD .................................................................................................................................5
Identification of the Model ..............................................................................................................5
Estimation & Verification of the Model ............................................................................................5
Derivation of Forecast .....................................................................................................................6
REGRESSION METHOD ........................................................................................................................8
CONCLUSION.................................................................................................................................... 11
APPENDIX ........................................................................................................................................ 12
APPENDIX - I ................................................................................................................................. 13
APPENDIX – II ............................................................................................................................... 14
APPENDIX – III .............................................................................................................................. 72
ARIMA(2,0,8)(0,0,0) ...................................................................................................................... 72
ERROR DIAGNOSTIC................................................................................................................... 74
ARIMA(5,1,13)(0,0,0) .................................................................................................................... 78
ERROR DIAGNOSTIC................................................................................................................... 80
ARIMA(4,0,4)(0,1,0) ...................................................................................................................... 83
ERROR DIAGNOSTIC................................................................................................................... 85
ARIMA(0,1,4)(0,4,0) ...................................................................................................................... 88
ERROR DIAGNOSTIC................................................................................................................... 90
ARIMA(4,1,6)(0,1,0) ...................................................................................................................... 93
ERROR DIAGNOSTIC................................................................................................................... 95
APPENDIX – IV .............................................................................................................................. 99
INTRODUCTION
Tata Steel formerly known as TISCO and Tata Iron and Steel Company Limited is the world's 7th largest
steel company, with an annual crude steel capacity of 31 million tons. It is the largest private sector steel
company in India in terms of domestic production. Ranked 258th on, it is based in, Jharkhand, India. It is
part of Tata Group of companies. Tata Steel is also India's second-largest and second-most profitable
company in private sector with consolidated revenues of 132,110 crore (US$ 29.99 billion) and net
profit of over 12,350 crore (US$ 2.8 billion) during the year ended March 31, 2008. Tata steel Company
in the 8th most valuable brand according to an annual survey conducted by Brand Finance and The
Economic Times in 2010.
This project is focused at forecasting the sales of TATA Steel. APPENDIX-I contains the consolidated data.
The forecast methodology used would be ARIMA and Regression.
Methodology
Regression In theory it is assumed that the Sales of Tat steel would be dependent on the following variables,
Price of Steel
Income data of India
Price of Cement
Price of Electricity
Interest rate data
Car sales (units)
Money Supply data
ARIMA The popular time series method known as ARIMA would be applied on Tata Steel Sales. The parameters
of ARIMA model would be found out through trial and error method by looking at the ACF
(Autocorrelation function) and PACF (Partial Autocorrelation function) significance.
2000 – 2010 quarterly data of all the variables have been extracted
2000-2008 data will be used for forecast model development
2008 – 2010 data will be used for testing and verification
2011-2012 will be forecasted using the appropriate model
PRELIMINARY ANALYSIS
Exhibit 1 shows the quarterly movement of all the variables in the past 10 years. It can be seen that the
yield and price data are suppressed in scale because of the magnanimity of the Money Supply data.
Hence the data has been normalized and the resulting graph is shown in Exhibit 2.
Exhibit 1: Consolidated quarterly progression of all variables
Exhibit 2: Normalized quarterly progression of all variables
A quick view shows that there seems to be a lead-lag relationship between Money Supply and price of
steel.
Also it can be seen that the sales data is fairly consistent throughout the years nevertheless there seems
to be an inverse relationship between price of steel and sales of steel. A positive relationship is seen
between car sales and Tata steel sales.
0
50000
100000
150000
200000
250000
300000
350000
400000
Jun
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-01
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-02
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-03
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-07
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-08
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c-08
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-09
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-10
cement-index
cement-prices
steel-prices
electricity
M3
yields
car sales(units)
0
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200
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400
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-07
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-09
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-10
cement index
cement pric
steel
electricity
M3
yields
car sales(units)
tatasales
ARIMA METHOD
The ARIMA model is obtained through the examination of auto correlation (AC) and partial auto
correlation (PAC) coefficients of various orders. The significance of these coefficients was tested through
the Q Statistic.
Identification of the Model
Exhibit 3 shows the different combinations of the sales data that was tried to develop the best ARIMA.
Trial No Difference (d) Seasonal Difference (s) Significant ACF Lags (q)
Significant PACF Lags (p)
1 0 0 8 2
2 1 0 13 5
3 0 1 4 4
4 0 4 4 0
5 1 2 4 0
6 1 3 4 0
7 1 1 6 4
Exhibit 3: The different trials used to identify the best model
The complete results obtained from SPSS executions are available in APPENDIX-II.
Estimation & Verification of the Model After multiple trial and error attempts, of the monthly data it was decided to run the following ARIMA
models and then check for diagnostics on the residuals to verify the model
Diagnostics of the residuals involves checking the significance of residuals’ AC and PAC coefficients.
Exhibit 4 shows the various ARIMA models that were executed in SPSS based on the ACF and PACF
results shown in Exhibit 3.
ARIMA Stationary R-SQUARED Significance of residuals
ARIMA(2,0,8)(0,0,0) 85% Stationary error
ARIMA(5,1,13)(0,0,0) 67.20% Non-stationary error
ARIMA(4,0,4)(0,1,0) 60.90% Non-stationary error
ARIMA(0,1,4)(0,4,0) 56.20% Non-stationary error
ARIMA(0,1,4)(0,2,0) 54.30% Non-stationary error
ARIMA(0,1,4)(0,3,0) 54.60% Non-stationary error
ARIMA(4,1,6)(0,1,0) 69.40% Stationary error Exhibit 4: Table showing the significant results of ARIMA model of Tata Steel Sales
Appendix-III shows the SPSS results obtained by execution of the ARIMA models shown in exhibit 4.
