1 Econometric Load Forecasting 2005 - 2011 Peak and Energy Forecast 06/14/2005 Econometric Load Forecasting 2005 - 2011 Peak and Energy Forecast 06/14/2005

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Econometric Load Forecasting2005 - 2011 Peak and Energy Forecast

06/14/2005

Econometric Load Forecasting2005 - 2011 Peak and Energy Forecast

06/14/2005

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Previous ERCOT Previous ERCOT Forecast MethodologyForecast Methodology

Previous ERCOT Previous ERCOT Forecast MethodologyForecast Methodology

• The previous load forecast methodology was based on a simplistic trending of historic ERCOT peak demand growth to develop the long-term forecast of summer peak demand, unadjusted for weather or economic conditions

• Several compound growth rates were calculated (10-year, 5-year, 2-year, etc). These growth rates were applied to the latest available peak to obtain forecasts, and the most reasonable forecast was selected, based on judgment

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Forecasting ImprovementForecasting ImprovementForecasting ImprovementForecasting Improvement

• Original Plan– Develop hourly load forecast for five years for smaller

regions of ERCOT (either weather zones or CM areas) for use in UPlan studies

– Sum of these forecasts across ERCOT would be used as the ERCOT System peak and energy forecast

• Revised Goal– Due to the immediate need for a more rigorous

forecasting approach, the goal for the current forecast cycle was changed to develop an ERCOT system forecast directly

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Econometric Forecasting BasicsEconometric Forecasting BasicsEconometric Forecasting BasicsEconometric Forecasting Basics

Regression Analysis• Develop an equation or equations that describe the

historic load as a function of certain independent variables– Variables must be logical, historically measurable and have an

available forecast

• Statistical analysis techniques are used to calculate the appropriate coefficients on each variable and to choose the best equations– Equations are chosen that minimize sum of the squares of the

differences between the actual, observed load levels and the load levels that are predicted by inserting the historic values of the independent variables into the equation

Projected values for each of the variables in the equations are then inserted into the equations to produce the forecast

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2005 Forecasting Process2005 Forecasting Process2005 Forecasting Process2005 Forecasting Process

ERCOT Total

System Hourly

Load Forecast

Allocate

Energy

Allocate

Energy

Allocate

Energy

ERCOT Peak and

Energy Forecast

Economic

Data

Weather

Data

Calendar

Data

Forecasted Data

Load

Data

Economic

Data

Weather

Data

Calendar

Data

Historic Data

ERCOT Total System

Summer Hourly

Load Shape Model

ERCOT Total System

Winter Hourly

Load Shape Model

ERCOT Total System

Spring/Fall Hourly

Load Shape Model

ERCOT Winter

Monthly Energy

Model

ERCOT Spring/Fall

Monthly Energy

Model

ERCOT Summer

Monthly Energy

Model

Six Regression Equations

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2005 Forecasting Process2005 Forecasting Process2005 Forecasting Process2005 Forecasting Process

1. Obtain weather and economic variables (historic and forecast)

2. Develop regression equations describing the historic actual:– Monthly Energy

• Using a different equation for each season

– Hourly Load Shape• Using a different equation for each season

3. Incorporate forecasted values of economic and normalized temperatures for 2005-2010 into Monthly Energy equation to produce forecasted monthly energy

4. Incorporate normalized temperatures for 2005-2010 into Monthly Energy equation to produce forecasted load shape

5. Produce hourly demand forecast by fitting forecasted monthly energy under projected hourly load shape

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Load

Data

Economic

Data

Weather

Data

Calendar

Data

Historic Data

2005 Forecasting Process2005 Forecasting ProcessHistoric DataHistoric Data

2005 Forecasting Process2005 Forecasting ProcessHistoric DataHistoric Data

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Historic Data - EconomicHistoric Data - Economic Historic Data - EconomicHistoric Data - Economic

1. Economic Data

• Economic data obtained from Economy.com

• Data includes economic and demographic data (such as income, employment, housing permits, GDP, population and migration patterns) for Texas at the state, county, Metropolitan Statistical Areas (MSAs), and national level

