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BSE 500 FORECAST

Correlogram of Raw Dataset:-

Its quiet evident from the correlogram that the autocorrelation exist since the ACF & PCF values are continuously

decreasing.Note that the dot lines in the graphs of AC and PAC are the approximate two standard error bounds computedas 2/sqr(T).Hence the null hypothesis that there is autocorrelation is getting accepted throughout.

Date: 07/24/12 Time: 00:46

Sample: 7/23/2001 7/23/2012

Included observations: 2747

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

|******* |******* 1 0.999 0.999 2744.1 0.000

|******* *| | 2 0.998 -0.068 5482.5 0.000

|******* | | 3 0.996 -0.015 8215.0 0.000

|******* | | 4 0.995 0.003 10942. 0.000

|******* | | 5 0.994 0.015 13663. 0.000|******* | | 6 0.993 0.019 16378. 0.000

|******* | | 7 0.992 0.010 19088. 0.000

|******* | | 8 0.990 -0.026 21793. 0.000

|******* | | 9 0.989 -0.034 24491. 0.000

|******* | | 10 0.988 -0.013 27184. 0.000

|******* | | 11 0.987 0.001 29870. 0.000

|******* | | 12 0.985 0.021 32550. 0.000

|******* | | 13 0.984 -0.014 35225. 0.000

|******* | | 14 0.983 -0.008 37893. 0.000

|******* | | 15 0.981 -0.032 40555. 0.000

|******* | | 16 0.980 -0.012 43210. 0.000

|******* | | 17 0.978 -0.014 45858. 0.000

|******* | | 18 0.977 -0.010 48499. 0.000

|******* | | 19 0.976 0.008 51134. 0.000

|******* | | 20 0.974 0.011 53761. 0.000

|******* | | 21 0.973 0.014 56383. 0.000

|******* | | 22 0.971 -0.005 58997. 0.000

|******* | | 23 0.970 0.002 61606. 0.000

|******* | | 24 0.969 0.011 64207. 0.000

|******* | | 25 0.967 -0.007 66803. 0.000

|******* | | 26 0.966 -0.011 69391. 0.000

|******* | | 27 0.964 -0.008 71973. 0.000

|******* | | 28 0.963 0.031 74549. 0.000

|******* | | 29 0.962 -0.013 77118. 0.000

|******* | | 30 0.960 0.004 79681. 0.000

|******* | | 31 0.959 0.011 82238. 0.000

|******* | | 32 0.958 0.009 84789. 0.000|******* | | 33 0.956 -0.003 87333. 0.000

|******* | | 34 0.955 -0.000 89871. 0.000

|******* | | 35 0.954 -0.007 92404. 0.000

|******* | | 36 0.952 0.015 94930. 0.000

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Correlogram of IR(1) :

Date: 07/24/12 Time: 00:56

Sample: 7/23/2001 7/23/2012

The AR order from PCF is (1) & the MAorder from the ACF is of order (1).Included observations: 2746

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

|* | |* | 1 0.117 0.117 37.546 0.000

| | | | 2 0.029 0.016 39.873 0.000

| | | | 3 -0.001 -0.006 39.875 0.000

| | | | 4 -0.027 -0.027 41.891 0.000

| | | | 5 -0.043 -0.037 47.034 0.000

| | | | 6 -0.032 -0.022 49.829 0.000

| | | | 7 0.041 0.050 54.552 0.000

| | | | 8 0.061 0.053 64.970 0.000

| | | | 9 0.033 0.016 67.991 0.000

| | | | 10 0.015 0.004 68.650 0.000

| | | | 11 -0.054 -0.059 76.709 0.000

| | | | 12 0.013 0.031 77.183 0.000

| | | | 13 0.016 0.022 77.857 0.000

| | | | 14 0.063 0.064 88.944 0.000

| | | | 15 0.034 0.015 92.152 0.000

| | | | 16 0.041 0.025 96.878 0.000

| | | | 17 0.046 0.033 102.74 0.000

| | | | 18 -0.020 -0.023 103.85 0.000

| | | | 19 -0.029 -0.015 106.15 0.000

| | | | 20 -0.033 -0.022 109.13 0.000

| | | | 21 0.001 0.007 109.13 0.000

| | | | 22 -0.002 -0.011 109.15 0.000| | | | 23 -0.009 -0.015 109.39 0.000

| | | | 24 0.020 0.011 110.48 0.000

| | | | 25 0.028 0.024 112.58 0.000

| | | | 26 0.003 -0.004 112.60 0.000

| | | | 27 -0.054 -0.052 120.61 0.000

| | | | 28 0.002 0.016 120.63 0.000

| | | | 29 -0.006 -0.011 120.73 0.000

| | | | 30 -0.015 -0.016 121.38 0.000

| | | | 31 -0.026 -0.031 123.25 0.000

| | | | 32 0.005 0.009 123.33 0.000

| | | | 33 0.009 0.004 123.55 0.000

| | | | 34 0.029 0.033 125.86 0.000

| | | | 35 -0.039 -0.040 130.03 0.000

| | | | 36 0.026 0.040 131.96 0.000

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Parameter estimates of MA(1) model :

Dependent Variable: DCLOSE

Method: Least Squares

Date: 07/24/12 Time: 01:12

Sample (adjusted): 7/24/2001 7/23/2012

Included observations: 2746 after adjustments

Convergence achieved after 5 iterations

MA Backcast: 7/23/2001

Variable Coefficient Std. Error t-Statistic Prob.

