NDM Data Sample Analysis: Final Results Option C: Regression Analysis

Contents Regression Analysis Implementation/Mechanics and Acceptance Criteria Initial In-Sample Results Revised In-Sample Results Out-of-Sample Model fit using 2009/2010 data Conclusion and Recommendations

Regression Analysis: Formula Regression Model as follows: Each EUC (1 through to 9) is to be modelled AQ Ratio only available for EUC1 to EUC4

Regression Analysis: Input Data It was decided by DESC on 7th November that Gas Year 2009/2010 is the out-of-sample data. WM was the LDZ chosen to perform analysis upon. Various stretches of data, prior to 2009/2010, were used (1, 2 and 3 year-stretch) in identifying best regression model on out-of-sample 2010/2011 data. In the event of the application of the 2 or 3 year-stretch of data, parameter smoothing (Appendix 4) should be implemented.

Regression Analysis: Explanatory Variables Time intervals used based on office hours and domestic habits were devised and applied to weather parameters (temperature, solar radiation, rainfall etc…) Slot 1 from 5am to 8am Slot 2 from 9am to 4pm Slot 3 from 5pm to 10pm Slot 4 from 11pm to 4am Explanatory variables such as weather, CWV, Bank holidays, School Holidays, Industrial shutdown (2-week period starting end of July), lagged effects and so forth.

INITIAL IN-SAMPLE RESULTS Regression Analysis

In-Sample Results Poor results were obtained when applying regression analysis to the whole series Winter and Summer piecewise regression analysis hence conducted Overall MAPE 16.69% Average BIAS 0.88% Adjusted R² 94.77%

Piecewise Regression Analysis REVISED IN-SAMPLE RESULTS Piecewise Regression Analysis

In-Sample Results: EUC1 Graphical Output OVERALL WINTER SUMMER MAPE 4.04% 3.73% 4.63% BIAS 0.03% 0.17% -0.23% R² 99.64% Adjusted R² 99.12% 93.26%

Regression Analysis: EUC1 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt January 22314.60 0.00% February 22984.18 December 23299.95 November 22724.65 March 22464.76 April 24031.48 October 22785.54 May 23734.64 September 23182.55 CWV -1442.61 Slot4_Temp 162.57 Slot2_GlobalRadiation -0.11 Mon_Thurs -563.80 mean_Temp -367.38 mean_Windspeed_lag1 143.94 mean_Temp_lag2 102.13 Pre_NY_Period -1331.77 Xmas -2980.30 Slot2_Temp 239.81 0.01% Boxing_Day -2680.48 New_Year -2544.26 0.02% Pre_Xmas_WE -940.88 0.10% Bank__Hols 1110.17 0.52% Friday -304.48 0.87% Slot2_Windspeed 57.82 2.54% Parameter Estimate Probt September 17123.50 0.00% June 17115.03 July 16828.82 August 16501.91 May 16739.55 CWV -1068.42 Slot4_Temp 92.52 mean_Humidity 23.25 Slot2_Temp -132.18 0.01% Mon_Thurs -203.53 0.02% Slot1_Humidity_lag2 14.98 0.14% Slot3_Rainfall_lag1 -294.96 0.17% Slot3_Temp_lag1 -80.18 0.18% Slot2_Temp_lag2 -41.21 0.30% Slot4_Humidity -12.78 0.39% mean_Temp 130.97 0.40% mean_WindDirection 2.14 0.41% mean_Temp_lag1 94.39 0.46% Slot1_WindDirection -1.53 1.08% Friday -198.62 1.12% Aug_BHper -263.45 3.41%

In-Sample Results: EUC2 Graphical Output OVERALL WINTER SUMMER MAPE 4.65% 4.39% 5.13% BIAS -0.12% -0.04% -0.27% R² 99.30% Adjusted R² 98.01% 88.01%