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Historic Data - WeatherHistoric Data - WeatherHistoric Data - WeatherHistoric Data - Weather

2. Weather Data

• Ten years of weather data obtained from Weather Bank for 20 weather stations

• The data is first weighted by individual weather stations using ERCOT’s standard weighing factor, and then for the total system using weights proportional to the load in each weather zone

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Historic Data - LoadHistoric Data - LoadHistoric Data - LoadHistoric Data - Load

3. Load Data

• Settlement load data available on an hourly basis since July 31, 2001

• Prior to 2001, we have Transmission and Distribution Service Providers (TDSP) hourly data

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Load

Data

Economic

Data

Weather

Data

Calendar

Data

Historic Data

ERCOT Total System

Summer Hourly

Load Shape Model

ERCOT Total System

Winter Hourly

Load Shape Model

ERCOT Total System

Spring/Fall Hourly

Load Shape Model

ERCOT Winter

Monthly Energy

Model

ERCOT Spring/Fall

Monthly Energy

Model

ERCOT Summer

Monthly Energy

Model


2005 Forecasting Process2005 Forecasting ProcessRegression EquationsRegression Equations

2005 Forecasting Process2005 Forecasting ProcessRegression EquationsRegression Equations

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Develop monthly energy and hourly load shape equations for each season

• The general formulation of the energy equations is:

Energy Month i = f {Cdd, Hdd, Income, Population, Monthly Indicators}

• The general formulation of the load shape equations is:

Load hour i =f {Max Temps, Lagged Temps, Heat Index, Non- Linear Temp Components (square and cube),

Temp Gains (diff between daily high and Low temps), Temp Build-up, Dew Point, Month*Temp Interactions, Cdd, Hdd, Hour of Day Indicators,

Weekday/Weekend, Holidays, Population, income}

Regression EquationsRegression EquationsRegression EquationsRegression Equations

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Variable Selection andVariable Selection andRegression Estimation DetailsRegression Estimation Details

Variable Selection andVariable Selection andRegression Estimation DetailsRegression Estimation Details

• Multiple Regression Analysis was use to develop the forecasting equations

• Initial selection of variables came from a stepwise procedure to determine those that were the most statistically significant

• A subset of those variables was carefully chosen on the basis of empirical results and judgment– Variables had to be logical, historically measurable and have an

available forecast

• Ordinary Least Squares techniques with some of the models including autoregressive error terms were used to calculate the appropriate coefficients on each variable and to choose the best equations

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Load Shape Model FitLoad Shape Model FitLoad Shape Model FitLoad Shape Model Fit

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Model FitModel FitModel FitModel Fit

• Detailed SAS output is included at the end of the presentation, showing:

– Model Variables

– Coefficients

– Statistical analysis

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Load

Data

Economic

Data

Weather

Data

Calendar

Data

Historic Data

ERCOT Total System

Summer Hourly

Load Shape Model

ERCOT Total System

Winter Hourly

Load Shape Model

ERCOT Total System

Spring/Fall Hourly

Load Shape Model

ERCOT Winter

Monthly Energy

Model

ERCOT Spring/Fall

Monthly Energy

Model

ERCOT Summer

Monthly Energy

Model


Economic

Data

Weather

Data

Calendar

Data

Forecasted Data

2005 Forecasting Process2005 Forecasting ProcessForecasted DataForecasted Data

2005 Forecasting Process2005 Forecasting ProcessForecasted DataForecasted Data

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Economic ForecastEconomic ForecastEconomic ForecastEconomic Forecast

• ERCOT obtains the economic forecasts used in the models from Economy.com

• Economy.com is a leading national provider of economic data and forecasts, with over 500 clients worldwide including AEP, LCRA and Entergy

• Forecasts and data received includes economic and demographic data (such as income, employment, housing permits, GDP, population and migration patterns) for Texas at state, county and MSA, and some national economic data

