Econometrics - Research Paper Example

c) Calculate the first order autocorrelation coefficient for the returns on the three stocks and comment upon them, relating the results to relevant financial theory. Carry out an appropriate Dickey-Fuller test to for stationarity in each stock price (or log of stock price) and each stock return, and explain the importance of your results. Correlogram for Barclays Date: 08/17/09 Time: 20:58 Sample: 1/01/1990 12/31/2008 Included observations: 225 Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|* | .|* | 1 0.073 0.073 1.2002 0.273 *|. | *|. | 2 -0.070 -0.075 2.3099 0.315 *|. | *|. | 3 -0.095 -0.085 4.4057 0.221 .|* | .|* | 4 0.141 0.152 8.9855 0.061 .|* | .|* | 5 0.123 0.091 12.493 0.029 .|. | .|. | 6 0.039 0.033 12.841 0.046 *|. | *|. | 7 -0.142 -0.113 17.563 0.014 *|. | *|. | 8 -0.105 -0.090 20.150 0.010 *|. | *|. | 9 -0.067 -0.097 21.215 0.012 .|. | .|. | 10 0.065 0.026 22.224 0.014 .|. | .|. | 11 -0.043 -0.046 22.672 0.020 .|. | .|. | 12 -0.046 0.004 23.178 0.026 .|. | .|* | 13 0.010 0.072 23.204 0.039 .|. | .|. | 14 0.033 0.018 23.469 0.053 .|. | .|. | 15 0.033 0.019 23.729 0.070 .|. | .|. | 16 0.016 0.004 23.793 0.094 .|. | .|. | 17 0.040 0.037 24.178 0.115 .|. | .|. | 18 -0.004 -0.031 24.182 0.149 .|* | .|* | 19 0.077 0.070 25.667 0.140 .|. | *|. | 20 -0.039 -0.062 26.041 0.164 *|. | *|. | 21 -0.093 -0.094 28.221 0.134 .|. | .|. | 22 0.012 0.043 28.255 0.167 .|. | *|. | 23 -0.051 -0.096 28.919 0.183 .|. | .|. | 24 -0.017 -0.001 28.995 0.220 *|. | .|. | 25 -0.063 -0.028 30.003 0.224 .|. | .|* | 26 0.027 0.067 30.196 0.260 *|. | *|. | 27 -0.065 -0.067 31.280 0.260 *|. | *|. | 28 -0.079 -0.077 32.913 0.239 .|. | .|. | 29 -0.020 -0.019 33.016 0.277 .|. | .|. | 30 0.029 -0.015 33.237 0.312 .|. | .|. | 31 -0.029 -0.035 33.462 0.349 .|* | .|** | 32 0.183 0.197 42.344 0.104 .|. | .|. | 33 -0.019 -0.013 42.444 0.126 .|. | .|. | 34 0.027 0.042 42.636 0.147 .|. | .|. | 35 -0.052 -0.047 43.368 0.157 .|. | *|. | 36 0.019 -0.072 43.470 0.183 Correlogram for Vodafone Date: 08/17/09 Time: 21:05 Sample: 1/01/1990 12/31/2008 Included observations: 224 Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|. | .|. | 1 0.002 0.002 0.0007 0.979 .|. | .|. | 2 0.019 0.019 0.0826 0.960 .|* | .|* | 3 0.182 0.182 7.6489 0.054 *|. | *|. | 4 -0.061 -0.063 8.4992 0.075 .|* | .|* | 5 0.146 0.145 13.451 0.019 .|. | .|. | 6 0.015 -0.021 13.502 0.036 .|* | .|* | 7 0.088 0.116 15.322 0.032 .|* | .|* | 8 0.132 0.076 19.422 0.013 .|. | .|. | 9 -0.027 -0.009 19.596 0.021 .|. | .|. | 10 0.048 -0.006 20.139 0.028 .|* | .|* | 11 0.153 0.140 25.713 0.007 .|* | .|* | 12 0.115 0.116 28.881 0.004 .|. | .|. | 13 0.006 -0.033 28.889 0.007 .|. | .|. | 14 0.009 -0.041 28.907 0.011 .|. | *|. | 15 -0.032 -0.083 29.153 0.015 .|. | .|. | 16 -0.016 -0.038 29.218 0.023 .|. | *|. | 17 -0.053 -0.089 29.894 0.027 *|. | *|. | 18 -0.087 -0.112 31.743 0.024 .|* | .|* | 19 0.128 0.089 35.794 0.011 *|. | *|. | 20 -0.155 -0.160 41.753 0.003 .|. | .|. | 21 -0.042 -0.006 42.203 0.004 .|* | .|* | 22 0.119 0.075 45.745 0.002 *|. | .|. | 23 -0.090 -0.021 47.806 0.002 .|* | .|. | 24 0.079 0.057 49.390 0.002 *|. | .|. | 25 -0.068 -0.029 50.556 0.002 *|. | .|. | 26 -0.085 -0.030 52.412 0.002 .|. | *|. | 27 -0.041 -0.074 52.843 0.002 *|. | .|. | 28 -0.150 -0.046 58.630 0.001 .|. | .|. | 29 -0.029 -0.026 58.850 0.001 .|. | .|. | 30 -0.047 -0.045 59.418 0.001 **|. | **|. | 31 -0.211 -0.199 71.094 0.000 *|. | *|. | 32 -0.124 -0.120 75.150 0.000 .|. | .|. | 33 0.032 0.063 75.414 0.000 .|. | .|* | 34 0.019 0.085 75.506 0.000 .