Week 3
Exercise 1:
• An investment subsidy scheme where energy companies are offered below market interest rate loans for renewable energy investments (solar and wind power):
The main idea of the below market interest rates is that energy companies can now invest in renewable energy with a lower risk. This also lowers the investment costs through paying a lower interest rate (WACC goes down as r_E is lower). With new investment the produced amount can go up and/or the marginal costs go down. This changes the supply curve and lowers the market price.
At the same this means the residual demand of coal/other fossil fuels is lower, which means lower prices and rents for the companies producing with these technologies. In the long term this can also make some plants not feasible anymore, leading to exits.
• Reducing the amount of emission allowances offered in auctions:
This lowers amount of C02 allowed on the electricity market as whole. Thus the price of C02 also goes up, especially hitting the sectors that produce a lot of emissions. This shifts the supply curve to right as marginal costs go up. So also the market price goes up and rents as well. Usually the price increase is passed on to the consumer, which means that the consumer will change to lower cost electricity (at least in theory).
This is also a good way of giving companies that lower their C02 emissions a chance to make profit by selling their emission allowances. Also incentives entry due to higher rents.
I mostly prefer subsidies as it incentivizes for innovation if done correctly (for example auction). Innovations have potentially for to alter the market long term in my opinion. But depending on the situation, carbon pricing can make much more sense and lead to better results. It also doesn’t cost the government directly but instead produces returns.
Excercise 2:
Lets import the data and necessary packages.
Attaching package: 'dplyr'
The following objects are masked from 'package:stats':
filter, lag
The following objects are masked from 'package:base':
intersect, setdiff, setequal, union
Attaching package: 'lubridate'
The following objects are masked from 'package:base':
date, intersect, setdiff, union
The following objects are masked from 'package:dplyr':
between, lag, lead
library ("tidyr" )library ("data.table" )
Attaching package: 'data.table'
The following object is masked from 'package:plm':
between
The following objects are masked from 'package:lubridate':
hour, isoweek, mday, minute, month, quarter, second, wday, week,
yday, year
The following objects are masked from 'package:dplyr':
between, first, last
library ("ggplot2" )library ("knitr" )<- read.csv ("/Users/henrivirtanen/Documents/Energiamarkkinoita/Week3/PS3_data.csv" )#View(data) #Modifying the data and calculating the necessary variables <- data |> mutate (Time = as_datetime (Time))<- data |> mutate (Wind = Wind_onshore.generation..MwH.)<- data |> mutate (Solar = Solar.generation..MwH.)<- data |> mutate (Wind2 = Wind^ 2 )<- data |> mutate (Solar2 = Solar^ 2 )<- data |> mutate (Demand_2= Demand..MwH.^ 2 )<- data |> mutate (Tempt_2= temperature..Celsius.^ 2 )<- data |> mutate (Interaction_W= Demand..MwH.* Wind)<- data |> mutate (Interaction_S= Demand..MwH.* Solar)<- data |> mutate (Output = Biomass.generation..MwH.+ Lignite.generation..MwH.+ Natural.gas.generation..MwH.+ Hard_coal.generation..MwH.+ Oil.generation..MwH.+ Hydro_pumped.generation..MwH.+ Hydro_poundage..generation..MwH.+ Hydro_reservoir.generation..MwH.)<- data |> mutate (Imports= Demand..MwH.- Output)setDT (data)#Creating the lags <- c ("Wind" , "Solar" , "Wind2" , "Solar2" , "Interaction_W" ,"Interaction_S" , "temperature..Celsius." , "Tempt_2" , "Demand..MwH." , "Demand_2" , "Output" )for (col in cols_to_lag) {for (i in 1 : 24 ) {paste0 (col, "_lag" , i) : = shift (get (col), i, type = "lag" )]
Here we calculate the models and make the table and plot
#As we can't use panel data models here with only one country, we will use a regular regression with lagged values. Implementation in really hard to due the large amount of variables. #colnames(data) #Lets calculate models (13 and 15) #Equation 13 <- (Output ~ + Solar + Wind2 + Solar2 + Interaction_W + Interaction_S + + natural.gas.price..EUR.MwH. + emission.allowance.price..EUR.Tn_CO2. + + Tempt_2 + + Demand_2 + Wind_lag1 + Wind_lag2 + Wind_lag3 + Wind_lag4 + Wind_lag5 + Wind_lag6 + + Wind_lag8 + Wind_lag9 + Wind_lag10 + Wind_lag11 + Wind_lag12 + + Wind_lag14 + Wind_lag15 + Wind_lag16 + Wind_lag17 + Wind_lag18 + + Wind_lag20 + Wind_lag21 + Wind_lag22 + Wind_lag23 + Wind_lag24 + + Solar_lag2 + Solar_lag3 + Solar_lag4 + Solar_lag5 + Solar_lag6 + + Solar_lag8 + Solar_lag9 + Solar_lag10 + Solar_lag11 + Solar_lag12 + + Solar_lag14 + Solar_lag15 + Solar_lag16 + Solar_lag17 + Solar_lag18 + + Solar_lag20 + Solar_lag21 + Solar_lag22 + Solar_lag23 + Solar_lag24 + + Output_lag2 + Output_lag3 + Output_lag4 + Output_lag5 + Output_lag6 + + Output_lag8 + Output_lag9 + Output_lag10 + Output_lag11 + Output_lag12 + + Output_lag14 + Output_lag15 + Output_lag16 + Output_lag17 + Output_lag18 + + Output_lag20 + Output_lag21 + Output_lag22 + Output_lag23 + Output_lag24 + + Demand..MwH._lag2 + Demand..MwH._lag3 + Demand..MwH._lag4 + + Demand..MwH._lag6 + Demand..MwH._lag7 + Demand..MwH._lag8 + + Demand..MwH._lag10 + Demand..MwH._lag11 + Demand..MwH._lag12 + + Demand..MwH._lag14 + Demand..MwH._lag15 + Demand..MwH._lag16 + + Demand..MwH._lag18 + Demand..MwH._lag19 + Demand..MwH._lag20 + + Demand..MwH._lag22 + Demand..MwH._lag23 + Demand..MwH._lag24 + + temperature..Celsius._lag2 + temperature..Celsius._lag3 + + temperature..Celsius._lag5 + temperature..Celsius._lag6 + + temperature..Celsius._lag8 + temperature..Celsius._lag9 + + temperature..Celsius._lag11 + temperature..Celsius._lag12 + + temperature..Celsius._lag14 + temperature..Celsius._lag15 + + temperature..Celsius._lag17 + temperature..Celsius._lag18 + + temperature..Celsius._lag20 + temperature..Celsius._lag21 + + temperature..Celsius._lag23 + temperature..Celsius._lag24 + + Tempt_2_lag2 + Tempt_2_lag3 + Tempt_2_lag4 + Tempt_2_lag5 + + Tempt_2_lag7 + Tempt_2_lag8 + Tempt_2_lag9 + Tempt_2_lag10 + + Tempt_2_lag12 + Tempt_2_lag13 + Tempt_2_lag14 + Tempt_2_lag15 + + Tempt_2_lag17 + Tempt_2_lag18 + Tempt_2_lag19 + Tempt_2_lag20 + + Tempt_2_lag22 + Tempt_2_lag23 + Tempt_2_lag24 + + Interaction_S + + Interaction_W_lag2 + Interaction_W_lag3 + + Interaction_W_lag5 + Interaction_W_lag6 + + Interaction_W_lag8 + Interaction_W_lag9 + + Interaction_W_lag11 + Interaction_W_lag12 + + Interaction_W_lag14 + Interaction_W_lag15 + + Interaction_W_lag17 + Interaction_W_lag18 + + Interaction_W_lag20 + Interaction_W_lag21 + + Interaction_W_lag23 + Interaction_W_lag24 + + Interaction_S_lag2 + Interaction_S_lag3 + + Interaction_S_lag5 + Interaction_S_lag6 + + Interaction_S_lag8 + Interaction_S_lag9 + + Interaction_S_lag11 + Interaction_S_lag12 + + Interaction_S_lag14 + Interaction_S_lag15 + + Interaction_S_lag17 + Interaction_S_lag18 + + Interaction_S_lag20 + Interaction_S_lag21 + + Interaction_S_lag23 + Interaction_S_lag24 + + Wind2_lag2 + Wind2_lag3 + Wind2_lag4 + Wind2_lag5 + Wind2_lag6 + + Wind2_lag8 + Wind2_lag9 + Wind2_lag10 + Wind2_lag11 + Wind2_lag12 + + Wind2_lag14 + Wind2_lag15 + Wind2_lag16 + Wind2_lag17 + Wind2_lag18 + + Wind2_lag20 + Wind2_lag21 + Wind2_lag22 + Wind2_lag23 + Wind2_lag24 + + Solar2_lag2 + Solar2_lag3 + Solar2_lag4 + Solar2_lag5 + Solar2_lag6 + + Solar2_lag8 + Solar2_lag9 + Solar2_lag10 + Solar2_lag11 + Solar2_lag12 + + Solar2_lag14 + Solar2_lag15 + Solar2_lag16 + Solar2_lag17 + Solar2_lag18 + + Solar2_lag20 + Solar2_lag21 + Solar2_lag22 + Solar2_lag23 + Solar2_lag24)<- lm (model_formula, data = data)summary (model1)
Call:
lm(formula = model_formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-7246.6 -233.8 -9.1 229.2 6822.1
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.226e+02 2.575e+02 1.641 0.100877
Wind -2.784e-01 8.751e-02 -3.181 0.001471
Solar -4.408e-01 8.187e-02 -5.385 7.45e-08
Wind2 -3.168e-06 6.228e-06 -0.509 0.610966
Solar2 5.885e-06 2.679e-06 2.196 0.028087
Interaction_W -9.612e-06 3.942e-06 -2.438 0.014770
Interaction_S -2.975e-06 3.690e-06 -0.806 0.420114
coal.price..EUR.tn. -2.043e-01 1.111e+00 -0.184 0.854177
natural.gas.price..EUR.MwH. 3.341e+00 1.510e+00 2.212 0.026975
emission.allowance.price..EUR.Tn_CO2. 6.499e-01 1.350e+00 0.481 0.630325
temperature..Celsius. 3.071e+01 1.572e+01 1.953 0.050799
Tempt_2 -1.227e+00 5.636e-01 -2.178 0.029463
Demand..MwH. 6.492e-01 2.693e-02 24.112 < 2e-16
Demand_2 9.217e-07 5.599e-07 1.646 0.099731
Wind_lag1 3.238e-02 1.781e-01 0.182 0.855762
Wind_lag2 8.403e-02 1.992e-01 0.422 0.673161
Wind_lag3 3.462e-01 2.001e-01 1.730 0.083636
Wind_lag4 -3.287e-01 2.001e-01 -1.643 0.100501
Wind_lag5 9.526e-02 2.003e-01 0.476 0.634295
Wind_lag6 9.876e-02 2.005e-01 0.493 0.622364
Wind_lag7 -5.025e-02 2.006e-01 -0.251 0.802168
Wind_lag8 -1.287e-01 2.006e-01 -0.641 0.521224
Wind_lag9 1.250e-01 2.006e-01 0.623 0.533106
Wind_lag10 -2.153e-01 2.009e-01 -1.072 0.283897
Wind_lag11 2.785e-01 2.010e-01 1.385 0.166014
Wind_lag12 -1.295e-01 2.011e-01 -0.644 0.519767
Wind_lag13 1.220e-01 2.011e-01 0.607 0.544075
Wind_lag14 -1.259e-01 2.009e-01 -0.627 0.530843
Wind_lag15 1.408e-01 2.008e-01 0.701 0.483225
Wind_lag16 -2.809e-01 2.008e-01 -1.399 0.161930
Wind_lag17 3.974e-01 2.007e-01 1.981 0.047678
Wind_lag18 -4.417e-01 2.009e-01 -2.199 0.027913
Wind_lag19 4.481e-01 2.012e-01 2.227 0.025989
Wind_lag20 -2.949e-01 2.015e-01 -1.464 0.143288
Wind_lag21 1.036e-01 2.014e-01 0.515 0.606749
Wind_lag22 -1.798e-01 2.003e-01 -0.898 0.369349
Wind_lag23 2.238e-01 1.787e-01 1.252 0.210456
Wind_lag24 -4.498e-02 8.784e-02 -0.512 0.608616
Solar_lag1 4.986e-01 1.572e-01 3.172 0.001520
Solar_lag2 -2.266e-01 1.729e-01 -1.310 0.190157
Solar_lag3 2.955e-01 1.741e-01 1.697 0.089679
Solar_lag4 -8.689e-02 1.746e-01 -0.498 0.618808
Solar_lag5 -1.824e-01 1.750e-01 -1.042 0.297415
Solar_lag6 9.432e-02 1.755e-01 0.538 0.590893
Solar_lag7 8.440e-02 1.756e-01 0.481 0.630831
Solar_lag8 -2.946e-01 1.756e-01 -1.677 0.093486
Solar_lag9 2.560e-01 1.753e-01 1.460 0.144265
Solar_lag10 9.449e-03 1.751e-01 0.054 0.956967
Solar_lag11 -5.060e-02 1.751e-01 -0.289 0.772602
Solar_lag12 -1.169e-01 1.750e-01 -0.668 0.503999
Solar_lag13 1.891e-01 1.751e-01 1.080 0.280231
Solar_lag14 -3.497e-02 1.748e-01 -0.200 0.841489
Solar_lag15 -2.211e-02 1.741e-01 -0.127 0.898959
Solar_lag16 2.855e-02 1.741e-01 0.164 0.869737
Solar_lag17 -1.706e-01 1.740e-01 -0.980 0.326905
Solar_lag18 1.257e-01 1.735e-01 0.724 0.469021
Solar_lag19 7.027e-02 1.719e-01 0.409 0.682630
Solar_lag20 -1.969e-01 1.713e-01 -1.150 0.250378
Solar_lag21 3.251e-01 1.717e-01 1.893 0.058405
Solar_lag22 -3.692e-01 1.706e-01 -2.164 0.030468
Solar_lag23 1.922e-01 1.540e-01 1.248 0.212016
Solar_lag24 -1.135e-01 7.935e-02 -1.430 0.152775
Output_lag1 8.164e-01 1.086e-02 75.183 < 2e-16
Output_lag2 -9.733e-02 1.402e-02 -6.943 4.13e-12
Output_lag3 4.638e-02 1.407e-02 3.297 0.000981
Output_lag4 4.408e-03 1.408e-02 0.313 0.754183
Output_lag5 8.451e-03 1.406e-02 0.601 0.547854
Output_lag6 2.712e-02 1.406e-02 1.928 0.053836
Output_lag7 -1.726e-02 1.408e-02 -1.226 0.220245
Output_lag8 2.389e-02 1.409e-02 1.696 0.089928
Output_lag9 -1.655e-02 1.409e-02 -1.174 0.240302
Output_lag10 2.683e-02 1.409e-02 1.904 0.056950
Output_lag11 6.314e-03 1.409e-02 0.448 0.654125
Output_lag12 1.760e-02 1.408e-02 1.250 0.211234
Output_lag13 1.690e-02 1.407e-02 1.201 0.229796
Output_lag14 -3.250e-02 1.408e-02 -2.308 0.020997
Output_lag15 -7.771e-03 1.409e-02 -0.552 0.581222
Output_lag16 4.168e-02 1.408e-02 2.960 0.003081
Output_lag17 -2.436e-02 1.408e-02 -1.730 0.083611
Output_lag18 5.842e-03 1.408e-02 0.415 0.678163
Output_lag19 -1.287e-02 1.408e-02 -0.914 0.360734
Output_lag20 1.480e-02 1.408e-02 1.051 0.293349
Output_lag21 6.152e-03 1.408e-02 0.437 0.662241
Output_lag22 1.248e-02 1.405e-02 0.889 0.374295
Output_lag23 3.496e-02 1.390e-02 2.515 0.011934