Regression Analysis: EUC2 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt February 24896.99 0.00% December 25910.03 January 25216.75 November 25253.96 March 25687.92 April 26978.34 October 24366.63 May 24823.64 September 23896.28 Mon_Thurs 3569.35 Friday 3567.11 CWV -1572.13 Bank__Hols -3395.76 Early_May_BHper 3165.03 Pre_NY_Period -2302.80 sum_Global_Radiation_lag1 -1.70 Slot2_GlobalRadiation_lag1 1.67 0.01% Slot2_Temp_lag1 453.67 Post_NY -2894.35 mean_Temp_lag1 -516.88 Slot3_GlobalRadiation_lag1 1.68 0.02% mean_Windspeed_lag1 203.93 Saturday 802.64 0.10% Slot3_Temp 143.82 0.28% mean_Humidity -27.98 0.65% Slot3_Humidity_lag2 26.34 0.79% mean_Temp_lag3 -83.73 Slot4_Humidity 22.09 0.96% Slot4_Humidity_lag2 -25.13 1.11% Slot2_Temp_lag2 88.46 2.12% Slot1_Rainfall 354.62 3.55% Parameter Estimate Probt September 22404.81 0.00% June 22480.93 May 22967.33 July 22067.84 August 21791.29 Mon_Thurs 1091.14 Friday 1258.90 CWV -994.35 mean_WindDirection_lag2 -3.92 Slot4_Temp 174.83 0.11% Slot2_Windspeed_lag2 -144.27 0.64% Slot3_Windspeed_lag2 168.66 0.66% Slot1_Temp 774.38 0.75% Saturday 379.51 0.81% Slot4_Temp_lag1 979.63 0.88% Slot4_Windspeed_lag2 -119.73 0.96% Slot3_Temp 1104.06 1.03% mean_Temp -4157.04 Slot3_Temp_lag2 -87.07 1.27% Slot2_Temp 1293.20 1.51% Slot4_Temp_lag2 856.64 1.55% mean_Temp_lag3 -58.38 1.59% mean_Temp_lag1 -3624.30 2.55% Slot3_Temp_lag1 939.97 2.76% Slot2_Temp_lag1 1177.51 2.78% Slot1_Temp_lag1 579.16 4.28% Slot4_Humidity_lag2 -12.54 4.68%

In-Sample Results: EUC3 Graphical Output OVERALL WINTER SUMMER MAPE 8.82% 9.71% 7.02% BIAS 0.13% 0.36% -0.34% R² 97.12% Adjusted R² 93.60% 88.72%

Regression Analysis: EUC3 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt January 79747.71 0.00% December 82444.32 February 81233.05 November 78598.08 April 86723.18 March 78496.77 Mon_Thurs 28933.57 October 80329.88 CWV -5623.89 May 82647.26 Friday 19619.18 September 74577.23 Bank__Hols -24845.79 Pre_NY_Period -22010.77 Early_May_BHper 17189.30 0.01% Pre_Xmas_WE -12655.00 0.03% Slot2_GlobalRadiation_lag2 7.70 0.66% sum_Global_Radiation_lag2 -7.35 0.73% Slot3_GlobalRadiation_lag2 7.84 0.74% Slot3_Rainfall_lag2 4042.24 0.99% Slot1_Windspeed_lag1 533.05 3.81% Parameter Estimate Probt Mon_Thurs 7401.74 0.00% Friday 5077.28 Industrial_Shutdown -5244.54 June 62777.11 September 60868.34 July 62070.14 May 61974.80 August 60168.91 CWV -3170.48 mean_Temp -1399.99 0.42% Slot4_Temp_lag1 617.68 0.77% Slot3_Temp 662.84 1.46% Slot1_WindDirection_lag2 -6.86 1.69% sum_Global_Radiation_lag1 0.32 3.73% mean_Humidity 56.44 3.95% Slot2_GlobalRadiation_lag1 -0.37 4.58%