Derivation of Forecast
With 87% Stationary R-Squared and strong stationary residual count, ARIMA(2,0,8)(0,0,0) was chosen as
the best model.
After checking the earlier phase it was found that the following MA and AR values are significant,
AR = 1,2
MA=1,2,3,4,5,6,7,8
Because of the presence of significant MA this model becomes nonlinear in Parameters.
The equation would be:
Xt= .838*Xt-1 +.359*Zt-2 -.512*et-1 +.838*et-2 + .809*et-3 +.696*et-4+
.652*et-5 + 546* et-6 +.493*et-7+.387*et-8+.357*et-9
The ex-post forecast (between 2009 and 2010) is shown in Exhibit 5
Quarter Short-Date Actuals Forecasted Residual
1 Jun-09 5554.02 6159.35 -605.33
2 Sep-09 5629.85 6390.23 -760.38
3 Dec-09 6307.48 5845.63 461.85
4 Mar-10 7225.47 6042.92 1182.55
1 Jun-10 6471.27 5401.25 1070.02
2 Sep-10 7038.13 6251.31 786.82
Exhibit 5: Tata sales Quarterly ex-post forecast from 2009-2010.
Exhibit 6 shows the ex-ante forecast from ARIMA for 2011-2013 of Tata steel
Quarter Short-Date Forecasted 3 Dec-10 5592.53
4 Mar-11 5693
1 Jun-11 5622.42
2 Sep-11 5565.29
3 Dec-11 5509.27
4 Mar-12 5455.11
1 Jun-12 5402.71
2 Sep-12 5352.01
3 Dec-12 5302.96
4 Mar-13 5255.5
Exhibit 6: Tata sales Quarterly ex-ante forecast from 2011-2013
REGRESSION METHOD The next model used for forecast is regression. Based on the preliminary analysis and theory of
economics, it is hypothesized that,
Sales of Tata Steel
is inversely related to price of steel (ST)
Is directly related to sales of cars (CS)
Is directly related to money supply (M3)
Is inversely related to interest rate, long-term rate, (Y)
Is directly related to price of cement (CI)
Is directly related or price of electricity (EL)
The equation would be as following,
TS = b0 + b1*CI + b2*CS + b3*M3 – b4*Y – b5*ST + b6*EL
APPENDIX –IV shows the SPSS results of the regression.
The regression equation estimated is:
TS=-1936.427 + 2.450*CI + .010*CS + .002*M3 - 62.82*Y - 11.436*ST + 9.995*EL
As can be seen the model conforms to the economic theory hypothesized above.
Fitness of the Model:
R-SQUARED = 94.9%
Durbin Watson = 1.970
Exhibit 7 shows the VIF values of each parameter and of the overall model.
Variable VIF 1/VIF
EL 6.94 0.144191
CS 6.77 0.147785
ST 6.37 0.156883
CI 5.94 0.16849
M3 2.29 0.436125
Y 1.65 0.604865
Mean VIF 4.99 0.200400802 Exhibit 7: VIF values
The model is also homoscedastic. Exhibit 8 shows the variance of the residuals.
Exhibit 8: Shows that the residuals are insignificant and random.
This regression model is expected to be the best forecast of the Sales of TATA Steel. The model has been
diagnosed for the common regression assumptions,
Autocorrelation: DW of 1.97 is close to the required DW of 2
Multicollinearity: VIF of 4.99 is less than required 10
Homoscedasticity: as shows in exhibit 8 the residuals are homoscedastic and random.
And the model conforms to economic theory
Exhibit 9 shows the forecast obtained through ex-post forecast obtained through regression equation
Quarter Short-Date Actuals Forecasted Residual 1 Jun-09 5554.02 4887.629478 666.3905
2 Sep-09 5629.85 5292.812682 337.0373
3 Dec-09 6307.48 5490.476696 817.0033
4 Mar-10 7225.47 6548.756815 676.7132
1 Jun-10 6471.27 6355.713014 115.557
2 Sep-10 7038.13 6651.213221 386.9168
Exhibit 9: Tata sales Quarterly ex-post forecast from 2009-2010.
Exhibit 10 shows the ex-ante forecast from Regression for 2011-2013 of Tata steel
Quarter Short-Date Forecasted 3 Dec-10 6287.861387
4 Mar-11 7646.294791
1 Jun-11 7264.161005
2 Sep-11 7686.26784 3 Dec-11 7205.096263
4 Mar-12 8951.878836
1 Jun-12 8296.357874
2 Sep-12 8906.727713 3 Dec-12 7205.096263
4 Mar-13 8951.878836
Exhibit 10: Tata sales Quarterly ex-ante forecast from 2011-2013
CONCLUSION
After thorough analysis and execution of both Regression and ARIMA method to forecast sales pattern
of TATA Steel it has been found that the sales of the company is fairly predictable.
It is exhibited that Regression is a better and stronger forecasting technique as sales of the company is
extremely dependant on exogenous factors and doesn’t have a particular time -series pattern.
Some interesting finds are the lead-lag relationship between money supply and price of steel which
again affects the sales of TATA steel directly. Hence Money supply is a strong indicator of the sales of
Tata steel. Car sales are also a strong indicator of the sales.
Although all forecasts methods are subject errors, as per the current analysis it can be said that the Sales
of TATA steel would hopefully be close to 8000 Crores by the end of Mar 2013.