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year Population Income per Capita

pop_gr inc_gr

1998 17,597,260 26,9851999 17,981,920 27,699 2.19% 2.65%2000 18,359,130 29,218 2.10% 5.48%2001 18,739,920 29,226 2.07% 0.03%2002 19,121,200 28,832 2.03% -1.35%2003 19,481,730 28,393 1.89% -1.52%2004 19,764,350 28,954 1.45% 1.98%2005 20,046,060 29,702 1.43% 2.58%2006 20,327,210 30,427 1.40% 2.44%2007 20,605,950 31,098 1.37% 2.21%2008 20,882,210 31,921 1.34% 2.65%2009 21,157,140 32,781 1.32% 2.69%2010 21,431,110 33,625 1.29% 2.57%2011 21,705,010 34,481 1.28% 2.55%

Economic Forecast Growth RatesEconomic Forecast Growth RatesEconomic Forecast Growth RatesEconomic Forecast Growth Rates

19

year Population Income per Capita

pop_gr inc_gr

1998 17,597,260 26,9851999 17,981,920 27,699 2.19% 2.65%2000 18,359,130 29,218 2.10% 5.48%2001 18,739,920 29,226 2.07% 0.03%2002 19,121,200 28,832 2.03% -1.35%2003 19,481,730 28,393 1.89% -1.52%2004 19,764,350 28,954 1.45% 1.98%2005 20,046,060 29,702 1.43% 2.58%2006 20,327,210 30,427 1.40% 2.44%2007 20,605,950 31,098 1.37% 2.21%2008 20,882,210 31,921 1.34% 2.65%2009 21,157,140 32,781 1.32% 2.69%2010 21,431,110 33,625 1.29% 2.57%2011 21,705,010 34,481 1.28% 2.55%

Economic Forecast Growth RatesEconomic Forecast Growth RatesEconomic Forecast Growth RatesEconomic Forecast Growth Rates

1.95% 1.18%

1.33% 2.52%

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Forecasted Weather DataForecasted Weather DataForecasted Weather DataForecasted Weather Data

Weather Forecast Assumptions• Calculation of the normalized temperature profile

involves the following steps:1) Compute an overall system temperature for every year by

combining the weather zone temperatures and weighing them according to the load in each zone

2) Rank the hourly temperatures for each year from highest to lowest

3) Determine the median temperature from all years for every hour

4) Calculate the sum of the absolute values of the difference of the median and the hourly temperatures for all hourly temperatures in each year

5) Determine the year with the minimum summed value and select this year as the typical year profile

6) Use this year’s profile to resort the median temperatures

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Allocate

Energy

Allocate

Energy

Allocate

Energy

Load

Data

Economic

Data

Weather

Data

Calendar

Data

Historic Data

ERCOT Total System

Summer Hourly

Load Shape Model

ERCOT Total System

Winter Hourly

Load Shape Model

ERCOT Total System

Spring/Fall Hourly

Load Shape Model

ERCOT Winter

Monthly Energy

Model

ERCOT Spring/Fall

Monthly Energy

Model

ERCOT Summer

Monthly Energy

Model


ERCOT Total

System Hourly

Load Forecast

ERCOT Peak and

Energy Forecast

Economic

Data

Weather

Data

Calendar

Data

Forecasted Data

2005 Forecasting Process2005 Forecasting ProcessHourly ForecastHourly Forecast

2005 Forecasting Process2005 Forecasting ProcessHourly ForecastHourly Forecast

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Hourly ForecastHourly ForecastHourly ForecastHourly Forecast

• The forecasted hourly shape from the load shape equations is scaled to produce the final hourly forecast– Each hour’s load is scaled so that the amount of energy under

the load shape for a month is equal to the amount of energy projected for that month by the energy forecast from the energy equations

– The percent of a month’s energy that is contained in an each hour from the load shape equation is maintained

• The peak forecast is the highest hourly load from this final hourly forecast

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55,121

53,691

58,506

56,08654,980

57,981

60,037

66,20164,24562,148

65,09763,13260,475

50,000

52,000

54,000

56,000

58,000

60,000

62,000

64,000

66,000

68,000

70,000

1997 1999 2001 2003 2005 2007 2009 2011

MW

ERCOT Peak ForecastERCOT Peak ForecastERCOT Peak ForecastERCOT Peak Forecast

1.83% Avg. Growth

24

267 266

285

277281

285

296

302

308

315

321

328

289

2 5 0

2 6 0

2 7 0

2 8 0

2 9 0

3 0 0

3 1 0

3 2 0

3 3 0

3 4 0

3 5 0

1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0

MW

h

ERCOT Energy ForecastERCOT Energy ForecastERCOT Energy ForecastERCOT Energy Forecast