In-Sample Results: EUC4 Graphical Output OVERALL WINTER SUMMER MAPE 5.10% 5.63% 4.04% BIAS 0.15% 0.27% -0.07% R² 98.61% Adjusted R² 96.60% 93.82%

Regression Analysis: EUC4 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt February 951838.59 0.00% January 952137.32 December 1012568.20 April 1059346.61 November 963798.92 March 962704.57 Mon_Thurs 240090.84 October 988564.44 May 986919.44 September 954741.26 CWV -69074.37 Friday 144578.20 Pre_NY_Period -312068.95 Pre_Xmas_WE -167265.75 Xmas -316269.84 Post_NY -161857.94 Early_May_BHper 130178.10 0.01% Saturday -45233.59 New_Year -229269.64 0.03% Boxing_Day -216058.86 0.08% Bank__Hols -131933.52 0.10% Slot3_Rainfall_lag2 35317.62 0.18% Slot1_Temp_lag1 4354.08 0.30% Slot2_GlobalRadiation_lag1 52.63 0.79% Slot3_Humidity_lag1 -2144.04 0.87% sum_Global_Radiation_lag1 -49.15 1.03% Slot2_Temp 6765.19 1.43% Slot2_WindDirection -118.27 1.52% mean_WindDirection_lag1 326.30 2.57% Slot2_WindDirection_lag1 -256.96 2.81% Slot3_Rainfall_lag1 25485.27 2.88% Slot3_GlobalRadiation_lag1 44.41 3.19% Slot4_Humidity_lag2 -1699.36 3.93% Slot2_Humidity 656.93 4.20% mean_Humidity_lag1 3010.43 4.59% mean_Rainfall -38849.79 4.72% Parameter Estimate Probt Mon_Thurs 104464.67 0.00% Friday 73651.30 June 426700.83 September 438252.59 July 412836.50 August 401466.76 May 416762.73 Bank__Hols -79936.53 Slot2_Temp -6101.32 mean_Humidity_lag1 2302.06 0.04% Slot3_Humidity_lag1 -1231.76 0.06% mean_Temp_lag3 -2894.08 0.16% Slot4_Humidity_lag2 -1011.96 0.26% Slot2_Rainfall_lag1 -13593.10 0.67% Industrial_Shutdown -14939.32 1.08% Slot3_Temp -3343.80 1.17% Slot4_Windspeed_lag2 -2297.07 3.55% Slot3_Humidity -277.74 4.40%

In-Sample Results: EUC5 Graphical Output OVERALL WINTER SUMMER MAPE 4.47% 4.73% 3.95% BIAS 0.06% 0.12% -0.07% R² 98.53% Adjusted R² 96.65% 95.69%

Regression Analysis: EUC5 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt January 4056668985.56 0.00% December 4217561383.48 February 4003227727.92 November 4149330396.49 April 4561443248.71 March 3933174374.55 October 4201617902.20 Mon_Thurs 1338177604.44 May 4243557350.11 September 3868740067.92 CWV -253774484.28 Friday 762285774.98 Pre_NY_Period -1521619903.09 Pre_Xmas_WE -892474674.70 Post_NY -762232437.47 Bank__Hols -898083477.63 Xmas -1233254585.96 New_Year -1070297536.44 0.01% Late_May_BHper -341433198.33 0.22% Slot2_GlobalRadiation_lag1 268250.12 0.23% sum_Global_Radiation_lag1 -259261.13 0.24% Slot3_GlobalRadiation_lag1 253959.80 0.46% Early_May_BHper 392808819.42 0.50% mean_Temp_lag1 23708783.68 0.64% Slot3_Rainfall_lag2 130819006.45 0.67% Boxing_Day -730124287.73 0.82% Slot2_Rainfall_lag1 300298224.19 1.08% mean_Rainfall_lag1 -440442987.03 1.11% Slot3_Rainfall_lag1 164369622.33 1.16% Parameter Estimate Mon_Thurs 752557557.46 Friday 446119347.70 September 3099216686.14 June 3142671499.11 May 3095608759.82 July 3040633417.07 August 3032545434.48 Industrial_Shutdown -165810995.67 Bank__Hols -526980673.30 CWV -115081675.25 mean_Temp -34751632.99 Slot4_Temp_lag1 16474169.20 Aug_BHper -90101691.04 Slot4_Rainfall -36677064.93