APPENDIX
APPENDIX – I
Quarter Mon-yy cement-index cement-prices steel-prices electricity M3 yields car sales(units) tatasales1 Jun-00 125.9 125.33 118.7333333 191.4 80,666.00 6.76 32077 1401.226087
2 Sep-00 128.7333333 132.17 117.8333333 195.8333333 21,512.00 7.08 34847 1666.318966
3 Dec-00 137.7333333 137.67 114.2666667 202.2666667 70,446.00 7.11 34649 1868.17
4 Mar-01 154.1 145.5 106.8666667 210.7 44,347.00 7.26 48782 2353.5
1 Jun-01 151.7 139 103.5 213.4 70,376.00 6.98 30207 1611.41
2 Sep-01 149.3 141.58 103.5 219.9333333 29,435.00 7.12 37856 1932.93
3 Dec-01 147 138.83 103.5 232.9666667 44,340.00 7.28 38316 1902.21
4 Mar-02 146.7666667 127.67 102.1333333 233 50,285.00 7.34 51960 2150.52
1 Jun-02 144.6333333 131.17 103.9666667 230.5 117,345.00 7.57 41580 1988.05
2 Sep-02 143.2333333 130.83 119.3 239.4 21,349.00 7.20 47142 2332.62
3 Dec-02 145.8333333 131.33 119.3 241 41,373.00 6.46 50209 2491.29
4 Mar-03 147.6 122.83 128.7 241 44,508.00 5.91 63937 2981.31
1 Jun-03 147.6 128.17 140.5666667 245.8 81,381.00 5.62 49211 2522.93
2 Sep-03 144.3 122.83 145.4 247.2333333 31,739.00 5.11 66850 2940.98
3 Dec-03 145.2666667 130 151.8333333 250.5666667 61,371.00 5.14 73237 2967
4 Mar-04 151.3333333 153 167.9 251.6 104,033.00 5.30 88253 3490.05
1 Jun-04 153.2666667 153.67 205.8666667 252.8 73,914.00 6.15 71997 3405.93
2 Sep-04 150.9333333 144 201.6333333 252.2 20,226.00 7.21 81373 4107.35
3 Dec-04 148.9 137.51 203.6333333 252.2 50,872.00 7.21 89994 4090.46
4 Mar-05 158.1 151.17 216.8333333 254.8 119,940.00 6.88 105157 4273.13
1 Jun-05 163.8333333 155.4 229.9666667 259.1333333 91,735.00 7.21 74947 3961.45
2 Sep-05 162.8666667 157.78 190.2666667 267.8 63,508.00 7.31 93883 4395.08
3 Dec-05 165.2 161.31 177 261.8 105,989.00 7.39 97953 4185.21
4 Mar-06 174.7 176.66 171.4333333 264.7666667 200,249.00 8.28 124859 4602.48
1 Jun-06 192.7666667 199.56 205.9 266.3 58,060.00 7.64 109589 4390.2
2 Sep-06 194.7 199.23 216 270.0666667 154,822.00 7.95 123165 4202.28
3 Dec-06 198.0666667 199.97 215.6 277.1666667 70,960.00 7.41 133967 4469.46
4 Mar-07 203.2 205.46 221.3 273.3666667 283,542.00 7.92 154439 5609.58
1 Jun-07 212.2666667 213.79 234.5 272.6 89,554.00 7.92 112951 4745.3
2 Sep-07 216.8333333 216.69 229.1 272.7 197,021.00 7.64 127130 4785.9
3 Dec-07 219.7666667 221.8 230.8 272.7 119,300.00 7.92 142289 4973.92
4 Mar-08 221 221.88 247.6333333 274.1 303,928.00 8.72 166806 5736.69
1 Jun-08 221.8333333 224.49 292.2666667 276.4666667 84,387.00 6 123241 6087.23
2 Sep-08 223.5333333 223.8 295.4333333 276.5 176,249.00 6.29 126348 6725.89
3 Dec-08 224.3 222.54 280.6333333 276.5 162,910.00 7.12 75391 4750.61
4 Mar-09 223.4666667 220 240.2333333 274.0666667 333,751.00 7.59 102597 6209.12
1 Jun-09 228.6333333 228.66 228.0666667 269.2 172,702.00 7.86 103844 5554.02
2 Sep-09 229.3 232.21 230.3333333 277.6666667 159,091.00 7.52 134569 5629.85
3 Dec-09 221.5666667 229.97 241.6333333 281.9 132,685.00 7.46 145297 6307.48
4 Mar-10 213.9333333 232.09 249.1 281.9 351,070.00 7.83 193088 7225.47
1 Jun-10 223.8 232.91 296.7333333 293.5 106,297.00 7.58 164066 6471.27
2 Sep-10 208 218.92 290.7 299.3 186,330.00 7.9 180919 7038.13
APPENDIX – II ACF VARIABLES=TS
/NOLOG
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 12:48:48
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:02.059
Elapsed Time 00 00:00:02.207
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_1
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 0
Seasonal Differencing 0
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_1
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Computable First Lags 41
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 .864 .149 33.648 1 .000
2 .811 .147 64.019 2 .000
3 .718 .145 88.430 3 .000
4 .681 .143 110.952 4 .000
5 .607 .141 129.360 5 .000
6 .584 .140 146.854 6 .000
7 .477 .138 158.860 7 .000
8 .465 .136 170.611 8 .000
9 .355 .134 177.659 9 .000
10 .281 .132 182.215 10 .000
11 .202 .130 184.649 11 .000
12 .177 .127 186.586 12 .000
13 .102 .125 187.246 13 .000
14 .069 .123 187.558 14 .000
15 -.014 .121 187.572 15 .000
16 -.042 .119 187.696 16 .000
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 .864 .154
2 .254 .154
3 -.102 .154
4 .120 .154
5 -.066 .154
6 .096 .154
7 -.257 .154
8 .185 .154
9 -.267 .154
10 -.141 .154
11 .074 .154
12 .053 .154
13 -.078 .154
14 -.086 .154
15 .013 .154
16 -.017 .154
ACF VARIABLES=TS
/NOLOG
/DIFF=1
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 12:50:18
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/DIFF=1