Output_lag24 2.695e-02 1.078e-02 2.501 0.012399
Demand..MwH._lag1 -3.589e-01 3.733e-02 -9.616 < 2e-16
Demand..MwH._lag2 -2.216e-01 4.093e-02 -5.414 6.32e-08
Demand..MwH._lag3 1.168e-01 4.136e-02 2.823 0.004765
Demand..MwH._lag4 -5.637e-02 4.132e-02 -1.364 0.172523
Demand..MwH._lag5 -2.064e-02 4.142e-02 -0.498 0.618230
Demand..MwH._lag6 2.256e-02 4.173e-02 0.541 0.588834
Demand..MwH._lag7 1.663e-02 4.174e-02 0.398 0.690332
Demand..MwH._lag8 -3.891e-02 4.167e-02 -0.934 0.350457
Demand..MwH._lag9 2.253e-02 4.148e-02 0.543 0.586936
Demand..MwH._lag10 2.439e-03 4.161e-02 0.059 0.953255
Demand..MwH._lag11 -5.989e-02 4.170e-02 -1.436 0.150918
Demand..MwH._lag12 9.298e-02 4.169e-02 2.230 0.025765
Demand..MwH._lag13 -8.060e-02 4.172e-02 -1.932 0.053374
Demand..MwH._lag14 -4.778e-02 4.169e-02 -1.146 0.251745
Demand..MwH._lag15 8.467e-02 4.170e-02 2.031 0.042325
Demand..MwH._lag16 -3.005e-02 4.174e-02 -0.720 0.471613
Demand..MwH._lag17 3.032e-02 4.175e-02 0.726 0.467805
Demand..MwH._lag18 -8.495e-02 4.177e-02 -2.034 0.041989
Demand..MwH._lag19 1.619e-01 4.173e-02 3.879 0.000106
Demand..MwH._lag20 -1.392e-01 4.181e-02 -3.329 0.000875
Demand..MwH._lag21 2.089e-02 4.187e-02 0.499 0.617958
Demand..MwH._lag22 -7.675e-02 4.175e-02 -1.838 0.066080
Demand..MwH._lag23 1.096e-01 3.815e-02 2.873 0.004071
Demand..MwH._lag24 -9.782e-02 2.075e-02 -4.715 2.45e-06
temperature..Celsius._lag1 -2.095e+01 2.207e+01 -0.949 0.342543
temperature..Celsius._lag2 9.577e-01 2.207e+01 0.043 0.965388
temperature..Celsius._lag3 -1.736e+01 2.207e+01 -0.786 0.431597
temperature..Celsius._lag4 1.432e+01 2.207e+01 0.649 0.516330
temperature..Celsius._lag5 -7.712e+00 2.206e+01 -0.350 0.726671
temperature..Celsius._lag6 -1.523e+01 2.201e+01 -0.692 0.488884
temperature..Celsius._lag7 -2.810e-01 2.203e+01 -0.013 0.989824
temperature..Celsius._lag8 -1.876e+01 2.201e+01 -0.852 0.394010
temperature..Celsius._lag9 1.131e+01 2.200e+01 0.514 0.607254
temperature..Celsius._lag10 -4.386e+00 2.199e+01 -0.199 0.841920
temperature..Celsius._lag11 1.594e+01 2.199e+01 0.725 0.468440
temperature..Celsius._lag12 -3.592e+00 2.199e+01 -0.163 0.870244
temperature..Celsius._lag13 4.220e+00 2.198e+01 0.192 0.847742
temperature..Celsius._lag14 2.637e+01 2.197e+01 1.200 0.230086
temperature..Celsius._lag15 -1.236e+01 2.197e+01 -0.563 0.573731
temperature..Celsius._lag16 3.404e+00 2.196e+01 0.155 0.876838
temperature..Celsius._lag17 -1.221e+00 2.196e+01 -0.056 0.955643
temperature..Celsius._lag18 2.321e+01 2.195e+01 1.058 0.290279
temperature..Celsius._lag19 -1.591e+01 2.194e+01 -0.725 0.468380
temperature..Celsius._lag20 -1.240e+01 2.194e+01 -0.565 0.571832
temperature..Celsius._lag21 1.274e+01 2.194e+01 0.581 0.561336
temperature..Celsius._lag22 -9.035e+00 2.194e+01 -0.412 0.680435
temperature..Celsius._lag23 2.797e+00 2.194e+01 0.128 0.898545
temperature..Celsius._lag24 -8.171e+00 1.559e+01 -0.524 0.600161
Tempt_2_lag1 4.183e-01 7.898e-01 0.530 0.596414
Tempt_2_lag2 1.722e-01 7.902e-01 0.218 0.827475
Tempt_2_lag3 4.155e-01 7.905e-01 0.526 0.599160
Tempt_2_lag4 -5.915e-02 7.904e-01 -0.075 0.940351
Tempt_2_lag5 5.627e-01 7.904e-01 0.712 0.476558
Tempt_2_lag6 5.262e-02 7.899e-01 0.067 0.946892
Tempt_2_lag7 -3.959e-01 7.902e-01 -0.501 0.616366
Tempt_2_lag8 1.649e+00 7.911e-01 2.084 0.037157
Tempt_2_lag9 -1.120e+00 7.910e-01 -1.416 0.156930
Tempt_2_lag10 4.324e-01 7.911e-01 0.547 0.584647
Tempt_2_lag11 -5.983e-01 7.911e-01 -0.756 0.449480
Tempt_2_lag12 2.253e-01 7.911e-01 0.285 0.775796
Tempt_2_lag13 -9.608e-02 7.909e-01 -0.121 0.903312
Tempt_2_lag14 -9.338e-01 7.904e-01 -1.181 0.237489
Tempt_2_lag15 6.567e-01 7.900e-01 0.831 0.405824
Tempt_2_lag16 -1.015e+00 7.896e-01 -1.286 0.198636
Tempt_2_lag17 6.537e-01 7.895e-01 0.828 0.407674
Tempt_2_lag18 2.823e-01 7.890e-01 0.358 0.720495
Tempt_2_lag19 -5.868e-01 7.889e-01 -0.744 0.457006
Tempt_2_lag20 2.644e-01 7.889e-01 0.335 0.737517
Tempt_2_lag21 -1.239e-01 7.888e-01 -0.157 0.875227
Tempt_2_lag22 1.241e+00 7.884e-01 1.574 0.115410
Tempt_2_lag23 -7.354e-01 7.885e-01 -0.933 0.351050
Tempt_2_lag24 -1.057e-01 5.617e-01 -0.188 0.850763
Interaction_W_lag1 -8.135e-07 8.130e-06 -0.100 0.920297
Interaction_W_lag2 2.427e-05 9.149e-06 2.653 0.007990
Interaction_W_lag3 -2.859e-05 9.201e-06 -3.107 0.001899
Interaction_W_lag4 1.400e-05 9.207e-06 1.521 0.128395
Interaction_W_lag5 -4.120e-07 9.213e-06 -0.045 0.964327
Interaction_W_lag6 -3.061e-06 9.229e-06 -0.332 0.740136
Interaction_W_lag7 1.528e-06 9.233e-06 0.166 0.868546
Interaction_W_lag8 5.233e-06 9.237e-06 0.567 0.571029
Interaction_W_lag9 -1.067e-05 9.232e-06 -1.156 0.247628
Interaction_W_lag10 1.155e-05 9.250e-06 1.248 0.211938
Interaction_W_lag11 -4.492e-06 9.260e-06 -0.485 0.627633
Interaction_W_lag12 -7.567e-06 9.262e-06 -0.817 0.413979
Interaction_W_lag13 2.917e-06 9.264e-06 0.315 0.752841
Interaction_W_lag14 6.138e-06 9.254e-06 0.663 0.507152
Interaction_W_lag15 -3.673e-06 9.244e-06 -0.397 0.691133
Interaction_W_lag16 6.790e-06 9.248e-06 0.734 0.462844
Interaction_W_lag17 -1.762e-05 9.247e-06 -1.905 0.056775
Interaction_W_lag18 2.176e-05 9.260e-06 2.349 0.018823
Interaction_W_lag19 -1.859e-05 9.284e-06 -2.002 0.045283
Interaction_W_lag20 7.568e-06 9.305e-06 0.813 0.416061
Interaction_W_lag21 -2.059e-06 9.307e-06 -0.221 0.824951
Interaction_W_lag22 1.241e-05 9.254e-06 1.341 0.179971
Interaction_W_lag23 -1.404e-05 8.200e-06 -1.713 0.086825
Interaction_W_lag24 4.452e-06 3.964e-06 1.123 0.261452
Interaction_S_lag1 -1.395e-05 7.159e-06 -1.949 0.051384
Interaction_S_lag2 1.976e-05 7.937e-06 2.490 0.012789
Interaction_S_lag3 -1.126e-05 7.969e-06 -1.412 0.157842
Interaction_S_lag4 4.279e-06 7.964e-06 0.537 0.591108
Interaction_S_lag5 2.604e-06 7.997e-06 0.326 0.744705
Interaction_S_lag6 2.354e-06 8.046e-06 0.293 0.769815
Interaction_S_lag7 -1.161e-05 8.056e-06 -1.441 0.149684
Interaction_S_lag8 2.253e-05 8.058e-06 2.796 0.005187
Interaction_S_lag9 -1.640e-05 8.052e-06 -2.038 0.041629
Interaction_S_lag10 -5.782e-06 8.052e-06 -0.718 0.472732
Interaction_S_lag11 1.257e-05 8.058e-06 1.559 0.118929