In-Sample Results: EUC6 Graphical Output OVERALL WINTER SUMMER MAPE 6.21% 5.88% 6.89% BIAS -0.18% -0.25% -0.05% R² 96.44% Adjusted R² 94.30% 93.88%

Regression Analysis: EUC6 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt January 3031702702.02 0.00% April 3705225830.67 November 3380308808.02 February 3107825591.11 December 3224580338.58 October 3461870402.92 March 2984695147.39 Mon_Thurs 1418333628.90 May 3460942914.60 CWV -156834473.09 September 3333975863.14 Pre_NY_Period -1744182029.71 Friday 583482250.37 Pre_Xmas_WE -1192973646.38 Late_May_BHper -726306113.28 New_Year -1740969389.19 Xmas -1674566801.13 Post_NY -919233864.37 Bank__Hols -710902088.13 Saturday -219092095.68 0.01% Boxing_Day -805324660.93 0.65% Slot3_WindDirection_lag1 -844542.90 3.61% mean_WindDirection_lag1 975048.84 3.96% Parameter Estimate Probt Mon_Thurs 1235026452.77 0.00% Friday 674544235.32 Industrial_Shutdown -651609324.63 Bank__Hols -960563021.18 mean_Humidity_lag2 6707546.88 0.08% September 145164024.55 0.19% mean_Humidity 10704477.27 0.68% Slot2_WindDirection_lag1 700399.08 0.93% sum_Global_Radiation_lag2 105229.38 1.26% Slot2_WindDirection_lag2 1490553.04 1.73% June 98764661.72 1.87% Slot3_Humidity -6088847.99 2.05% Slot2_GlobalRadiation_lag2 -101698.95 2.13% mean_WindDirection_lag2 -1745398.16 2.38% Slot3_GlobalRadiation_lag2 -107700.22 2.73%

In-Sample Results: EUC7 Graphical Output OVERALL WINTER SUMMER MAPE 6.60% 6.75% 6.30% BIAS -0.33% -0.38% -0.22% R² 95.59% Adjusted R² 92.35% 93.38%

Regression Analysis: EUC7 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt Mon_Thurs 1177872159.61 0.00% February 2766253487.31 January 2607863010.04 April 2955967683.56 November 2675659524.59 December 2556640984.92 CWV -128456746.67 October 2761541118.39 March 2412360674.29 May 2709774019.22 Pre_NY_Period -1621182999.46 September 2496078257.66 Pre_Xmas_WE -1071297108.01 Friday 474335150.07 Bank__Hols -1100825624.74 Post_NY -946274838.56 Late_May_BHper -547991094.60 New_Year -1248421347.67 Saturday -239632858.18 Xmas -1109813441.56 0.01% mean_Windspeed_lag1 26492029.18 2.13% Slot1_Humidity_lag2 2257180.73 3.24% mean_WindDirection_lag1 1060929.28 3.28% Slot3_WindDirection_lag1 -862911.89 4.00% Parameter Estimate Probt Mon_Thurs 853266264.96 0.00% September 2117041805.79 June 2067553308.09 July 2004947843.23 August 1910268225.93 Friday 397444383.51 May 2002471496.98 Industrial_Shutdown -383893983.61 Bank__Hols -796904440.07 Saturday -221764249.02 Aug_BHper -227593976.68 0.28% Slot2_GlobalRadiation -12801.70 0.37% Slot3_Humidity -4279630.34 0.58% mean_Temp -21648884.02 0.64%