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:00.920
Elapsed Time 00 00:00:00.936
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_2
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 1
Seasonal Differencing 0
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_2
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Values Lost Due to Differencing 1
Number of Computable First Lags After Differencing 40
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.539 .151 12.787 1 .000
2 .144 .149 13.722 2 .001
3 -.205 .147 15.681 3 .001
4 .247 .145 18.588 4 .001
5 -.364 .143 25.087 5 .000
6 .474 .141 36.424 6 .000
7 -.442 .139 46.556 7 .000
8 .287 .137 50.956 8 .000
9 -.140 .135 52.040 9 .000
10 .096 .133 52.569 10 .000
11 -.214 .130 55.271 11 .000
12 .321 .128 61.516 12 .000
13 -.288 .126 66.721 13 .000
14 .181 .124 68.855 14 .000
15 -.139 .121 70.159 15 .000
16 .207 .119 73.175 16 .000
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 -.539 .156
2 -.206 .156
3 -.328 .156
4 -.028 .156
5 -.393 .156
6 .143 .156
7 -.258 .156
8 -.071 .156
9 .013 .156
10 -.173 .156
11 -.105 .156
12 -.083 .156
13 -.064 .156
14 -.129 .156
15 -.170 .156
16 .079 .156
ACF VARIABLES=TS
/NOLOG
/SDIFF=1
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 12:51:42
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/SDIFF=1
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:00.795
Elapsed Time 00 00:00:00.811
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_3
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 0
Seasonal Differencing 1
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_3
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Values Lost Due to Differencing 4
Number of Computable First Lags After Differencing 37
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 .212 .156 1.852 1 .174
2 -.057 .154 1.987 2 .370
3 .020 .152 2.004 3 .572
4 -.517 .150 13.941 4 .007
5 -.094 .147 14.347 5 .014
6 .182 .145 15.918 6 .014
7 -.148 .143 16.998 7 .017
8 .005 .140 17.000 8 .030
9 .017 .138 17.015 9 .048
10 -.171 .136 18.594 10 .046
11 .000 .133 18.594 11 .069
12 .019 .131 18.616 12 .098
13 -.059 .128 18.828 13 .129
14 .083 .126 19.263 14 .155
15 .118 .123 20.182 15 .165
16 .042 .120 20.301 16 .207
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 .212 .162
2 -.106 .162
3 .059 .162
4 -.575 .162
5 .294 .162
6 -.016 .162
7 -.152 .162
8 -.295 .162
9 .173 .162
10 -.056 .162
11 -.195 .162
12 -.175 .162
13 .152 .162
14 .014 .162
15 -.053 .162
16 -.081 .162
ACF VARIABLES=TS
/NOLOG
/SDIFF=4
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 12:53:31
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/SDIFF=4
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:00.718
Elapsed Time 00 00:00:00.837
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_5
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 0
Seasonal Differencing 4
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_5
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Values Lost Due to Differencing 16
Number of Computable First Lags After Differencing 25
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 .250 .185 1.821 1 .177
2 -.032 .182 1.851 2 .396
3 .080 .178 2.056 3 .561
4 -.471 .174 9.402 4 .052
5 -.174 .170 10.447 5 .064
6 .154 .166 11.311 6 .079
7 -.098 .162 11.678 7 .112
8 .023 .157 11.699 8 .165
9 .009 .153 11.702 9 .231
10 -.205 .148 13.622 10 .191
11 -.085 .144 13.972 11 .235
12 -.035 .139 14.034 12 .299
13 .018 .134 14.052 13 .370
14 .192 .128 16.282 14 .296
15 .190 .123 18.671 15 .229
16 .124 .117 19.799 16 .229
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 .250 .196
2 -.100 .196
3 .123 .196
4 -.579 .196
5 .274 .196
6 -.020 .196
7 .008 .196
8 -.294 .196
9 .032 .196
10 -.077 .196
11 -.058 .196
12 -.163 .196
13 .146 .196
14 .069 .196
15 .112 .196
16 -.068 .196
ACF VARIABLES=TS
/NOLOG
/DIFF=1
/SDIFF=2
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 12:55:05
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/DIFF=1
/SDIFF=2
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:00.671
Elapsed Time 00 00:00:00.732
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_7
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 1
Seasonal Differencing 2
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_7
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Values Lost Due to Differencing 9
Number of Computable First Lags After Differencing 32
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.337 .166 4.098 1 .043
2 -.186 .164 5.380 2 .068
3 .417 .161 12.074 3 .007
4 -.471 .158 20.894 4 .000