Interaction_S_lag12 -1.580e-06 8.055e-06 -0.196 0.844525
Interaction_S_lag13 -2.942e-06 8.061e-06 -0.365 0.715141
Interaction_S_lag14 -3.561e-06 8.041e-06 -0.443 0.657893
Interaction_S_lag15 3.449e-06 7.996e-06 0.431 0.666206
Interaction_S_lag16 -3.749e-06 7.997e-06 -0.469 0.639278
Interaction_S_lag17 1.203e-05 8.004e-06 1.503 0.132775
Interaction_S_lag18 -6.863e-06 7.993e-06 -0.859 0.390564
Interaction_S_lag19 -1.119e-05 7.929e-06 -1.412 0.158119
Interaction_S_lag20 1.858e-05 7.906e-06 2.350 0.018819
Interaction_S_lag21 -1.892e-05 7.923e-06 -2.388 0.016985
Interaction_S_lag22 1.778e-05 7.822e-06 2.273 0.023037
Interaction_S_lag23 -6.733e-06 6.981e-06 -0.965 0.334798
Interaction_S_lag24 2.911e-06 3.558e-06 0.818 0.413179
Wind2_lag1 1.535e-05 1.213e-05 1.266 0.205689
Wind2_lag2 -3.046e-05 1.331e-05 -2.288 0.022156
Wind2_lag3 1.832e-05 1.341e-05 1.366 0.171918
Wind2_lag4 7.143e-06 1.343e-05 0.532 0.594691
Wind2_lag5 -1.296e-05 1.345e-05 -0.964 0.335249
Wind2_lag6 -2.346e-06 1.346e-05 -0.174 0.861635
Wind2_lag7 2.752e-06 1.346e-05 0.204 0.838031
Wind2_lag8 2.491e-06 1.347e-05 0.185 0.853331
Wind2_lag9 1.499e-05 1.348e-05 1.112 0.266146
Wind2_lag10 -1.356e-05 1.350e-05 -1.004 0.315321
Wind2_lag11 -4.974e-06 1.350e-05 -0.368 0.712652
Wind2_lag12 1.976e-05 1.351e-05 1.463 0.143574
Wind2_lag13 -1.767e-05 1.351e-05 -1.308 0.190938
Wind2_lag14 1.065e-06 1.351e-05 0.079 0.937170
Wind2_lag15 -3.806e-06 1.352e-05 -0.282 0.778271
Wind2_lag16 1.539e-05 1.353e-05 1.138 0.255141
Wind2_lag17 -1.274e-05 1.352e-05 -0.942 0.346104
Wind2_lag18 7.815e-06 1.353e-05 0.578 0.563401
Wind2_lag19 -1.015e-05 1.356e-05 -0.749 0.453882
Wind2_lag20 1.823e-05 1.359e-05 1.341 0.179848
Wind2_lag21 -3.979e-06 1.357e-05 -0.293 0.769327
Wind2_lag22 -1.393e-05 1.345e-05 -1.036 0.300111
Wind2_lag23 1.078e-05 1.222e-05 0.882 0.377590
Wind2_lag24 -3.207e-06 6.267e-06 -0.512 0.608848
Solar2_lag1 -1.651e-06 4.918e-06 -0.336 0.737093
Solar2_lag2 -5.117e-06 5.670e-06 -0.903 0.366783
Solar2_lag3 -4.740e-06 5.876e-06 -0.807 0.419883
Solar2_lag4 1.592e-06 5.909e-06 0.269 0.787681
Solar2_lag5 5.838e-06 5.917e-06 0.987 0.323867
Solar2_lag6 -3.715e-06 5.922e-06 -0.627 0.530429
Solar2_lag7 6.768e-06 5.923e-06 1.143 0.253223
Solar2_lag8 -1.203e-05 5.923e-06 -2.032 0.042202
Solar2_lag9 8.998e-06 5.924e-06 1.519 0.128834
Solar2_lag10 5.418e-06 5.928e-06 0.914 0.360776
Solar2_lag11 -1.234e-05 5.931e-06 -2.080 0.037562
Solar2_lag12 1.117e-05 5.934e-06 1.883 0.059743
Solar2_lag13 -1.332e-05 5.938e-06 -2.244 0.024870
Solar2_lag14 1.141e-05 5.939e-06 1.921 0.054726
Solar2_lag15 -4.676e-06 5.941e-06 -0.787 0.431216
Solar2_lag16 1.984e-06 5.941e-06 0.334 0.738460
Solar2_lag17 -1.518e-06 5.940e-06 -0.256 0.798288
Solar2_lag18 -3.124e-06 5.938e-06 -0.526 0.598773
Solar2_lag19 1.249e-05 5.938e-06 2.104 0.035390
Solar2_lag20 -1.358e-05 5.941e-06 -2.286 0.022273
Solar2_lag21 4.863e-06 5.916e-06 0.822 0.411052
Solar2_lag22 4.531e-06 5.737e-06 0.790 0.429654
Solar2_lag23 -3.149e-06 5.029e-06 -0.626 0.531154
Solar2_lag24 3.699e-06 2.734e-06 1.353 0.176013
(Intercept)
Wind **
Solar ***
Wind2
Solar2 *
Interaction_W *
Interaction_S
coal.price..EUR.tn.
natural.gas.price..EUR.MwH. *
emission.allowance.price..EUR.Tn_CO2.
temperature..Celsius. .
Tempt_2 *
Demand..MwH. ***
Demand_2 .
Wind_lag1
Wind_lag2
Wind_lag3 .
Wind_lag4
Wind_lag5
Wind_lag6
Wind_lag7
Wind_lag8
Wind_lag9
Wind_lag10
Wind_lag11
Wind_lag12
Wind_lag13
Wind_lag14
Wind_lag15
Wind_lag16
Wind_lag17 *
Wind_lag18 *
Wind_lag19 *
Wind_lag20
Wind_lag21
Wind_lag22
Wind_lag23
Wind_lag24
Solar_lag1 **
Solar_lag2
Solar_lag3 .
Solar_lag4
Solar_lag5
Solar_lag6
Solar_lag7
Solar_lag8 .
Solar_lag9
Solar_lag10
Solar_lag11
Solar_lag12
Solar_lag13
Solar_lag14
Solar_lag15
Solar_lag16
Solar_lag17
Solar_lag18
Solar_lag19
Solar_lag20
Solar_lag21 .
Solar_lag22 *
Solar_lag23
Solar_lag24
Output_lag1 ***
Output_lag2 ***
Output_lag3 ***
Output_lag4
Output_lag5
Output_lag6 .
Output_lag7
Output_lag8 .
Output_lag9
Output_lag10 .
Output_lag11
Output_lag12
Output_lag13
Output_lag14 *
Output_lag15
Output_lag16 **
Output_lag17 .
Output_lag18
Output_lag19
Output_lag20
Output_lag21
Output_lag22
Output_lag23 *
Output_lag24 *
Demand..MwH._lag1 ***
Demand..MwH._lag2 ***
Demand..MwH._lag3 **
Demand..MwH._lag4
Demand..MwH._lag5
Demand..MwH._lag6
Demand..MwH._lag7
Demand..MwH._lag8
Demand..MwH._lag9
Demand..MwH._lag10
Demand..MwH._lag11
Demand..MwH._lag12 *
Demand..MwH._lag13 .
Demand..MwH._lag14
Demand..MwH._lag15 *
Demand..MwH._lag16
Demand..MwH._lag17
Demand..MwH._lag18 *
Demand..MwH._lag19 ***
Demand..MwH._lag20 ***
Demand..MwH._lag21
Demand..MwH._lag22 .
Demand..MwH._lag23 **
Demand..MwH._lag24 ***
temperature..Celsius._lag1
temperature..Celsius._lag2
temperature..Celsius._lag3
temperature..Celsius._lag4
temperature..Celsius._lag5
temperature..Celsius._lag6
temperature..Celsius._lag7
temperature..Celsius._lag8
temperature..Celsius._lag9
temperature..Celsius._lag10
temperature..Celsius._lag11
temperature..Celsius._lag12
temperature..Celsius._lag13
temperature..Celsius._lag14
temperature..Celsius._lag15
temperature..Celsius._lag16
temperature..Celsius._lag17
temperature..Celsius._lag18
temperature..Celsius._lag19
temperature..Celsius._lag20
temperature..Celsius._lag21
temperature..Celsius._lag22
temperature..Celsius._lag23
temperature..Celsius._lag24
Tempt_2_lag1
Tempt_2_lag2
Tempt_2_lag3
Tempt_2_lag4
Tempt_2_lag5
Tempt_2_lag6
Tempt_2_lag7
Tempt_2_lag8 *
Tempt_2_lag9
Tempt_2_lag10
Tempt_2_lag11
Tempt_2_lag12
Tempt_2_lag13
Tempt_2_lag14
Tempt_2_lag15
Tempt_2_lag16
Tempt_2_lag17
Tempt_2_lag18
Tempt_2_lag19
Tempt_2_lag20
Tempt_2_lag21
Tempt_2_lag22
Tempt_2_lag23
Tempt_2_lag24
Interaction_W_lag1
Interaction_W_lag2 **
Interaction_W_lag3 **
Interaction_W_lag4
Interaction_W_lag5
Interaction_W_lag6
Interaction_W_lag7
Interaction_W_lag8
Interaction_W_lag9
Interaction_W_lag10
Interaction_W_lag11
Interaction_W_lag12
Interaction_W_lag13
Interaction_W_lag14
Interaction_W_lag15
Interaction_W_lag16
Interaction_W_lag17 .