C 2.000176 1.598992 1.250898 0.2111

MA(1) 0.111984 0.018976 5.901340 0.0000

R-squared 0.013082 Mean dependent var 2.004782

Adjusted R-squared 0.012723 S.D. dependent var 75.83919

S.E. of regression 75.35521 Akaike info criterion 11.48303

Sum squared resid 15581549 Schwarz criterion 11.48734

Log likelihood -15764.20 Hannan-Quinn criter. 11.48459

F-statistic 36.37376 Durbin-Watson stat 1.992840

Prob(F-statistic) 0.000000

Inverted MA Roots -.11

-300

-200

-100

0

100

200

02 04 06 08 10 12

DCLOSEF 2 S.E.

Forecast: DCLOSEF

Actual: DCLOSE

Forecast sample: 7/23/2001 7/23/2012

Included observations: 2746

Root Mean Squared Error 75.79757

Mean Absolute Error 47.71814

Mean Abs. Percent Error 125.6167

Theil Inequality Coefficient 0.963230Bias Proportion 0.000000

Variance Proportion 0.947273

Covariance Proportion 0.052727

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Parameter estimates of AR(1) MA(1) model :

Dependent Variable: DCLOSE

Method: Least Squares

Date: 07/24/12 Time: 01:13

Sample (adjusted): 7/25/2001 7/23/2012

Included observations: 2745 after adjustments

Convergence achieved after 11 iterations

MA Backcast: 7/24/2001

Variable Coefficient Std. Error t-Statistic Prob.

C 2.005477 1.653074 1.213181 0.2252

AR(1) 0.226005 0.156899 1.440449 0.1499

MA(1) -0.110417 0.160079 -0.689767 0.4904

R-squared 0.013877 Mean dependent var 2.009362

Adjusted R-squared 0.013158 S.D. dependent var 75.85263

S.E. of regression 75.35195 Akaike info criterion 11.48331

Sum squared resid 15568847 Schwarz criterion 11.48978Log likelihood -15757.84 Hannan-Quinn criter. 11.48565

F-statistic 19.29302 Durbin-Watson stat 2.000007

Prob(F-statistic) 0.000000

Inverted AR Roots .23

Inverted MA Roots .11

-160

-120

-80

-40

0

40

80

120

160

02 04 06 08 10 12

DCLOSEF 2 S.E.

Forecast: DCLOSEF

Actual: DCLOSE

Forecast sample: 7/23/2001 7/23/2012

Adjusted sample: 7/25/2001 7/23/2012

Included observations: 2745

Root Mean Squared Error 75.83856

Mean Absolute Error 47.76835

Mean Abs. Percent Error 125.7223

Theil Inequality Coefficient 0.973908

Bias Proportion 0.000000

Variance Proportion 0.998448

Covariance Proportion 0.001552

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Parameter estimates of AR(1) model :

Dependent Variable: DCLOSE

Method: Least SquaresDate: 07/24/12 Time: 01:11

Sample (adjusted): 7/25/2001 7/23/2012

Included observations: 2745 after adjustments

Convergence achieved after 3 iterations

Variable Coefficient Std. Error t-Statistic Prob.

C 2.004777 1.628571 1.231004 0.2184

AR(1) 0.116954 0.018969 6.165358 0.0000

R-squared 0.013668 Mean dependent var 2.009362

Adjusted R-squared 0.013309 S.D. dependent var 75.85263

S.E. of regression 75.34619 Akaike info criterion 11.48279

Sum squared resid 15572142 Schwarz criterion 11.48710

Log likelihood -15758.13 Hannan-Quinn criter. 11.48435

F-statistic 38.01164 Durbin-Watson stat 2.002984

Prob(F-statistic) 0.000000

Inverted AR Roots .12

-160

-120

-80

-40

0

40

80

120

160

02 04 06 08 10 12

DCLOSEF 2 S.E.

Forecast: DCLOSEF

Actual: DCLOSE

Forecast sample: 7/23/2001 7/23/2012

Adjusted sample: 7/25/2001 7/23/2012

Included observations: 2745

Root Mean Squared Error 75.83869

Mean Absolute Error 47.76919

Mean Abs. Percent Error 125.7215

Theil Inequality Coefficient 0.973917

Bias Proportion 0.000000

Variance Proportion 0.999258

Covariance Proportion 0.000742

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ComparativeTable for Various Criterion :

AR(1) MA(1) ARIMA(1,1,1)

AIC 11.48279 11.48303 11.48331

SIC 11.4871 11.48734 11.48978

Adj R2

0.013309 0.012723 0.013158Inverse AR Roots 0.12 ----------- 0.23

Inverse MA Roots ----------- -0.11 0.11

Mean Absolute %

Error125.7215 125.6167 125.7223

Hence based on the above criterion we select the AR(1,1,0) model as the best fit model for the given data set.

The same can be validated by AUTO ARIMA CRITERION OUTPUT which also suggest as AR(1,1,0) model as the best fit

model.

AR / MA 0.000000 1.000000 2.000000 3.000000

0.000000 11.49798 11.48770 11.48973 11.49257

1.000000 11.48710 11.48978 11.49259 11.49541

2.000000 11.49009 11.49297 11.48906 11.49026

The proposed model equation of AR(1) :-

Yt(Close Price) = 2.004777 + 0.116954 Yt-1(DClose_Price)