|. | .|. | 35 0.006 0.053 75.517 0.000 .|. | .|. | 36 -0.057 -0.029 76.393 0.000 Correlogram for FTSE ALL-Price Index Date: 08/17/09 Time: 21:06 Sample: 1/01/1990 12/31/2008 Included observations: 224 Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|. | .|. | 1 0.012 0.012 0.0347 0.852 .|. | .|. | 2 -0.031 -0.031 0.2555 0.880 .|. | .|. | 3 -0.026 -0.025 0.4116 0.938 .|. | .|. | 4 0.001 0.000 0.4116 0.982 .|. | .|. | 5 0.020 0.019 0.5068 0.992 .|* | .|* | 6 0.088 0.087 2.2985 0.890 *|. | *|. | 7 -0.067 -0.069 3.3522 0.851 .|. | .|. | 8 0.049 0.058 3.9109 0.865 .|. | .|. | 9 0.033 0.031 4.1606 0.901 .|. | .|. | 10 0.054 0.053 4.8437 0.901 .|. | .|. | 11 0.002 0.002 4.8448 0.938 .|* | .|* | 12 0.094 0.095 6.9382 0.862 .|. | .|. | 13 -0.011 -0.001 6.9649 0.904 .|. | .|. | 14 0.047 0.041 7.4999 0.914 *|. | *|. | 15 -0.156 -0.158 13.385 0.573 .|* | .|* | 16 0.090 0.098 15.363 0.498 .|. | .|. | 17 0.062 0.048 16.307 0.502 .|. | .|. | 18 0.016 -0.007 16.372 0.567 .|. | .|. | 19 0.037 0.052 16.717 0.609 .|. | .|. | 20 -0.008 -0.021 16.731 0.670 .|. | .|. | 21 0.013 0.043 16.770 0.725 .|* | .|. | 22 0.098 0.048 19.185 0.634 *|. | *|. | 23 -0.101 -0.095 21.739 0.536 .|. | .|. | 24 -0.003 0.006 21.741 0.595 .|. | .|. | 25 -0.022 -0.028 21.860 0.644 .|. | *|. | 26 -0.035 -0.058 22.176 0.679 .|* | .|* | 27 0.068 0.087 23.358 0.666 .|. | .|. | 28 0.013 -0.032 23.404 0.713 *|. | *|. | 29 -0.117 -0.095 26.985 0.573 .|. | .|. | 30 0.057 0.023 27.846 0.579 *|. | *|. | 31 -0.094 -0.099 30.154 0.509 *|. | .|. | 32 -0.058 -0.039 31.052 0.514 .|. | .|. | 33 -0.025 -0.056 31.215 0.556 .|. | .|. | 34 -0.006 -0.002 31.226 0.604 .|. | .|. | 35 0.028 0.054 31.440 0.641 .|. | *|. | 36 -0.053 -0.095 32.208 0.650 Correlogram for GSK Date: 08/17/09 Time: 21:10 Sample: 1990:01 2008:12 Included observations: 224 Autocorrelation Partial Correlation AC PAC Q-Stat Prob *|. | *|. | 1 -0.188 -0.188 8.0226 0.005 .|. | .|. | 2 -0.003 -0.040 8.0247 0.018 .|. | .|. | 3 -0.010 -0.019 8.0469 0.045 .|. | .|. | 4 -0.033 -0.040 8.2986 0.081 .|* | .|* | 5 0.136 0.127 12.594 0.027 *|. | .|. | 6 -0.063 -0.016 13.523 0.035 .|. | .|. | 7 0.045 0.037 13.994 0.051 .|. | .|. | 8 -0.015 0.001 14.048 0.081 .|* | .|* | 9 0.070 0.079 15.212 0.085 .|. | .|. | 10 -0.028 -0.020 15.402 0.118 .|. | .|. | 11 0.026 0.034 15.562 0.158 .|* | .|* | 12 0.159 0.170 21.610 0.042 **|. | *|. | 13 -0.219 -0.165 33.070 0.002 .|* | .|. | 14 0.077 0.000 34.503 0.002 .|. | .|. | 15 -0.038 -0.019 34.855 0.003 .|. | .|. | 16 0.052 0.032 35.521 0.003 .|. | *|. | 17 -0.040 -0.080 35.921 0.005 .|. | .|* | 18 0.053 0.101 36.601 0.006 .|. | .|. | 19 -0.006 -0.015 36.609 0.009 .|. | .|. | 20 -0.048 -0.045 37.189 0.011 .|* | .|. | 21 0.077 0.041 38.661 0.011 .|. | .|. | 22 -0.057 0.010 39.482 0.012 .|* | .|. | 23 0.107 0.058 42.375 0.008 *|. | *|. | 24 -0.110 -0.093 45.457 0.005 *|. | *|. | 25 -0.130 -0.107 49.753 0.002 .|. | .|. | 26 0.059 -0.047 50.653 0.003 .|. | .|. | 27 0.037 0.060 51.004 0.003 .|. | .|. | 28 -0.006 -0.040 51.014 0.005 .|. | .|. | 29 -0.010 0.047 51.041 0.007 .|* | .|* | 30 0.105 0.102 53.919 0.005 .|. | .|. | 31 -0.017 0.057 53.990 0.006 .|. | *|. | 32 -0.057 -0.082 54.835 0.007 .|. | .|. | 33 -0.040 -0.055 55.253 0.009 .|. | .|. | 34 -0.004 0.006 55.257 0.012 .|. | .|. | 35 0.023 -0.043 55.400 0.016 .|. | .