Interaction_W_lag18 *
Interaction_W_lag19 *
Interaction_W_lag20
Interaction_W_lag21
Interaction_W_lag22
Interaction_W_lag23 .
Interaction_W_lag24
Interaction_S_lag1 .
Interaction_S_lag2 *
Interaction_S_lag3
Interaction_S_lag4
Interaction_S_lag5
Interaction_S_lag6
Interaction_S_lag7
Interaction_S_lag8 **
Interaction_S_lag9 *
Interaction_S_lag10
Interaction_S_lag11
Interaction_S_lag12
Interaction_S_lag13
Interaction_S_lag14
Interaction_S_lag15
Interaction_S_lag16
Interaction_S_lag17
Interaction_S_lag18
Interaction_S_lag19
Interaction_S_lag20 *
Interaction_S_lag21 *
Interaction_S_lag22 *
Interaction_S_lag23
Interaction_S_lag24
Wind2_lag1
Wind2_lag2 *
Wind2_lag3
Wind2_lag4
Wind2_lag5
Wind2_lag6
Wind2_lag7
Wind2_lag8
Wind2_lag9
Wind2_lag10
Wind2_lag11
Wind2_lag12
Wind2_lag13
Wind2_lag14
Wind2_lag15
Wind2_lag16
Wind2_lag17
Wind2_lag18
Wind2_lag19
Wind2_lag20
Wind2_lag21
Wind2_lag22
Wind2_lag23
Wind2_lag24
Solar2_lag1
Solar2_lag2
Solar2_lag3
Solar2_lag4
Solar2_lag5
Solar2_lag6
Solar2_lag7
Solar2_lag8 *
Solar2_lag9
Solar2_lag10
Solar2_lag11 *
Solar2_lag12 .
Solar2_lag13 *
Solar2_lag14 .
Solar2_lag15
Solar2_lag16
Solar2_lag17
Solar2_lag18
Solar2_lag19 *
Solar2_lag20 *
Solar2_lag21
Solar2_lag22
Solar2_lag23
Solar2_lag24
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 405 on 8481 degrees of freedom
(49 observations deleted due to missingness)
Multiple R-squared: 0.9823, Adjusted R-squared: 0.9818
F-statistic: 1860 on 253 and 8481 DF, p-value: < 2.2e-16
#Equation 15 <- Day.ahead.Price..EUR.MWh. ~ + Solar + Wind2 + Solar2 + Interaction_W + Interaction_S + Demand..MwH. + Demand_2 + coal.price..EUR.tn. + natural.gas.price..EUR.MwH. + emission.allowance.price..EUR.Tn_CO2.<- lm (model_formula2, data = data)summary (model2)
Call:
lm(formula = model_formula2, data = data)
Residuals:
Min 1Q Median 3Q Max
-105.00 -18.97 -3.35 12.47 465.09
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.672e+02 1.438e+01 -18.588 < 2e-16
Wind -1.156e-02 1.184e-03 -9.757 < 2e-16
Solar -1.181e-02 1.165e-03 -10.140 < 2e-16
Wind2 1.125e-07 8.215e-08 1.369 0.171
Solar2 -4.238e-07 4.982e-08 -8.507 < 2e-16
Interaction_W 5.068e-08 5.647e-08 0.898 0.369
Interaction_S 3.527e-07 5.828e-08 6.052 1.48e-09
Demand..MwH. 1.915e-02 1.273e-03 15.046 < 2e-16
Demand_2 -3.285e-07 3.362e-08 -9.769 < 2e-16
coal.price..EUR.tn. 4.442e-01 8.196e-02 5.420 6.12e-08
natural.gas.price..EUR.MwH. 8.705e-01 9.401e-02 9.260 < 2e-16
emission.allowance.price..EUR.Tn_CO2. 1.395e+00 9.300e-02 14.996 < 2e-16
(Intercept) ***
Wind ***
Solar ***
Wind2
Solar2 ***
Interaction_W
Interaction_S ***
Demand..MwH. ***
Demand_2 ***
coal.price..EUR.tn. ***
natural.gas.price..EUR.MwH. ***
emission.allowance.price..EUR.Tn_CO2. ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 34.71 on 8771 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared: 0.5113, Adjusted R-squared: 0.5107
F-statistic: 834.1 on 11 and 8771 DF, p-value: < 2.2e-16
#Average replacement and price effect: 1st attempt: #Model1 #Wind -2.784e-01 8.751e-02 -3.181 0.001471 ** #Solar -4.408e-01 8.187e-02 -5.385 7.45e-08 *** #Wind2 -3.168e-06 6.228e-06 -0.509 0.610966 #Solar2 5.885e-06 2.679e-06 2.196 0.028087 * #Interaction_W -9.612e-06 3.942e-06 -2.438 0.014770 * $ hour <- hour (data$ Time)<- data %>% group_by (hour) %>% summarise (avg_value = mean (Wind, na.rm = TRUE )) <- data %>% group_by (hour) %>% summarise (avg_value = mean (Solar, na.rm = TRUE )) <- data %>% group_by (hour) %>% summarise (avg_value = mean (Demand..MwH., na.rm = TRUE ))
# A tibble: 24 × 2
hour avg_value
<int> <dbl>
1 0 0
2 1 0
3 2 0
4 3 0
5 4 25.4
6 5 150.
7 6 557.
8 7 1599.
9 8 3105.
10 9 4528.
