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NDM Data Sample Analysis: Final Results
Option C: Regression Analysis
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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
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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
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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.
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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.
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INITIAL IN-SAMPLE RESULTS
Regression Analysis
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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%
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Piecewise Regression Analysis
REVISED IN-SAMPLE RESULTS Piecewise Regression Analysis
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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%
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Regression Analysis: EUC1 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt January 0.00% February December November March April October May September CWV Slot4_Temp 162.57 Slot2_GlobalRadiation -0.11 Mon_Thurs mean_Temp mean_Windspeed_lag1 143.94 mean_Temp_lag2 102.13 Pre_NY_Period Xmas Slot2_Temp 239.81 0.01% Boxing_Day New_Year 0.02% Pre_Xmas_WE 0.10% Bank__Hols 0.52% Friday 0.87% Slot2_Windspeed 57.82 2.54% Parameter Estimate Probt September 0.00% June July August May CWV Slot4_Temp 92.52 mean_Humidity 23.25 Slot2_Temp 0.01% Mon_Thurs 0.02% Slot1_Humidity_lag2 14.98 0.14% Slot3_Rainfall_lag1 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 1.12% Aug_BHper 3.41%
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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%
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Regression Analysis: EUC2 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt February 0.00% December January November March April October May September Mon_Thurs Friday CWV Bank__Hols Early_May_BHper Pre_NY_Period sum_Global_Radiation_lag1 -1.70 Slot2_GlobalRadiation_lag1 1.67 0.01% Slot2_Temp_lag1 453.67 Post_NY mean_Temp_lag1 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 0.00% June May July August Mon_Thurs Friday CWV mean_WindDirection_lag2 -3.92 Slot4_Temp 174.83 0.11% Slot2_Windspeed_lag2 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 0.96% Slot3_Temp 1.03% mean_Temp Slot3_Temp_lag2 -87.07 1.27% Slot2_Temp 1.51% Slot4_Temp_lag2 856.64 1.55% mean_Temp_lag3 -58.38 1.59% mean_Temp_lag1 2.55% Slot3_Temp_lag1 939.97 2.76% Slot2_Temp_lag1 2.78% Slot1_Temp_lag1 579.16 4.28% Slot4_Humidity_lag2 -12.54 4.68%
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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%
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Regression Analysis: EUC3 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt January 0.00% December February November April March Mon_Thurs October CWV May Friday September Bank__Hols Pre_NY_Period Early_May_BHper 0.01% Pre_Xmas_WE 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 0.99% Slot1_Windspeed_lag1 533.05 3.81% Parameter Estimate Probt Mon_Thurs 0.00% Friday Industrial_Shutdown June September July May August CWV mean_Temp 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%
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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%
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Regression Analysis: EUC4 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt February 0.00% January December April November March Mon_Thurs October May September CWV Friday Pre_NY_Period Pre_Xmas_WE Xmas Post_NY Early_May_BHper 0.01% Saturday New_Year 0.03% Boxing_Day 0.08% Bank__Hols 0.10% Slot3_Rainfall_lag2 0.18% Slot1_Temp_lag1 0.30% Slot2_GlobalRadiation_lag1 52.63 0.79% Slot3_Humidity_lag1 0.87% sum_Global_Radiation_lag1 -49.15 1.03% Slot2_Temp 1.43% Slot2_WindDirection 1.52% mean_WindDirection_lag1 326.30 2.57% Slot2_WindDirection_lag1 2.81% Slot3_Rainfall_lag1 2.88% Slot3_GlobalRadiation_lag1 44.41 3.19% Slot4_Humidity_lag2 3.93% Slot2_Humidity 656.93 4.20% mean_Humidity_lag1 4.59% mean_Rainfall 4.72% Parameter Estimate Probt Mon_Thurs 0.00% Friday June September July August May Bank__Hols Slot2_Temp mean_Humidity_lag1 0.04% Slot3_Humidity_lag1 0.06% mean_Temp_lag3 0.16% Slot4_Humidity_lag2 0.26% Slot2_Rainfall_lag1 0.67% Industrial_Shutdown 1.08% Slot3_Temp 1.17% Slot4_Windspeed_lag2 3.55% Slot3_Humidity 4.40%
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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%
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Regression Analysis: EUC5 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt January 0.00% December February November April March October Mon_Thurs May September CWV Friday Pre_NY_Period Pre_Xmas_WE Post_NY Bank__Hols Xmas New_Year 0.01% Late_May_BHper 0.22% Slot2_GlobalRadiation_lag1 0.23% sum_Global_Radiation_lag1 0.24% Slot3_GlobalRadiation_lag1 0.46% Early_May_BHper 0.50% mean_Temp_lag1 0.64% Slot3_Rainfall_lag2 0.67% Boxing_Day 0.82% Slot2_Rainfall_lag1 1.08% mean_Rainfall_lag1 1.11% Slot3_Rainfall_lag1 1.16% Parameter Estimate Mon_Thurs Friday September June May July August Industrial_Shutdown Bank__Hols CWV mean_Temp Slot4_Temp_lag1 Aug_BHper Slot4_Rainfall