2.10% Avg. Growth

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Year MW gr _MW MWh gr_MWh Load Factor

1998 53,691 266,958,502 56.91%

1999 54,980 2.40% 265,741,736 -0.46% 55.05%

2000 57,981 5.46% 285,385,794 7.39% 55.48%

2001 55,214 -4.77% 277,017,595 -2.93% 57.89%

2002 56,086 1.58% 280,772,267 1.36% 57.77%

2003 60,037 7.04% 284,984,108 1.50% 53.95%

2004 58,506 -2.55% 289,138,893 1.46% 56.16%

2005 60,475 3.37% 295,652,784 2.25% 55.81%

2006 62,148 2.77% 301,917,463 2.12% 55.46%

2007 63,132 1.58% 307,817,502 1.95% 55.66%

2008 64,245 1.76% 314,507,734 2.17% 55.88%

2009 65,097 1.33% 321,367,162 2.18% 56.36%

2010 66,201 1.70% 328,150,527 2.11% 56.59%

Forecast Growth Rates - AnnualForecast Growth Rates - Annual

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Year MW gr _MW MWh gr_MWh Load Factor

1998 53,691 266,958,502 56.91%

1999 54,980 2.40% 265,741,736 -0.46% 55.05%

2000 57,981 5.46% 285,385,794 7.39% 55.48%

2001 55,214 -4.77% 277,017,595 -2.93% 57.89%

2002 56,086 1.58% 280,772,267 1.36% 57.77%

2003 60,037 7.04% 284,984,108 1.50% 53.95%

2004 58,506 -2.55% 289,138,893 1.46% 56.16%

2005 60,475 3.37% 295,652,784 2.25% 55.81%

2006 62,148 2.77% 301,917,463 2.12% 55.46%

2007 63,132 1.58% 307,817,502 1.95% 55.66%

2008 64,245 1.76% 314,507,734 2.17% 55.88%

2009 65,097 1.33% 321,367,162 2.18% 56.36%

2010 66,201 1.70% 328,150,527 2.11% 56.59%

Forecast Growth Rates - AnnualForecast Growth Rates - Annual

1.44%

1.81%

1.34%

2.10%

AV

G=

56.1

6%

27

Questions?

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AppendixAppendix Model Parameters and Statistics Model Parameters and Statistics

AppendixAppendix Model Parameters and Statistics Model Parameters and Statistics

SAS Output

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Summer SeasonSummer SeasonLoad Shape EquationLoad Shape Equation

Sum of MeanSource DF Squares Square F Value Pr > F

Model 36 9.131699E11 25365830475 19705.3 <.0001Error 15419 19848283413 1287261Corrected Total 15455 9.330182E11

Root MSE 1134.57542 R-Square 0.9787Dependent Mean 39141 Adj R-Sq 0.9787Coeff Var 2.89867