5 .012 .156 20.899 5 .001
6 .310 .153 25.004 6 .000
7 -.264 .150 28.112 7 .000
8 .014 .147 28.121 8 .000
9 .166 .144 29.450 9 .001
10 -.180 .141 31.070 10 .001
11 .037 .138 31.142 11 .001
12 .034 .135 31.204 12 .002
13 -.072 .132 31.502 13 .003
14 .044 .128 31.621 14 .005
15 .070 .125 31.932 15 .007
16 .057 .121 32.156 16 .010
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 -.337 .174
2 -.337 .174
3 .280 .174
4 -.369 .174
5 -.134 .174
6 .034 .174
7 .054 .174
8 -.170 .174
9 -.039 .174
10 .018 .174
11 -.001 .174
12 -.185 .174
13 .001 .174
14 .009 .174
15 .080 .174
16 .108 .174
ACF VARIABLES=TS
/NOLOG
/DIFF=1
/SDIFF=3
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 12:56:27
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/DIFF=1
/SDIFF=3
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:00.764
Elapsed Time 00 00:00:00.770
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_9
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 1
Seasonal Differencing 3
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_9
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Values Lost Due to Differencing 13
Number of Computable First Lags After Differencing 28
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.321 .176 3.318 1 .069
2 -.134 .173 3.918 2 .141
3 .441 .170 10.630 3 .014
4 -.451 .167 17.929 4 .001
5 -.049 .163 18.018 5 .003
6 .291 .160 21.319 6 .002
7 -.233 .156 23.546 7 .001
8 .050 .153 23.655 8 .003
9 .137 .149 24.494 9 .004
10 -.180 .145 26.021 10 .004
11 .007 .141 26.024 11 .006
12 -.021 .138 26.047 12 .011
13 -.054 .133 26.210 13 .016
14 .058 .129 26.410 14 .023
15 .042 .125 26.524 15 .033
16 .090 .120 27.081 16 .041
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.321 .176 3.318 1 .069
2 -.134 .173 3.918 2 .141
3 .441 .170 10.630 3 .014
4 -.451 .167 17.929 4 .001
5 -.049 .163 18.018 5 .003
6 .291 .160 21.319 6 .002
7 -.233 .156 23.546 7 .001
8 .050 .153 23.655 8 .003
9 .137 .149 24.494 9 .004
10 -.180 .145 26.021 10 .004
11 .007 .141 26.024 11 .006
12 -.021 .138 26.047 12 .011
13 -.054 .133 26.210 13 .016
14 .058 .129 26.410 14 .023
15 .042 .125 26.524 15 .033
16 .090 .120 27.081 16 .041
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 -.321 .186
2 -.265 .186
3 .361 .186
4 -.294 .186
5 -.199 .186
6 .029 .186
7 .113 .186
8 -.024 .186
9 -.093 .186
10 -.033 .186
11 -.035 .186
12 -.162 .186
13 -.039 .186
14 .030 .186
15 .077 .186
16 .109 .186
ACF VARIABLES=TS
/NOLOG
/DIFF=1
/SDIFF=1
/MXAUTO 16
/SERROR=IND
/PACF.
ACF
Notes
Output Created 30-Nov-2010 13:04:24
Comments
Input Data D:\IIM Data Recovery\MBA
Related\BusF\group_project_TATAST
EELSALES.sav
Active Dataset DataSet0
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data
File
42
Date YEAR, not periodic, QUARTER, period
4
Missing Value Handling Definition of Missing User-defined missing values are
treated as missing.
Cases Used For a given time series variable, cases
with missing values are not used in the
analysis. Also, cases with negative or
zero values are not used, if the log
transform is requested.
Syntax ACF VARIABLES=TS
/NOLOG
/DIFF=1
/SDIFF=1
/MXAUTO 16
/SERROR=IND
/PACF.
Resources Processor Time 00 00:00:00.718
Elapsed Time 00 00:00:00.909
Use From First observation
To Last observation
Time Series Settings (TSET) Amount of Output PRINT = DEFAULT
Saving New Variables NEWVAR = CURRENT
Maximum Number of Lags in
Autocorrelation or Partial
Autocorrelation Plots
MXAUTO = 16
Maximum Number of Lags
Per Cross-Correlation Plots
MXCROSS = 7
Maximum Number of New
Variables Generated Per
Procedure
MXNEWVAR = 60
Maximum Number of New
Cases Per Procedure
MXPREDICT = 1000
Treatment of User-Missing
Values
MISSING = EXCLUDE
Confidence Interval
Percentage Value
CIN = 95
Tolerance for Entering
Variables in Regression
Equations
TOLER = .0001
Maximum Iterative
Parameter Change
CNVERGE = .001
Method of Calculating Std.
Errors for Autocorrelations
ACFSE = IND
Length of Seasonal Period PERIOD = 4
Variable Whose Values
Label Observations in Plots
Unspecified
Equations Include CONSTANT
[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav
Model Description
Model Name MOD_16
Series Name 1 TS
Transformation None
Non-Seasonal Differencing 1
Seasonal Differencing 1
Length of Seasonal Period 4
Maximum Number of Lags 16
Process Assumed for Calculating the
Standard Errors of the Autocorrelations
Independence(white noise)
Display and Plot All lags
Applying the model specifications from MOD_16
a. Not applicable for calculating the standard errors of the partial
autocorrelations.