In-Sample Results: EUC8 Graphical Output OVERALL WINTER SUMMER MAPE 4.44% 4.32% 4.68% BIAS -0.34% -0.36% -0.30% R² 93.14% Adjusted R² 90.57% 82.64%

Regression Analysis: EUC8 Significant Parameters Winter Modelling Summer Modelling Parameter Estimate Probt February 3249751059.12 0.00% January 2999862661.01 November 3073062159.28 April 3077952704.51 October 2989550045.27 December 2929380642.38 March 2801971524.71 May 2905814544.62 Pre_NY_Period -1724684267.53 Pre_Xmas_WE -1465039587.23 September 2832227740.90 Mon_Thurs 496295840.93 mean_Temp -43931329.54 Late_May_BHper -958337606.90 Xmas -1976569842.91 New_Year -1427312450.24 Saturday -257805759.58 Boxing_Day -1372176229.42 mean_Rainfall_lag2 344494383.40 Post_NY -609776043.00 mean_WindDirection_lag1 -860048.56 0.48% Slot2_GlobalRadiation_lag2 218043.03 0.92% sum_Global_Radiation_lag2 -208542.40 1.03% Slot3_Windspeed_lag1 20576331.38 1.04% Slot4_WindDirection_lag2 714663.95 1.11% Slot3_Windspeed 17869826.34 1.35% Slot3_GlobalRadiation_lag2 211519.64 1.37% Slot3_Humidity_lag2 2019759.38 1.44% Slot1_Windspeed_lag1 17975171.30 2.85% Early_May_BHper 274635838.15 2.98% Bank__Hols -334870256.77 3.44% Friday 91343652.51 4.43% Parameter Estimate Probt June 3824909570.89 0.00% Industrial_Shutdown -691905755.12 September 4022558247.89 July 3856048815.12 August 3783610270.53 May 3645177747.82 Mon_Thurs 354547473.50 Saturday -201003740.64 0.06% Slot2_Temp -77616027.31 0.22% Slot2_Humidity -6209248.41 0.32% Slot2_Humidity_lag1 -5203090.29 1.70% Friday 137127120.01 1.79% Slot2_Temp_lag1 -57828658.37 2.06% mean_Temp 63627989.46 2.76% mean_Temp_lag1 54856830.68 4.83%

In-Sample Results: EUC9 Graphical Output OVERALL WINTER SUMMER MAPE 10.38% 9.66% 11.82% BIAS -1.42% -1.54% -1.18% R² 88.82% Adjusted R² 83.58% 79.93%

Regression Analysis: EUC9 Significant Parameters Summer Modelling Winter Modelling Parameter Estimate Probt February 3232691551.91 0.00% April 3630762719.85 November 3089039689.20 December 2943796690.17 March 2916582706.71 January 2571455436.72 October 2595606351.57 Mon_Thurs 1240189754.91 May 3081540761.55 Pre_NY_Period -2938852335.85 Pre_Xmas_WE -2123977952.44 Late_May_BHper -1798731934.66 September 2213613476.69 Xmas -2685504110.12 Slot1_Temp -44515692.34 Friday 420964696.76 0.01% Boxing_Day -2104784457.45 0.02% Slot4_Windspeed_lag1 68801497.72 0.05% New_Year -1676950178.65 0.28% Slot4_Windspeed 49754117.36 0.51% Bank__Hols -853483153.59 1.19% Post_NY -821945208.82 1.29% Slot2_GlobalRadiation_lag2 469596.92 1.71% sum_Global_Radiation_lag2 -449216.95 1.89% mean_Rainfall_lag2 424523111.16 2.10% Slot3_GlobalRadiation_lag2 434315.19 3.26% Saturday -223357226.55 3.49% Parameter Estimate Probt Mon_Thurs 969815450.65 0.00% June 1040475405.67 Industrial_Shutdown -1004888359.20 CWV 206480903.67 September 782860909.99 Slot2_Temp -83080425.33 0.02% Friday 418088121.67 0.05% July 352170260.88 0.07% Slot3_Rainfall_lag2 -421618925.40 1.02% Slot2_Rainfall_lag2 -367640368.20 3.26% mean_Rainfall_lag2 633592143.33 4.31%