Parameter EstimatesParameter Standard

Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 -106720 2762.25031 -38.64 <.0001heat_in 1 164.19929 5.95631 27.57 <.0001tpl 1 1191.25393 16.76044 71.08 <.0001temp2 1 -12.75826 0.35976 -35.46 <.0001temp3 1 0.06579 0.00224 29.34 <.0001tpmax 1 548.29029 60.94637 9.00 <.0001tpmax2 1 -2.80995 0.33846 -8.30 <.0001temp_buildup 1 133.90217 5.36791 24.94 <.0001school 1 -198.38508 43.67881 -4.54 <.0001df_6 1 2179.05163 137.16514 15.89 <.0001df_20 1 -621.68872 196.40055 -3.17 0.0016daytype 1 2482.42898 20.01264 124.04 <.0001hr1 1 -2069.31450 63.46861 -32.60 <.0001hr2 1 -3270.13267 64.09623 -51.02 <.0001hr3 1 -4020.66323 64.98564 -61.87 <.0001hr4 1 -4401.14301 66.00848 -66.68 <.0001hr5 1 -4269.75252 67.14096 -63.59 <.0001hr6 1 -3182.65451 68.28276 -46.61 <.0001hr7 1 -1291.55052 74.32536 -17.38 <.0001hr8 1 -687.72590 88.11498 -7.80 <.0001hr9 1 -96.28171 92.97342 -1.04 0.3004hr10 1 629.97934 92.14316 6.84 <.0001hr11 1 1587.76281 91.09184 17.43 <.0001hr12 1 2457.49823 89.90791 27.33 <.0001hr13 1 3156.41726 89.23808 35.37 <.0001hr14 1 3878.98247 88.82236 43.67 <.0001hr15 1 4429.78433 88.00600 50.34 <.0001hr16 1 4839.80134 86.46615 55.97 <.0001hr17 1 5038.22864 84.04716 59.95 <.0001hr18 1 4838.59226 80.69409 59.96 <.0001hr19 1 4194.35774 77.61281 54.04 <.0001hr20 1 3564.99138 74.84852 47.63 <.0001hr21 1 4207.26004 68.58354 61.35 <.0001hr22 1 4602.96528 64.72332 71.12 <.0001hr23 1 2642.44154 63.52496 41.60 <.0001rpcinc1 1 42954 1516.86796 28.32 <.0001fpopa1 1 1.49720 0.01735 86.29 <.0001

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Summer SeasonSummer SeasonEnergy EquationEnergy Equation

The REG ProcedureModel: MODEL1

Dependent Variable: mwh

Number of Observations Read 54Number of Observations Used 21Number of Observations with Missing Values 33

Analysis of Variance


Model 5 6.915084E13 1.383017E13 342.89 <.0001Error 15 6.050192E11 40334614582Corrected Total 20 6.975586E13

Root MSE 200835 R-Square 0.9913Dependent Mean 28807913 Adj R-Sq 0.9884Coeff Var 0.69715

Parameter Estimates

Parameter StandardVariable DF Estimate Error t Value Pr > |t|

Intercept 1 -11227591 2337403 -4.80 0.0002cdh70 1 662050 38994 16.98 <.0001mo7 1 1134729 160769 7.06 <.0001mo8 1 1461225 169345 8.63 <.0001rpcinc 1 35488397 7036352 5.04 0.0001FPOPA 1 1080.27344 97.12517 11.12 <.0001

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Winter SeasonWinter SeasonLoad Shape EquationLoad Shape Equation

Yule-Walker Estimates

SSE 3055348502 DFE 15121MSE 202060 Root MSE 449.51079SBC 228749.156 AIC 228390.69Regress R-Square 0.8201 Total R-Square 0.9892Durbin-Watson 1.1181

Standard ApproxVariable DF Estimate Error t Value Pr > |t|

Intercept 1 4374 2116 2.07 0.0387tpl 1 -222.4634 7.7055 -28.87 <.0001lag1_mxtp 1 -16.7377 2.1431 -7.81 <.0001temp2 1 -9.7354 1.7467 -5.57 <.0001temp3 1 0.0974 0.0103 9.43 <.0001tpmax 1 -16.6783 2.2423 -7.44 <.0001lag_cdd 1 147.2345 16.5051 8.92 <.0001lag_hdd 1 32.6579 2.8177 11.59 <.0001hdh40 1 98.1341 18.8372 5.21 <.0001lg_hdd40 1 45.6276 7.2085 6.33 <.0001rpcinc1 1 47748 4548 10.50 <.0001fpopa1 1 1.1363 0.0539 21.07 <.0001daytype 1 802.7727 32.3715 24.80 <.0001hr1 1 -1423 21.8976 -64.98 <.0001hr2 1 -2367 30.0497 -78.78 <.0001hr3 1 -2776 37.3471 -74.32 <.0001hr4 1 -2865 42.6448 -67.18 <.0001hr5 1 -2434 46.4276 -52.44 <.0001hr6 1 -823.1398 48.6109 -16.93 <.0001hr7 1 2026 49.3170 41.08 <.0001hr8 1 3387 48.8734 69.29 <.0001hr9 1 3696 50.0585 73.83 <.0001hr10 1 4135 51.3079 80.59 <.0001hr11 1 4422 50.9037 86.87 <.0001hr12 1 4329 51.5144 84.04 <.0001hr13 1 4033 53.5799 75.26 <.0001hr14 1 3779 55.8213 67.69 <.0001hr15 1 3547 56.8288 62.42 <.0001hr16 1 3498 57.9930 60.31 <.0001hr17 1 3820 57.7075 66.19 <.0001hr18 1 4980 55.5512 89.65 <.0001hr19 1 6621 51.2182 129.26 <.0001hr20 1 6359 44.6785 142.32 <.0001hr21 1 5578 38.0228 146.71 <.0001hr22 1 4324 30.2327 143.03 <.0001hr23 1 2275 19.5569 116.34 <.0001df_7 1 -1738 402.2885 -4.32 <.0001jantp 1 226.5634 98.1741 2.31 0.0210febtp 1 222.8573 98.1762 2.27 0.0232