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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%
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Regression Analysis: EUC6 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt January 0.00% April November February December October March Mon_Thurs May CWV September Pre_NY_Period Friday Pre_Xmas_WE Late_May_BHper New_Year Xmas Post_NY Bank__Hols Saturday 0.01% Boxing_Day 0.65% Slot3_WindDirection_lag1 3.61% mean_WindDirection_lag1 3.96% Parameter Estimate Probt Mon_Thurs 0.00% Friday Industrial_Shutdown Bank__Hols mean_Humidity_lag2 0.08% September 0.19% mean_Humidity 0.68% Slot2_WindDirection_lag1 0.93% sum_Global_Radiation_lag2 1.26% Slot2_WindDirection_lag2 1.73% June 1.87% Slot3_Humidity 2.05% Slot2_GlobalRadiation_lag2 2.13% mean_WindDirection_lag2 2.38% Slot3_GlobalRadiation_lag2 2.73%
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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%
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Regression Analysis: EUC7 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt Mon_Thurs 0.00% February January April November December CWV October March May Pre_NY_Period September Pre_Xmas_WE Friday Bank__Hols Post_NY Late_May_BHper New_Year Saturday Xmas 0.01% mean_Windspeed_lag1 2.13% Slot1_Humidity_lag2 3.24% mean_WindDirection_lag1 3.28% Slot3_WindDirection_lag1 4.00% Parameter Estimate Probt Mon_Thurs 0.00% September June July August Friday May Industrial_Shutdown Bank__Hols Saturday Aug_BHper 0.28% Slot2_GlobalRadiation 0.37% Slot3_Humidity 0.58% mean_Temp 0.64%
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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%
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Regression Analysis: EUC8 Significant Parameters
Winter Modelling Summer Modelling Parameter Estimate Probt February 0.00% January November April October December March May Pre_NY_Period Pre_Xmas_WE September Mon_Thurs mean_Temp Late_May_BHper Xmas New_Year Saturday Boxing_Day mean_Rainfall_lag2 Post_NY mean_WindDirection_lag1 0.48% Slot2_GlobalRadiation_lag2 0.92% sum_Global_Radiation_lag2 1.03% Slot3_Windspeed_lag1 1.04% Slot4_WindDirection_lag2 1.11% Slot3_Windspeed 1.35% Slot3_GlobalRadiation_lag2 1.37% Slot3_Humidity_lag2 1.44% Slot1_Windspeed_lag1 2.85% Early_May_BHper 2.98% Bank__Hols 3.44% Friday 4.43% Parameter Estimate Probt June 0.00% Industrial_Shutdown September July August May Mon_Thurs Saturday 0.06% Slot2_Temp 0.22% Slot2_Humidity 0.32% Slot2_Humidity_lag1 1.70% Friday 1.79% Slot2_Temp_lag1 2.06% mean_Temp 2.76% mean_Temp_lag1 4.83%
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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%
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Regression Analysis: EUC9 Significant Parameters
Summer Modelling Winter Modelling Parameter Estimate Probt February 0.00% April November December March January October Mon_Thurs May Pre_NY_Period Pre_Xmas_WE Late_May_BHper September Xmas Slot1_Temp Friday 0.01% Boxing_Day 0.02% Slot4_Windspeed_lag1 0.05% New_Year 0.28% Slot4_Windspeed 0.51% Bank__Hols 1.19% Post_NY 1.29% Slot2_GlobalRadiation_lag2 1.71% sum_Global_Radiation_lag2 1.89% mean_Rainfall_lag2 2.10% Slot3_GlobalRadiation_lag2 3.26% Saturday 3.49% Parameter Estimate Probt Mon_Thurs 0.00% June Industrial_Shutdown CWV September Slot2_Temp 0.02% Friday 0.05% July 0.07% Slot3_Rainfall_lag2 1.02% Slot2_Rainfall_lag2 3.26% mean_Rainfall_lag2 4.31%
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OUT-OF-SAMPLE RESULTS
2009/2010 Gas year
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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%
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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%
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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%
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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%
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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%
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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%
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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%
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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%
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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%
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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.
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