OUT-OF-SAMPLE RESULTS 2009/2010 Gas year

Out-of-Sample Results: EUC1 Graphical Output OVERALL WINTER SUMMER MAPE 12.98% 10.48% 8.63% 9.70% 21.20% 11.96% BIAS -10.74% 1.96% -6.11% 6.06% -19.50% -5.79% R² 98.82% Adjusted R² 97.77% 73.93% AQ Ratio 88.53%

Out-of-Sample Results: EUC2 Graphical Output OVERALL WINTER SUMMER MAPE 19.39% 20.27% 11.85% 12.35% 33.66% 35.26% BIAS -15.43% -16.91% -6.15% -7.52% -32.98% -34.69% R² 97.44% Adjusted R² 94.10% 52.35% AQ Ratio 101.29%

Out-of-Sample Results: EUC3 Graphical Output OVERALL WINTER SUMMER MAPE 23.88% 20.70% 18.25% 18.10% 35.25% 25.95% BIAS -13.66% -5.30% -3.62% 3.99% -33.90% -24.06% R² 94.14% Adjusted R² 89.01% 69.54% AQ Ratio 92.65%

Out-of-Sample Results: EUC4 Graphical Output OVERALL WINTER SUMMER MAPE 11.63% 13.11% 11.40% 12.23% 12.09% 14.89% BIAS -5.82% -9.11% -3.34% -6.56% -10.81% -14.26% R² 96.06% Adjusted R² 91.51% 84.58% AQ Ratio 103.11%

Out-of-Sample Results: EUC5 Graphical Output OVERALL WINTER SUMMER MAPE 14.34% 13.95% 15.14% BIAS -12.42% -11.10% -15.08% R² 95.17% Adjusted R² 90.27% 93.58%

Out-of-Sample Results: EUC6 Graphical Output OVERALL WINTER SUMMER MAPE 18.09% 15.96% 22.38% BIAS -13.39% -10.77% -18.66% R² 87.05% Adjusted R² 78.82% 84.55%

Out-of-Sample Results: EUC7 Graphical Output OVERALL WINTER SUMMER MAPE 33.65% 29.74% 41.54% BIAS -32.81% -28.55% -41.41% R² 90.28% Adjusted R² 83.70% 84.63%

Out-of-Sample Results: EUC8 Graphical Output OVERALL WINTER SUMMER MAPE 12.55% 13.84% 9.96% BIAS 9.67% 11.86% 5.26% R² 72.05% Adjusted R² 56.04% 44.89%

Out-of-Sample Results: EUC9 Graphical Output OVERALL WINTER SUMMER MAPE 10.38% 9.66% 11.82% BIAS -1.42% -1.54% -1.18% R² 88.82% Adjusted R² 83.58% 79.93%

Conclusion and Recommendations The in-sample accuracy for WM (EUC1-9) is The out-of-sample accuracy for WM (EUC1-9) is OVERALL WINTER SUMMER MAPE 5.01% 5.00% 5.03% BIAS -0.18% -0.20% -0.15% R² 96.61% 94.77% 94.91% OVERALL WINTER SUMMER MAPE 14.54% 14.83% 15.43% BIAS -10.94% -10.51% -13.24% R² 87.97% 81.20% 88.00% The one-year stretch (in-sample) data gave the best forecast accuracy results each time per EUC Huge Benefits in Winter and Sumer piecewise modelling in terms of accuracy results. This could be possibly applied to ALPs and DAFs. Out-of-sample accuracy results poor. This could be because of the number of meters changing year on year.