|. | 36 -0.027 0.033 55.592 0.020 Interpretation: This is the Eviews Correlogram. "The column to the left of AC gives k, the number of time periods used to calculate k. The AC column gives k. The graph of k is shown by horizontal bars in the firstcolumn headed by "Autocorrelation". Positive k s are drawn to the right of the zero line. The two vertical lines in the first column enclose the 95% confidence interval. Id k that extends past the broken line, reject the null hypothesis that k = 0 at 5% level of significance. Otherwise, do not reject the null hypothesis" (Danao). In this particular tests, the result for BARC, VOD and FTALLSH show that we do not reject the null hypothesis that k = 0. But for the GSK graph, the result is opposite. We have necessary proof to reject the null hypothesis. AUGMENTED DICKEY-FULLER TEST Null Hypothesis: D(VOD) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=14) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.84022 0.0000 Test critical values: 1% level -3.459627 5% level -2.874317 10% level -2.573656 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(VOD,2) Method: Least Squares Date: 08/17/09 Time: 22:08 Sample(adjusted): 1990:03 2008:09 Included observations: 223 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(VOD(-1)) -0.998227 0.067265 -14.84022 0.0000 C 0.521087 0.794838 0.655589 0.5128 R-squared 0.499130 Mean dependent var 0.022377 Adjusted R-squared 0.496864 S.D. dependent var 16.71859 S.E. of regression 11.85885 Akaike info criterion 7.792954 Sum squared resid 31079.74 Schwarz criterion 7.823512 Log likelihood -866.9144 F-statistic 220.2322 Durbin-Watson stat 1.999808 Prob(F-statistic) 0.000000 Null Hypothesis: D(GSK) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=14) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -17.93081 0.0000 Test critical values: 1% level -3.459627 5% level -2.874317 10% level -2.573656 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GSK,2) Method: Least Squares Date: 08/17/09 Time: 22:09 Sample(adjusted): 1990:03 2008:09 Included observations: 223 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(GSK(-1)) -1.189928 0.066362 -17.93081 0.0000 C 4.950890 5.854124 0.845710 0.3986 R-squared 0.592637 Mean dependent var 0.791480 Adjusted R-squared 0.590794 S.D. dependent var 136.5532 S.E. of regression 87.35205 Akaike info criterion 11.78670 Sum squared resid 1686314. Schwarz criterion 11.81726 Log likelihood -1312.217 F-statistic 321.5139 Durbin-Watson stat 2.003737 Prob(F-statistic) 0.000000 Null Hypothesis: D(FTALLSH) has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=14) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.62647 0.0000 Test critical values: 1% level -3.459627 5% level -2.874317 10% level -2.573656 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(FTALLSH,2) Method: Least Squares Date: 08/17/09 Time: 22:09 Sample(adjusted): 1990:03 2008:09 Included observations: 223 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(FTALLSH(-1)) -0.987516 0.067516 -14.62647 0.0000 C 7.468127 6.142099 1.215892 0.2253 R-squared 0.491876 Mean dependent var 0.743632 Adjusted R-squared 0.489577 S.D. dependent var 128.0219 S.E. of regression 91.46379 Akaike info criterion 11.87869 Sum squared resid 1848803. Schwarz criterion 11.90925 Log likelihood -1322.474 F-statistic 213.9335 Durbin-Watson stat 1.991408 Prob(F-statistic) 0.000000 Decision Rule: "If the absolute value of the ADF Test Statistic is less than the value of the McKinnon Critical Values at the chosen level of significance, then the series has a unit root and is therefore non-stationary. Conclusion: The results show that the series are all stationary since all the absolute values of the ADF are more than the McKinnon Critical Values. d) Read More