Case Processing Summary
TS
Series Length 42
Number of Missing Values User-Missing 0
System-Missing 0
Number of Valid Values 42
Number of Values Lost Due to Differencing 5
Number of Computable First Lags After Differencing 36
TS
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.323 .158 4.172 1 .041
2 -.240 .156 6.551 2 .038
3 .376 .153 12.546 3 .006
4 -.502 .151 23.569 4 .000
5 .073 .149 23.810 5 .000
6 .359 .147 29.813 6 .000
7 -.284 .144 33.692 7 .000
8 -.015 .142 33.704 8 .000
9 .160 .139 35.030 9 .000
10 -.183 .137 36.828 10 .000
11 .083 .134 37.211 11 .000
12 .067 .132 37.472 12 .000
13 -.131 .129 38.498 13 .000
14 .039 .126 38.594 14 .000
15 .103 .123 39.285 15 .001
16 .021 .121 39.317 16 .001
Autocorrelations
Series:TS
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.323 .158 4.172 1 .041
2 -.240 .156 6.551 2 .038
3 .376 .153 12.546 3 .006
4 -.502 .151 23.569 4 .000
5 .073 .149 23.810 5 .000
6 .359 .147 29.813 6 .000
7 -.284 .144 33.692 7 .000
8 -.015 .142 33.704 8 .000
9 .160 .139 35.030 9 .000
10 -.183 .137 36.828 10 .000
11 .083 .134 37.211 11 .000
12 .067 .132 37.472 12 .000
13 -.131 .129 38.498 13 .000
14 .039 .126 38.594 14 .000
15 .103 .123 39.285 15 .001
16 .021 .121 39.317 16 .001
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:TS
Lag
Partial
Autocorrelation Std. Error
1 -.323 .164
2 -.384 .164
3 .189 .164
4 -.506 .164
5 -.110 .164
6 .021 .164
7 .043 .164
8 -.299 .164
9 -.035 .164
10 -.012 .164
11 .030 .164
12 -.240 .164
13 -.008 .164
14 -.069 .164
15 .131 .164
16 .062 .164
APPENDIX – III
ARIMA(2,0,8)(0,0,0)
Model Description
Model Type
Model ID TS Model_1 ARIMA(2,0,8)(0,0,0)
Model Summary
Fit Statistic Mean SE Minimum Maximum
Stationary R-squared .851 . .851 .851
R-squared .851 . .851 .851
RMSE 665.949 . 665.949 665.949
MAPE 12.402 . 12.402 12.402
MaxAPE 174.071 . 174.071 174.071
MAE 329.235 . 329.235 329.235
MaxAE 2439.123 . 2439.123 2439.123
Normalized BIC 14.097 . 14.097 14.097
Model Statistics
Model
Number of
Predictors
Model Fit statistics Ljung-Box Q(18)
Number of
Outliers
Stationary R-
squared Statistics DF Sig.
TS-Model_1 0 .851 5.842 8 .665 0
ERROR DIAGNOSTIC
Noise residual from TS-Model_1
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.048 .160 .089 1 .766
2 -.087 .158 .390 2 .823
3 -.127 .155 1.062 3 .786
4 .140 .153 1.895 4 .755
5 -.064 .151 2.076 5 .838
6 .040 .148 2.150 6 .905
7 -.041 .146 2.231 7 .946
8 .094 .143 2.663 8 .954
9 -.010 .140 2.668 9 .976
10 -.054 .138 2.822 10 .985
11 -.113 .135 3.523 11 .982
12 .046 .132 3.643 12 .989
13 -.089 .130 4.118 13 .990
14 .087 .127 4.592 14 .991
15 .014 .124 4.604 15 .995
16 .066 .121 4.905 16 .996
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.048 .160 .089 1 .766
2 -.087 .158 .390 2 .823
3 -.127 .155 1.062 3 .786
4 .140 .153 1.895 4 .755
5 -.064 .151 2.076 5 .838
6 .040 .148 2.150 6 .905
7 -.041 .146 2.231 7 .946
8 .094 .143 2.663 8 .954
9 -.010 .140 2.668 9 .976
10 -.054 .138 2.822 10 .985
11 -.113 .135 3.523 11 .982
12 .046 .132 3.643 12 .989
13 -.089 .130 4.118 13 .990
14 .087 .127 4.592 14 .991
15 .014 .124 4.604 15 .995
16 .066 .121 4.905 16 .996
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:Noise residual from TS-Model_1
Lag
Partial
Autocorrelation Std. Error
1 -.048 .167
2 -.089 .167
3 -.137 .167
4 .120 .167
5 -.077 .167
6 .042 .167
7 -.018 .167
8 .068 .167
9 .020 .167
10 -.064 .167
11 -.089 .167
12 .003 .167
13 -.117 .167
14 .073 .167
15 .027 .167
16 .046 .167
ARIMA(5,1,13)(0,0,0)
Model Description
Model Type
Model ID TS Model_1 ARIMA(5,1,13)(0,0,0)
Model Summary
Model Fit
Fit Statistic Mean SE Minimum Maximum
Stationary R-squared .672 . .672 .672
R-squared .956 . .956 .956
RMSE 462.990 . 462.990 462.990
MAPE 7.556 . 7.556 7.556