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dectp 1 222.6565 98.1838 2.27 0.0234wednesdaytp 1 1.9351 0.6272 3.09 0.0020fridaytp 1 -3.1044 0.6966 -4.46 <.0001

33


Backward Elimination of Autoregressive Terms

Lag Estimate t Value Pr > |t|

11 -0.002796 -0.24 0.813812 0.003348 0.60 0.54809 -0.013780 -1.16 0.24577 -0.018702 -1.57 0.11736 0.013952 1.45 0.14713 0.022073 1.84 0.06544 -0.009984 -1.05 0.2948

Preliminary MSE 343370

Estimates of Autoregressive Parameters

StandardLag Coefficient Error t Value

1 -1.065008 0.007973 -133.582 0.221874 0.008625 25.725 0.049739 0.005426 9.178 -0.067916 0.006191 -10.97

10 -0.018701 0.005510 -3.39

ExpectedAutocorrelations

Lag Autocorr

0 1.00001 0.87192 0.70153 0.54444 0.41365 0.31286 0.25347 0.2349

34

Winter SeasonWinter SeasonEnergy EquationEnergy Equation






Model 5 6.34754E13 1.269508E13 48.27 <.0001Error 15 3.944861E12 2.629907E11Corrected Total 20 6.742027E13


Parameter Estimates

Parameter StandardVariable DF Estimate Error t Value Pr > |t|

Intercept 1 -10325956 3931834 -2.63 0.0191hdh65 1 192102 40716 4.72 0.0003mo12 1 1779003 293255 6.07 <.0001mo1 1 1941667 291390 6.66 <.0001rpcinc 1 43685643 17388495 2.51 0.0239FPOPA 1 785.43994 201.96371 3.89 0.0015

35

Spring/Fall SeasonSpring/Fall SeasonLoad Shape EquationLoad Shape Equation

Yule-Walker Estimates

SSE 1.46763E10 DFE 30684MSE 478305 Root MSE 691.59612SBC 489878.865 AIC 489378.858Regress R-Square 0.8682 Total R-Square 0.9883Durbin-Watson 0.9709


