11.76738 0.14637 80.39 Cardiff 185.2261 1.517523 122.05 0.8305 12.66905 0.1562882 81.06 South end 200.6933 1.285398 156.13 0.8347 0.1375053 85.63 Brighton 191.2164 1.413662 135.26 0.8256 12.16372 0.1448235 83.99 Bristol 187.0117 1.517392 123.25 0.8350 0.1522111 78.32 Southampton 193.3418 1.483988 130.29 0.8005 11.82598 0.1478421 79.99 Carlisle 193.2944 1.500767 128.80 0.8013 11.76573 0.1644963 71.53 CHV 184.1587 1.463701 125.82 0.8490 0.1542591 80.83 Table – Regression Coefficients and N-W S.E. The and White tests will be conducted to test for Heteroscedasticity. The Null Hypothesis is that the error term has a constant variance, the error term is homoscedastic (Equation 12) and the alternate hypothesis is that the error variance varies with the dependent variables (Equation 13). H0: Homoscedasticity Equation H1:Heteroscedasticity Equation Table 34 illustrates that, with the exception of Manchester, all of the chosen locations either fail the Breusch-Pagan or White test, with Glasgow, Nottingham, Cardiff and Carlisle failing both tests. These two tests were also applied to the CHV regression, heteroscedasticity was found to be present using the White test, but the error term was found to be homoscedastic using the Breusch-Pagan test. Problems with heteroscedasticity cannot be ignored, it causes the estimators to be inefficient and have much larger variance, changing according to different values of the explanatory variables, hetero-consistent Standard Errors (S.E.) will be calculated after the models have been tested for serial correlation. As the regression is of AR (1) in nature,
Model adequacy was again verified using the methods applied in 5.4 and as the lagged GARCH terms are very significant we can confirm volatility clustering is again present in this time series. 5.62 ‘Volatility is greater in the winter than in the summer, this is because the high marginal cost of natural gas production and the inelastic winter mean that shocks of even a small magnitude can cause a large price swings’ Suenaga et al (2006). Four new variables were generated, each indicative of a weather season. Winter (Equation 44), Spring (Equation 45), Summer (Equation 46) and Autumn (Equation 47) dummy variables were constructed and are defined below. Equation Equation Equation Equation In initial testing the coefficient of ‘Autumn’ was found not to be statistically significant, this variable was dropped from the analysis and regression model re-run, this is shown below in Equation 48. Equation Equation Where denotes spot volatility (defined in Equation 22). Table 17 displays the estimated coefficients and their significant levels (95% Conf.). Summer and Spring were found to be very significant, and Winter and WSDummy were found to be significant. Spot Volatility Coefficients Std. Err. t Robust S.E Robust t VIF Equation 48 0.0207614 0.0050475 8.03 0.0051286 4.05 -0.0063683 0.0031445 -2.03 0.0038773 -1.64 1.80 -0.0088985 0.0035025 -2.54 0.0029643 -3.00 1.71
Mean -14 27 9.75 9.77 -0.87 2.60 HDD 0 33 8.86 8.88 0.21 2.44 CDD 0 8.5 0.55 0.06 9.79 119.96 Table – Carlisle Summary Statistics. Location Degree Days National Grid Demand London HDD 0.9134 CDD -0.3233 Birmingham HDD 0.9072 CDD -0.1590 Glasgow HDD 0.8678 CDD -0.1590 Sunderland HDD 0.8808 CDD -0.1762 Manchester HDD 0.8970 CDD -0.2227 Nottingham HDD 0.9114 CDD -0.2668 Cardiff HDD 0.9116 CDD -0.1871 South end HDD 0.9137 CDD -0.3469 Brighton HDD 0.9088 CDD -0.2261 Bristol HDD 0.9139 CDD -0.2308 Southampton HDD 0.8950 CDD -0.2215 Carlisle HDD 0.8952 CDD -0.2476 Table - Heating Degree Days and Location correlations. Location Breusch-Pagan Test White Test p-value Reject the Null? London 0.0697 0.0000 No/Yes Birmingham 0.0934 0.0000 No/Yes Glasgow 0.0221 0.0002 Yes/Yes Sunderland 0.5415 0.0000 No/Yes Manchester 0.3512 0.2964 No/No Nottingham 0.0170 0.0002 Yes/Yes Cardiff 0.0280 0.0004 Yes/Yes