MaxAPE 36.948 . 36.948 36.948
MAE 266.871 . 266.871 266.871
MaxAE 888.959 . 888.959 888.959
Normalized BIC 13.996 . 13.996 13.996
ERROR DIAGNOSTIC Noise residual from TS-Model_1
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.067 .151 .200 1 .654
2 -.034 .149 .251 2 .882
3 -.048 .147 .357 3 .949
4 .004 .145 .358 4 .986
5 -.014 .143 .367 5 .996
6 .041 .141 .451 6 .998
7 -.159 .139 1.763 7 .972
8 .051 .137 1.900 8 .984
9 -.045 .135 2.011 9 .991
10 -.080 .133 2.375 10 .993
11 -.100 .130 2.969 11 .991
12 .030 .128 3.024 12 .995
13 -.084 .126 3.464 13 .996
14 .026 .124 3.509 14 .998
15 -.025 .121 3.550 15 .999
16 .066 .119 3.860 16 .999
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.067 .151 .200 1 .654
2 -.034 .149 .251 2 .882
3 -.048 .147 .357 3 .949
4 .004 .145 .358 4 .986
5 -.014 .143 .367 5 .996
6 .041 .141 .451 6 .998
7 -.159 .139 1.763 7 .972
8 .051 .137 1.900 8 .984
9 -.045 .135 2.011 9 .991
10 -.080 .133 2.375 10 .993
11 -.100 .130 2.969 11 .991
12 .030 .128 3.024 12 .995
13 -.084 .126 3.464 13 .996
14 .026 .124 3.509 14 .998
15 -.025 .121 3.550 15 .999
16 .066 .119 3.860 16 .999
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:Noise residual from TS-Model_1
Lag
Partial
Autocorrelation Std. Error
1 -.067 .156
2 -.038 .156
3 -.053 .156
4 -.004 .156
5 -.018 .156
6 .036 .156
7 -.156 .156
8 .032 .156
9 -.051 .156
ARIMA(4,0,4)(0,1,0)
Model Description
Model Type
Model ID TS Model_1 ARIMA(4,0,4)(0,1,0)
Model Summary
Model Fit
Fit Statistic Mean SE Minimum Maximum
Stationary R-squared .609 . .609 .609
R-squared .946 . .946 .946
RMSE 411.566 . 411.566 411.566
MAPE 7.772 . 7.772 7.772
MaxAPE 29.703 . 29.703 29.703
MAE 286.839 . 286.839 286.839
MaxAE 897.260 . 897.260 897.260
Normalized BIC 12.901 . 12.901 12.901
Model
Number of
Predictors
Model Fit
statistics Ljung-Box Q(18)
Number of
Outliers
Stationary R-
squared Statistics DF Sig.
TS-Model_1 0 .609 7.161 10 .710 0
ERROR DIAGNOSTIC Noise residual from TS-Model_1
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 .107 .156 .473 1 .492
2 .077 .154 .722 2 .697
3 .053 .152 .845 3 .839
4 -.050 .150 .956 4 .916
5 .058 .147 1.112 5 .953
6 .139 .145 2.032 6 .917
7 .028 .143 2.070 7 .956
8 -.120 .140 2.795 8 .947
9 -.119 .138 3.541 9 .939
10 -.147 .136 4.709 10 .910
11 -.003 .133 4.709 11 .944
12 -.105 .131 5.352 12 .945
13 -.156 .128 6.832 13 .911
14 -.042 .126 6.945 14 .937
15 .007 .123 6.948 15 .959
16 -.010 .120 6.955 16 .974
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 .107 .156 .473 1 .492
2 .077 .154 .722 2 .697
3 .053 .152 .845 3 .839
4 -.050 .150 .956 4 .916
5 .058 .147 1.112 5 .953
6 .139 .145 2.032 6 .917
7 .028 .143 2.070 7 .956
8 -.120 .140 2.795 8 .947
9 -.119 .138 3.541 9 .939
10 -.147 .136 4.709 10 .910
11 -.003 .133 4.709 11 .944
12 -.105 .131 5.352 12 .945
13 -.156 .128 6.832 13 .911
14 -.042 .126 6.945 14 .937
15 .007 .123 6.948 15 .959
16 -.010 .120 6.955 16 .974
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:Noise residual from TS-Model_1
Lag
Partial
Autocorrelation Std. Error
1 .107 .162
2 .066 .162
3 .039 .162
4 -.065 .162
5 .065 .162
6 .136 .162
7 -.002 .162
8 -.158 .162
9 -.107 .162
10 -.096 .162
11 .041 .162
ARIMA(0,1,4)(0,4,0)
Model Description
Model Type
Model ID TS Model_1 ARIMA(0,1,4)(0,4,0)
Model Summary
Model Fit
Fit Statistic Mean SE Minimum Maximum
Stationary R-squared .562 . .562 .562
R-squared -3.610 . -3.610 -3.610
RMSE 2394.788 . 2394.788 2394.788
MAPE 30.224 . 30.224 30.224
MaxAPE 98.440 . 98.440 98.440
MAE 1605.532 . 1605.532 1605.532
MaxAE 6209.095 . 6209.095 6209.095
Normalized BIC 16.206 . 16.206 16.206
Model Statistics
Model
Number of
Predictors
Model Fit
statistics Ljung-Box Q(18)
Number of
Outliers
Stationary R-
squared Statistics DF Sig.