# ℹ 14 more rows
<- - 4.408489e-01 + (2 * 5.884858e-06 * hourly_avg2$ avg_value)+ (- 2.974753e-06 * hourly_avg3$ avg_value)<- - 4.408489e-01 + (2 * 5.884858e-06 * hourly_avg1$ avg_value)+ (- 2.974753e-06 * hourly_avg3$ avg_value)#Model2 #Wind -1.156e-02 1.184e-03 -9.757 < 2e-16 *** #Solar -1.181e-02 1.165e-03 -10.140 < 2e-16 *** #Wind2 1.125e-07 8.215e-08 1.369 0.171 #Solar2 -4.238e-07 4.982e-08 -8.507 < 2e-16 *** #Interaction_W 5.068e-08 5.647e-08 0.898 0.369 #Interaction_S 3.527e-07 <- - 1.181e-02 + (2 *- 4.238e-07 * hourly_avg2$ avg_value)+ (3.527e-07 * hourly_avg3$ avg_value)<- - 1.156e-02 + (2 * 1.125e-07 * hourly_avg1$ avg_value)+ (5.068e-08 * hourly_avg3$ avg_value)#Second attempt <- mean (na.omit (data$ Solar.generation..MwH.))<- mean (na.omit (data$ Wind_onshore.generation..MwH.))<- mean (data$ Demand..MwH., na.rm = TRUE )<- - 4.408489e-01 + (2 * 5.884858e-06 * solar_avg)+ (- 2.974753e-06 * mean_demand)<- - 1.181e-02 + (2 *- 4.238e-07 * solar_avg)+ (3.527e-07 * mean_demand)<- - 4.408489e-01 + (2 * 5.884858e-06 * wind_avg)+ (- 2.974753e-06 * mean_demand)<- - 1.156e-02 + (2 * 1.125e-07 * wind_avg)+ (5.068e-08 * mean_demand)#The table <- data.frame (Wind_replacement2 = Wind_replacement2,Solar_replacement2 = Solar_replacement2,Solar_price2 = Solar_price2,Wind_price2 = Wind_price2kable (summary_table, caption = "Energy Source Replacement" )
Energy Source Replacement
-0.464179
-0.4729873
-0.0069176
-0.0100037
#The plot <- data.frame (Hour = 1 : length (hourly_avg1$ avg_value), # Assuming hourly data Solar_replacement = - 4.408489e-01 + (2 * 5.884858e-06 * hourly_avg2$ avg_value) + (- 2.974753e-06 * hourly_avg3$ avg_value),Wind_replacement = - 4.408489e-01 + (2 * 5.884858e-06 * hourly_avg1$ avg_value) + (- 2.974753e-06 * hourly_avg3$ avg_value)# Convert to long format for ggplot library (tidyr)<- pivot_longer (plot_data, cols = c (Solar_replacement, Wind_replacement), names_to = "Variable" , values_to = "Value" )# Plot ggplot (plot_data_long, aes (x = Hour, y = Value, color = Variable)) + geom_line (linewidth = 1 ) + labs (title = "Solar & Wind Replacement Over Time" ,x = "Hour" , y = "Replacement Value" ,color = "Type" ) + theme_minimal ()
Loading required package: Matrix
Attaching package: 'Matrix'
The following objects are masked from 'package:tidyr':
expand, pack, unpack
The following object is masked from 'package:plm':
sargan
#Time fixed effect for Hour: <- felm (Output ~ Wind + Solar + Wind2 + Solar2 + Interaction_W + Interaction_S + + natural.gas.price..EUR.MwH. + emission.allowance.price..EUR.Tn_CO2. + + Tempt_2 + + Demand_2 + Wind_lag1 + Wind_lag2 + Wind_lag3 + Wind_lag4 + Wind_lag5 + Wind_lag6 + + Wind_lag8 + Wind_lag9 + Wind_lag10 + Wind_lag11 + Wind_lag12 + + Wind_lag14 + Wind_lag15 + Wind_lag16 + Wind_lag17 + Wind_lag18 + + Wind_lag20 + Wind_lag21 + Wind_lag22 + Wind_lag23 + Wind_lag24 + + Solar_lag2 + Solar_lag3 + Solar_lag4 + Solar_lag5 + Solar_lag6 + + Solar_lag8 + Solar_lag9 + Solar_lag10 + Solar_lag11 + Solar_lag12 + + Solar_lag14 + Solar_lag15 + Solar_lag16 + Solar_lag17 + Solar_lag18 + + Solar_lag20 + Solar_lag21 + Solar_lag22 + Solar_lag23 + Solar_lag24 + + Output_lag2 + Output_lag3 + Output_lag4 + Output_lag5 + Output_lag6 + + Output_lag8 + Output_lag9 + Output_lag10 + Output_lag11 + Output_lag12 + + Output_lag14 + Output_lag15 + Output_lag16 + Output_lag17 + Output_lag18 + + Output_lag20 + Output_lag21 + Output_lag22 + Output_lag23 + Output_lag24 + + Demand..MwH._lag2 + Demand..MwH._lag3 + Demand..MwH._lag4 + + Demand..MwH._lag6 + Demand..MwH._lag7 + Demand..MwH._lag8 + + Demand..MwH._lag10 + Demand..MwH._lag11 + Demand..MwH._lag12 + + Demand..MwH._lag14 + Demand..MwH._lag15 + Demand..MwH._lag16 + + Demand..MwH._lag18 + Demand..MwH._lag19 + Demand..MwH._lag20 + + Demand..MwH._lag22 + Demand..MwH._lag23 + Demand..MwH._lag24 + + temperature..Celsius._lag2 + temperature..Celsius._lag3 + + temperature..Celsius._lag5 + temperature..Celsius._lag6 + + temperature..Celsius._lag8 + temperature..Celsius._lag9 + + temperature..Celsius._lag11 + temperature..Celsius._lag12 + + temperature..Celsius._lag14 + temperature..Celsius._lag15 + + temperature..Celsius._lag17 + temperature..Celsius._lag18 + + temperature..Celsius._lag20 + temperature..Celsius._lag21 + + temperature..Celsius._lag23 + temperature..Celsius._lag24 + + Tempt_2_lag2 + Tempt_2_lag3 + Tempt_2_lag4 + Tempt_2_lag5 + + Tempt_2_lag7 + Tempt_2_lag8 + Tempt_2_lag9 + Tempt_2_lag10 + + Tempt_2_lag12 + Tempt_2_lag13 + Tempt_2_lag14 + Tempt_2_lag15 + + Tempt_2_lag17 + Tempt_2_lag18 + Tempt_2_lag19 + Tempt_2_lag20 + + Tempt_2_lag22 + Tempt_2_lag23 + Tempt_2_lag24 + + Interaction_S + + Interaction_W_lag2 + Interaction_W_lag3 + + Interaction_W_lag5 + Interaction_W_lag6 + + Interaction_W_lag8 + Interaction_W_lag9 + + Interaction_W_lag11 + Interaction_W_lag12 + + Interaction_W_lag14 + Interaction_W_lag15 + + Interaction_W_lag17 + Interaction_W_lag18 + + Interaction_W_lag20 + Interaction_W_lag21 + + Interaction_W_lag23 + Interaction_W_lag24 + + Interaction_S_lag2 + Interaction_S_lag3 + + Interaction_S_lag5 + Interaction_S_lag6 + + Interaction_S_lag8 + Interaction_S_lag9 + + Interaction_S_lag11 + Interaction_S_lag12 + + Interaction_S_lag14 + Interaction_S_lag15 + + Interaction_S_lag17 + Interaction_S_lag18 + + Interaction_S_lag20 + Interaction_S_lag21 + + Interaction_S_lag23 + Interaction_S_lag24 + + Wind2_lag2 + Wind2_lag3 + Wind2_lag4 + Wind2_lag5 + Wind2_lag6 + + Wind2_lag8 + Wind2_lag9 + Wind2_lag10 + Wind2_lag11 + Wind2_lag12 + + Wind2_lag14 + Wind2_lag15 + Wind2_lag16 + Wind2_lag17 + Wind2_lag18 + + Wind2_lag20 + Wind2_lag21 + Wind2_lag22 + Wind2_lag23 + Wind2_lag24 + + Solar2_lag2 + Solar2_lag3 + Solar2_lag4 + Solar2_lag5 + Solar2_lag6 + + Solar2_lag8 + Solar2_lag9 + Solar2_lag10 + Solar2_lag11 + Solar2_lag12 + + Solar2_lag14 + Solar2_lag15 + Solar2_lag16 + Solar2_lag17 + Solar2_lag18 + + Solar2_lag20 + Solar2_lag21 + Solar2_lag22 + Solar2_lag23 + Solar2_lag24| hour, data = data)summary (model_felm)
Warning in chol.default(mat, pivot = TRUE, tol = tol): the matrix is either
rank-deficient or not positive definite
Call:
felm(formula = Output ~ Wind + Solar + Wind2 + Solar2 + Interaction_W + Interaction_S + coal.price..EUR.tn. + natural.gas.price..EUR.MwH. + emission.allowance.price..EUR.Tn_CO2. + temperature..Celsius. + Tempt_2 + Demand..MwH. + Demand_2 + Wind_lag1 + Wind_lag2 + Wind_lag3 + Wind_lag4 + Wind_lag5 + Wind_lag6 + Wind_lag7 + Wind_lag8 + Wind_lag9 + Wind_lag10 + Wind_lag11 + Wind_lag12 + Wind_lag13 + Wind_lag14 + Wind_lag15 + Wind_lag16 + Wind_lag17 + Wind_lag18 + Wind_lag19 + Wind_lag20 + Wind_lag21 + Wind_lag22 + Wind_lag23 + Wind_lag24 + Solar_lag1 + Solar_lag2 + Solar_lag3 + Solar_lag4 + Solar_lag5 + Solar_lag6 + Solar_lag7 + Solar_lag8 + Solar_lag9 + Solar_lag10 + Solar_lag11 + Solar_lag12 + Solar_lag13 + Solar_lag14 + Solar_lag15 + Solar_lag16 + Solar_lag17 + Solar_lag18 + Solar_lag19 + Solar_lag20 + Solar_lag21 + Solar_lag22 + Solar_lag23 + Solar_lag24 + Output_lag1 + Output_lag2 + Output_lag3 + Output_lag4 + Output_lag5 + Output_lag6 + Output_lag7 + Output_lag8 + Output_lag9 + Output_lag10 + Output_lag11 + Output_lag12 + Output_lag13 + Output_lag14 + Output_lag15 + Output_lag16 + Output_lag17 + Output_lag18 + Output_lag19 + Output_lag20 + Output_lag21 + Output_lag22 + Output_lag23 + Output_lag24 + Demand..MwH._lag1 + Demand..MwH._lag2 + Demand..MwH._lag3 + Demand..MwH._lag4 + Demand..MwH._lag5 + Demand..MwH._lag6 + Demand..MwH._lag7 + Demand..MwH._lag8 + Demand..MwH._lag9 + Demand..MwH._lag10 + Demand..MwH._lag11 + Demand..MwH._lag12 + Demand..MwH._lag13 + Demand..MwH._lag14 + Demand..MwH._lag15 + Demand..MwH._lag16 + Demand..MwH._lag17 + Demand..MwH._lag18 + Demand..MwH._lag19 + Demand..MwH._lag20 + Demand..MwH._lag21 + Demand..MwH._lag22 + Demand..MwH._lag23 + Demand..MwH._lag24 + temperature..Celsius._lag1 + temperature..Celsius._lag2 + temperature..Celsius._lag3 + temperature..Celsius._lag4 + temperature..Celsius._lag5 + temperature..Celsius._lag6 + temperature..Celsius._lag7 + temperature..Celsius._lag8 + temperature..Celsius._lag9 + temperature..Celsius._lag10 + temperature..Celsius._lag11 + temperature..Celsius._lag12 + temperature..Celsius._lag13 + temperature..Celsius._lag14 + temperature..Celsius._lag15 + temperature..Celsius._lag16 + temperature..Celsius._lag17 + temperature..Celsius._lag18 + temperature..Celsius._lag19 + temperature..Celsius._lag20 + temperature..Celsius._lag21 + temperature..Celsius._lag22 + temperature..Celsius._lag23 + temperature..Celsius._lag24 + Tempt_2_lag1 + Tempt_2_lag2 + Tempt_2_lag3 + Tempt_2_lag4 + Tempt_2_lag5 + Tempt_2_lag6 + Tempt_2_lag7 + Tempt_2_lag8 + Tempt_2_lag9 + Tempt_2_lag10 + Tempt_2_lag11 + Tempt_2_lag12 + Tempt_2_lag13 + Tempt_2_lag14 + Tempt_2_lag15 + Tempt_2_lag16 + Tempt_2_lag17 + Tempt_2_lag18 + Tempt_2_lag19 + Tempt_2_lag20 + Tempt_2_lag21 + Tempt_2_lag22 + Tempt_2_lag23 + Tempt_2_lag24 + Interaction_W + Interaction_S + Interaction_W_lag1 + Interaction_W_lag2 + Interaction_W_lag3 + Interaction_W_lag4 + Interaction_W_lag5 + Interaction_W_lag6 + Interaction_W_lag7 + Interaction_W_lag8 + Interaction_W_lag9 + Interaction_W_lag10 + Interaction_W_lag11 + Interaction_W_lag12 + Interaction_W_lag13 + Interaction_W_lag14 + Interaction_W_lag15 + Interaction_W_lag16 + Interaction_W_lag17 + Interaction_W_lag18 + Interaction_W_lag19 + Interaction_W_lag20 + Interaction_W_lag21 + Interaction_W_lag22 + Interaction_W_lag23 + Interaction_W_lag24 + Interaction_S_lag1 + Interaction_S_lag2 + Interaction_S_lag3 + Interaction_S_lag4 + Interaction_S_lag5 + Interaction_S_lag6 + Interaction_S_lag7 + Interaction_S_lag8 + Interaction_S_lag9 + Interaction_S_lag10 + Interaction_S_lag11 + Interaction_S_lag12 + Interaction_S_lag13 + Interaction_S_lag14 + Interaction_S_lag15 + Interaction_S_lag16 + Interaction_S_lag17 + Interaction_S_lag18 + Interaction_S_lag19 + Interaction_S_lag20 + Interaction_S_lag21 + Interaction_S_lag22 + Interaction_S_lag23 + Interaction_S_lag24 + Wind2_lag1 + Wind2_lag2 + Wind2_lag3 + Wind2_lag4 + Wind2_lag5 + Wind2_lag6 + Wind2_lag7 + Wind2_lag8 + Wind2_lag9 + Wind2_lag10 + Wind2_lag11 + Wind2_lag12 + Wind2_lag13 + Wind2_lag14 + Wind2_lag15 + Wind2_lag16 + Wind2_lag17 + Wind2_lag18 + Wind2_lag19 + Wind2_lag20 + Wind2_lag21 + Wind2_lag22 + Wind2_lag23 + Wind2_lag24 + Solar2_lag1 + Solar2_lag2 + Solar2_lag3 + Solar2_lag4 + Solar2_lag5 + Solar2_lag6 + Solar2_lag7 + Solar2_lag8 + Solar2_lag9 + Solar2_lag10 + Solar2_lag11 + Solar2_lag12 + Solar2_lag13 + Solar2_lag14 + Solar2_lag15 + Solar2_lag16 + Solar2_lag17 + Solar2_lag18 + Solar2_lag19 + Solar2_lag20 + Solar2_lag21 + Solar2_lag22 + Solar2_lag23 + Solar2_lag24 | hour, data = data)
Residuals:
Min 1Q Median 3Q Max
-7160.4 -230.7 -7.0 226.4 6833.2
Coefficients:
Estimate Std. Error t value Pr(>|t|)
Wind -2.685e-01 8.735e-02 -3.074 0.002119
Solar -3.125e-01 8.471e-02 -3.688 0.000227
Wind2 -2.565e-06 6.205e-06 -0.413 0.679373
Solar2 4.528e-06 2.722e-06 1.664 0.096241
Interaction_W -1.069e-05 3.940e-06 -2.712 0.006691
Interaction_S -9.797e-06 3.836e-06 -2.554 0.010681
coal.price..EUR.tn. 2.732e-02 1.106e+00 0.025 0.980293
natural.gas.price..EUR.MwH. 3.339e+00 1.502e+00 2.223 0.026219
emission.allowance.price..EUR.Tn_CO2. 6.060e-01 1.343e+00 0.451 0.651723
temperature..Celsius. 3.290e+01 1.565e+01 2.102 0.035547
Tempt_2 -1.249e+00 5.611e-01 -2.226 0.026018
Demand..MwH. 7.214e-01 2.918e-02 24.724 < 2e-16
Demand_2 3.847e-07 5.978e-07 0.644 0.519846
Wind_lag1 3.039e-02 1.778e-01 0.171 0.864241
Wind_lag2 7.012e-02 1.986e-01 0.353 0.724078
Wind_lag3 3.513e-01 1.995e-01 1.761 0.078269
Wind_lag4 -3.466e-01 1.995e-01 -1.737 0.082359
Wind_lag5 1.030e-01 1.997e-01 0.516 0.605992
Wind_lag6 1.273e-01 1.999e-01 0.637 0.524312
Wind_lag7 -6.440e-02 1.999e-01 -0.322 0.747384
Wind_lag8 -1.394e-01 2.000e-01 -0.697 0.485965
Wind_lag9 1.667e-01 2.000e-01 0.833 0.404704
Wind_lag10 -2.531e-01 2.003e-01 -1.264 0.206286
Wind_lag11 2.544e-01 2.005e-01 1.269 0.204395
Wind_lag12 -1.214e-01 2.006e-01 -0.606 0.544842
Wind_lag13 1.381e-01 2.005e-01 0.689 0.491027
Wind_lag14 -9.976e-02 2.003e-01 -0.498 0.618487
Wind_lag15 1.056e-01 2.002e-01 0.528 0.597856
Wind_lag16 -2.450e-01 2.002e-01 -1.224 0.221116
Wind_lag17 3.569e-01 2.002e-01 1.783 0.074612