Intercept 1 5941 1080 5.50 <.0001tpl 1 76.6116 8.5684 8.94 <.0001lag1_mxtp 1 36.8470 2.8347 13.00 <.0001temp3 1 -0.006978 0.000649 -10.75 <.0001tpmax 1 -777.4931 20.2449 -38.40 <.0001tpmax2 1 5.9613 0.1458 40.89 <.0001tpmin 1 -10.5479 4.4709 -2.36 0.0183lag_cdd 1 213.4405 5.6542 37.75 <.0001lag_hdd 1 97.8367 5.2197 18.74 <.0001coldbuildup 1 -97.3315 6.9407 -14.02 <.0001hottempgain 1 -111.1555 5.4487 -20.40 <.0001mildtempgain 1 -49.6081 4.0804 -12.16 <.0001dewpoint_tot 1 58.5525 3.1123 18.81 <.0001cdh70 1 225.9636 9.2717 24.37 <.0001cdh80 1 323.1258 9.2609 34.89 <.0001hdh40 1 168.1583 30.8290 5.45 <.0001hdh50 1 333.2678 13.1529 25.34 <.0001daytype 1 665.5900 69.9671 9.51 <.0001hr1 1 -2073 24.7579 -83.73 <.0001hr2 1 -3031 29.2189 -103.73 <.0001hr3 1 -3702 35.0745 -105.55 <.0001hr4 1 -4058 38.8011 -104.58 <.0001hr5 1 -3915 41.3173 -94.77 <.0001hr6 1 -2708 43.5543 -62.18 <.0001hr7 1 -310.7215 45.3613 -6.85 <.0001hr8 1 785.4438 47.5181 16.53 <.0001hr9 1 1267 49.2498 25.73 <.0001hr10 1 1853 49.8815 37.16 <.0001hr11 1 2281 51.6632 44.14 <.0001hr12 1 2487 54.6478 45.51 <.0001hr13 1 2628 57.9480 45.35 <.0001hr14 1 2913 60.8508 47.87 <.0001hr15 1 3238 63.0086 51.40 <.0001hr16 1 3683 63.8282 57.71 <.0001hr17 1 4247 62.2876 68.18 <.0001hr18 1 4849 57.7419 83.98 <.0001hr19 1 5425 51.5520 105.22 <.0001hr20 1 5747 44.2105 129.99 <.0001hr21 1 5815 37.0548 156.92 <.0001hr22 1 4749 29.7766 159.48 <.0001hr23 1 2537 21.0801 120.37 <.0001

36


df_6 1 742.4679 79.4129 9.35 <.0001df_7 1 -684.5607 141.4910 -4.84 <.0001df_17 1 -1126 91.4238 -12.32 <.0001rpcinc1 1 47461 2684 17.68 <.0001fpopa1 1 1.0736 0.0293 36.66 <.0001mondaytp 1 10.4157 1.0940 9.52 <.0001tuesdaytp 1 16.3492 1.2043 13.58 <.0001wednesdaytp 1 17.5112 1.2141 14.42 <.0001thursdaytp 1 14.5742 1.1874 12.27 <.0001fridaytp 1 7.6649 1.1804 6.49 <.0001saturdaytp 1 3.1489 0.5862 5.37 <.0001

37


Backward Elimination ofAutoregressive Terms

Lag Estimate t Value Pr > |t|

2 0.005053 0.68 0.495310 0.007546 1.02 0.30854 0.011581 1.56 0.118112 -0.010258 -1.80 0.0722

Preliminary MSE 830282

Estimates of Autoregressive Parameters

StandardLag Coefficient Error t Value

1 -0.825233 0.004382 -188.333 0.087890 0.005170 17.005 -0.061742 0.006412 -9.636 0.036619 0.007389 4.967 0.080642 0.007370 10.948 -0.046873 0.007399 -6.339 -0.059525 0.006395 -9.31

11 0.022629 0.004378 5.17

ExpectedAutocorrelations

Lag Autocorr

0 1.00001 0.77932 0.58133 0.40554 0.28405 0.20276 0.12717 0.07138 0.06609 0.0820

10 0.086811 0.0744

38

Spring/Fall SeasonSpring/Fall SeasonEnergy EquationEnergy Equation






Model 8 2.671273E14 3.339091E13 396.86 <.0001Error 33 2.776557E12 84138088642Corrected Total 41 2.699038E14


Parameter Estimates

Parameter StandardVariable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 -5985627 1637685 -3.65 0.0009cdh70 1 625064 37752 16.56 <.0001hdh50 1 388536 142854 2.72 0.0103mo3 1 617669 141040 4.38 0.0001mo5 1 1224933 251373 4.87 <.0001mo9 1 825289 322666 2.56 0.0153mo10 1 1033423 152218 6.79 <.0001rpcinc 1 40235316 7216124 5.58 <.0001FPOPA 1 718.29458 79.11713 9.08 <.0001

Documents

1 Econometric Load Forecasting 2005 - 2011 Peak and Energy Forecast 06/14/2005 Econometric Load Forecasting 2005 - 2011 Peak and Energy Forecast 06/14/2005