TS-Model_1 0 .562 19.103 14 .161 0
ERROR DIAGNOSTIC Noise residual from TS-Model_1
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.122 .189 .421 1 .517
2 -.131 .185 .927 2 .629
3 .160 .181 1.711 3 .634
4 -.403 .176 6.922 4 .140
5 -.008 .172 6.924 5 .226
6 .227 .168 8.757 6 .188
7 -.176 .163 9.914 7 .193
8 .035 .159 9.964 8 .268
9 .081 .154 10.239 9 .332
10 -.123 .149 10.918 10 .364
11 -.003 .144 10.918 11 .450
12 -.119 .139 11.655 12 .474
13 -.086 .133 12.068 13 .522
14 .109 .128 12.791 14 .543
15 .121 .122 13.778 15 .542
16 .136 .115 15.175 16 .512
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.122 .189 .421 1 .517
2 -.131 .185 .927 2 .629
3 .160 .181 1.711 3 .634
4 -.403 .176 6.922 4 .140
5 -.008 .172 6.924 5 .226
6 .227 .168 8.757 6 .188
7 -.176 .163 9.914 7 .193
8 .035 .159 9.964 8 .268
9 .081 .154 10.239 9 .332
10 -.123 .149 10.918 10 .364
11 -.003 .144 10.918 11 .450
12 -.119 .139 11.655 12 .474
13 -.086 .133 12.068 13 .522
14 .109 .128 12.791 14 .543
15 .121 .122 13.778 15 .542
16 .136 .115 15.175 16 .512
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:Noise residual from TS-Model_1
Lag
Partial
Autocorrelation Std. Error
1 -.122 .200
2 -.148 .200
3 .128 .200
4 -.406 .200
5 -.058 .200
6 .105 .200
7 -.081 .200
8 -.116 .200
9 -.012 .200
10 .028 .200
ARIMA(4,1,6)(0,1,0)
Model Description
Model Type
Model ID TS Model_1 ARIMA(4,1,6)(0,1,0)
Model Summary
Model Fit
Fit Statistic Mean SE Minimum Maximum
Stationary R-squared .694 . .694 .694
R-squared .932 . .932 .932
RMSE 471.268 . 471.268 471.268
MAPE 7.149 . 7.149 7.149
MaxAPE 22.242 . 22.242 22.242
MAE 295.605 . 295.605 295.605
MaxAE 1056.621 . 1056.621 1056.621
Normalized BIC 13.384 . 13.384 13.384
Model Statistics
Model
Number of
Predictors
Model Fit
statistics Ljung-Box Q(18)
Number of
Outliers
Stationary R-
squared Statistics DF Sig.
TS-Model_1 0 .694 6.913 8 .546 0
ERROR DIAGNOSTIC Noise residual from TS-Model_1
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.042 .158 .071 1 .790
2 -.091 .156 .411 2 .814
3 -.122 .153 1.039 3 .792
4 -.195 .151 2.709 4 .608
5 -.028 .149 2.743 5 .739
6 .138 .147 3.628 6 .727
7 .074 .144 3.888 7 .793
8 -.072 .142 4.148 8 .844
9 -.062 .139 4.346 9 .887
10 -.102 .137 4.903 10 .898
11 .077 .134 5.231 11 .919
12 .001 .132 5.231 12 .950
13 -.058 .129 5.432 13 .964
14 .027 .126 5.479 14 .978
15 .089 .123 5.993 15 .980
16 .057 .121 6.217 16 .986
Autocorrelations
Series:Noise residual from TS-Model_1
Lag Autocorrelation Std. Errora
Box-Ljung Statistic
Value df Sig.b
1 -.042 .158 .071 1 .790
2 -.091 .156 .411 2 .814
3 -.122 .153 1.039 3 .792
4 -.195 .151 2.709 4 .608
5 -.028 .149 2.743 5 .739
6 .138 .147 3.628 6 .727
7 .074 .144 3.888 7 .793
8 -.072 .142 4.148 8 .844
9 -.062 .139 4.346 9 .887
10 -.102 .137 4.903 10 .898
11 .077 .134 5.231 11 .919
12 .001 .132 5.231 12 .950
13 -.058 .129 5.432 13 .964
14 .027 .126 5.479 14 .978
15 .089 .123 5.993 15 .980
16 .057 .121 6.217 16 .986
a. The underlying process assumed is independence (white noise).
b. Based on the asymptotic chi-square approximation.
Partial Autocorrelations
Series:Noise residual from TS-Model_1
Lag
Partial
Autocorrelation Std. Error
1 -.042 .164
2 -.093 .164
3 -.131 .164
4 -.223 .164
5 -.088 .164
6 .071 .164
7 .027 .164
8 -.106 .164
9 -.068 .164
10 -.086 .164
APPENDIX – IV
Variables Entered/Removedb
Model Variables Entered
Variables
Removed Method
1 CI, Y, M3, EL, ST,
CS
. Enter
Model Summaryb
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .974a .949 .938 362.71046 1.970
a. Predictors: (Constant), CI, Y, M3, EL, ST, CS
b. Dependent Variable: TS
ANOVAb
Model Sum of Squares df Mean Square F Sig.
1 Regression 70789330.809 6 11798221.801 89.680 .000a
Residual 3815207.373 29 131558.875
Total 74604538.181 35
a. Predictors: (Constant), CI, Y, M3, EL, ST, CS
b. Dependent Variable: TS
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) -1936.427 1322.093 -1.465 .154
ST -11.436 2.438 -.465 4.690 .000
M3 .002 .001 .134 2.146 .040
CS .010 .004 .263 2.646 .013
EL 9.995 5.833 .169 1.714 .097
Y -62.820 89.928 -.037 -.699 .490
CI 2.450 4.691 .054 .522 .605
ANOVAb
Model Sum of Squares df Mean Square F Sig.
1 Regression 70789330.809 6 11798221.801 89.680 .000a
Residual 3815207.373 29 131558.875
Total 74604538.181 35
a. Dependent Variable: TS
Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 1638.5338 6049.4902 3675.2163 1422.16466 36
Residual -614.99127 743.60608 .00000 330.16045 36
Std. Predicted Value -1.432 1.669 .000 1.000 36
Std. Residual -1.696 2.050 .000 .910 36
a. Dependent Variable: TS
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