Wind_lag18 -4.200e-01 2.004e-01 -2.096 0.036104
Wind_lag19 4.195e-01 2.007e-01 2.090 0.036632
Wind_lag20 -2.771e-01 2.009e-01 -1.379 0.167968
Wind_lag21 1.198e-01 2.008e-01 0.597 0.550787
Wind_lag22 -1.886e-01 1.998e-01 -0.944 0.345379
Wind_lag23 2.446e-01 1.783e-01 1.372 0.170174
Wind_lag24 -7.318e-02 8.761e-02 -0.835 0.403594
Solar_lag1 3.432e-01 1.595e-01 2.152 0.031406
Solar_lag2 -1.738e-01 1.749e-01 -0.993 0.320568
Solar_lag3 2.453e-01 1.760e-01 1.394 0.163416
Solar_lag4 -8.647e-02 1.765e-01 -0.490 0.624259
Solar_lag5 -1.521e-01 1.769e-01 -0.860 0.389945
Solar_lag6 1.314e-01 1.772e-01 0.741 0.458442
Solar_lag7 7.516e-02 1.773e-01 0.424 0.671676
Solar_lag8 -2.988e-01 1.773e-01 -1.685 0.092079
Solar_lag9 2.312e-01 1.771e-01 1.306 0.191674
Solar_lag10 2.627e-02 1.768e-01 0.149 0.881892
Solar_lag11 -1.288e-01 1.767e-01 -0.729 0.466238
Solar_lag12 -6.412e-02 1.766e-01 -0.363 0.716561
Solar_lag13 1.879e-01 1.768e-01 1.063 0.287824
Solar_lag14 -1.359e-02 1.766e-01 -0.077 0.938669
Solar_lag15 -6.457e-02 1.762e-01 -0.367 0.713962
Solar_lag16 9.689e-02 1.758e-01 0.551 0.581493
Solar_lag17 -1.895e-01 1.756e-01 -1.080 0.280396
Solar_lag18 4.446e-02 1.753e-01 0.254 0.799816
Solar_lag19 7.272e-02 1.745e-01 0.417 0.676815
Solar_lag20 -1.429e-01 1.740e-01 -0.821 0.411415
Solar_lag21 2.994e-01 1.740e-01 1.720 0.085394
Solar_lag22 -3.102e-01 1.729e-01 -1.794 0.072919
Solar_lag23 2.011e-01 1.567e-01 1.284 0.199271
Solar_lag24 -1.549e-01 8.085e-02 -1.916 0.055359
Output_lag1 8.119e-01 1.087e-02 74.682 < 2e-16
Output_lag2 -9.202e-02 1.401e-02 -6.568 5.38e-11
Output_lag3 5.213e-02 1.405e-02 3.710 0.000209
Output_lag4 8.490e-03 1.407e-02 0.604 0.546135
Output_lag5 9.827e-03 1.406e-02 0.699 0.484573
Output_lag6 2.208e-02 1.406e-02 1.571 0.116311
Output_lag7 -2.491e-02 1.407e-02 -1.770 0.076706
Output_lag8 2.153e-02 1.408e-02 1.529 0.126216
Output_lag9 -1.650e-02 1.408e-02 -1.172 0.241251
Output_lag10 2.871e-02 1.408e-02 2.039 0.041473
Output_lag11 1.284e-02 1.408e-02 0.912 0.361840
Output_lag12 2.324e-02 1.407e-02 1.652 0.098498
Output_lag13 1.614e-02 1.406e-02 1.148 0.251070
Output_lag14 -3.690e-02 1.407e-02 -2.623 0.008740
Output_lag15 -1.315e-02 1.408e-02 -0.934 0.350422
Output_lag16 3.918e-02 1.407e-02 2.785 0.005368
Output_lag17 -2.593e-02 1.407e-02 -1.843 0.065406
Output_lag18 1.269e-02 1.407e-02 0.902 0.367133
Output_lag19 -6.400e-03 1.407e-02 -0.455 0.649277
Output_lag20 1.636e-02 1.408e-02 1.163 0.245037
Output_lag21 5.365e-03 1.408e-02 0.381 0.703163
Output_lag22 6.488e-03 1.404e-02 0.462 0.644132
Output_lag23 2.901e-02 1.394e-02 2.081 0.037432
Output_lag24 2.658e-02 1.083e-02 2.454 0.014161
Demand..MwH._lag1 -4.340e-01 4.383e-02 -9.900 < 2e-16
Demand..MwH._lag2 -1.610e-01 4.858e-02 -3.314 0.000922
Demand..MwH._lag3 6.021e-02 4.903e-02 1.228 0.219425
Demand..MwH._lag4 -1.926e-02 4.904e-02 -0.393 0.694461
Demand..MwH._lag5 -4.215e-02 4.910e-02 -0.858 0.390643
Demand..MwH._lag6 6.239e-03 4.923e-02 0.127 0.899170
Demand..MwH._lag7 6.821e-02 4.922e-02 1.386 0.165881
Demand..MwH._lag8 -1.004e-01 4.924e-02 -2.039 0.041451
Demand..MwH._lag9 8.005e-02 4.912e-02 1.630 0.103216
Demand..MwH._lag10 -4.373e-02 4.909e-02 -0.891 0.373108
Demand..MwH._lag11 -4.538e-02 4.912e-02 -0.924 0.355625
Demand..MwH._lag12 8.289e-02 4.916e-02 1.686 0.091784
Demand..MwH._lag13 -7.187e-02 4.918e-02 -1.461 0.143933
Demand..MwH._lag14 -1.003e-02 4.916e-02 -0.204 0.838315
Demand..MwH._lag15 2.037e-02 4.917e-02 0.414 0.678636
Demand..MwH._lag16 1.898e-03 4.916e-02 0.039 0.969204
Demand..MwH._lag17 4.244e-02 4.911e-02 0.864 0.387549
Demand..MwH._lag18 -1.001e-01 4.917e-02 -2.036 0.041772
Demand..MwH._lag19 1.233e-01 4.927e-02 2.502 0.012359
Demand..MwH._lag20 -1.093e-01 4.935e-02 -2.214 0.026857
Demand..MwH._lag21 2.765e-02 4.937e-02 0.560 0.575417
Demand..MwH._lag22 -8.822e-02 4.912e-02 -1.796 0.072544
Demand..MwH._lag23 1.445e-01 4.419e-02 3.270 0.001078
Demand..MwH._lag24 -1.136e-01 2.355e-02 -4.823 1.44e-06
temperature..Celsius._lag1 -1.717e+01 2.196e+01 -0.782 0.434412
temperature..Celsius._lag2 -1.425e+00 2.196e+01 -0.065 0.948269
temperature..Celsius._lag3 -2.077e+01 2.196e+01 -0.946 0.344259
temperature..Celsius._lag4 1.146e+01 2.196e+01 0.522 0.601614
temperature..Celsius._lag5 -8.222e+00 2.195e+01 -0.375 0.707958
temperature..Celsius._lag6 -1.537e+01 2.189e+01 -0.702 0.482762
temperature..Celsius._lag7 3.046e+00 2.191e+01 0.139 0.889466
temperature..Celsius._lag8 -1.773e+01 2.190e+01 -0.810 0.418082
temperature..Celsius._lag9 1.128e+01 2.188e+01 0.516 0.606196
temperature..Celsius._lag10 -6.451e+00 2.187e+01 -0.295 0.768055
temperature..Celsius._lag11 1.782e+01 2.187e+01 0.815 0.415040
temperature..Celsius._lag12 -4.284e+00 2.187e+01 -0.196 0.844704
temperature..Celsius._lag13 3.816e+00 2.186e+01 0.175 0.861455
temperature..Celsius._lag14 2.751e+01 2.185e+01 1.259 0.208184
temperature..Celsius._lag15 -1.247e+01 2.185e+01 -0.571 0.568178
temperature..Celsius._lag16 2.802e+00 2.184e+01 0.128 0.897925
temperature..Celsius._lag17 -2.494e+00 2.184e+01 -0.114 0.909089
temperature..Celsius._lag18 2.363e+01 2.183e+01 1.082 0.279160
temperature..Celsius._lag19 -1.676e+01 2.182e+01 -0.768 0.442497
temperature..Celsius._lag20 -1.181e+01 2.182e+01 -0.541 0.588214
temperature..Celsius._lag21 1.353e+01 2.182e+01 0.620 0.535331
temperature..Celsius._lag22 -8.419e+00 2.182e+01 -0.386 0.699601
temperature..Celsius._lag23 2.019e+00 2.182e+01 0.092 0.926306
temperature..Celsius._lag24 -8.077e+00 1.551e+01 -0.521 0.602428
Tempt_2_lag1 2.830e-01 7.856e-01 0.360 0.718706
Tempt_2_lag2 2.173e-01 7.861e-01 0.276 0.782198
Tempt_2_lag3 4.519e-01 7.863e-01 0.575 0.565513
Tempt_2_lag4 5.225e-02 7.862e-01 0.066 0.947018
Tempt_2_lag5 5.690e-01 7.862e-01 0.724 0.469271
Tempt_2_lag6 8.954e-02 7.857e-01 0.114 0.909264
Tempt_2_lag7 -4.321e-01 7.859e-01 -0.550 0.582471
Tempt_2_lag8 1.679e+00 7.870e-01 2.134 0.032872
Tempt_2_lag9 -1.122e+00 7.870e-01 -1.426 0.153975
Tempt_2_lag10 4.066e-01 7.870e-01 0.517 0.605438
Tempt_2_lag11 -6.816e-01 7.871e-01 -0.866 0.386511
Tempt_2_lag12 2.359e-01 7.871e-01 0.300 0.764353
Tempt_2_lag13 -4.911e-02 7.868e-01 -0.062 0.950229
Tempt_2_lag14 -9.531e-01 7.862e-01 -1.212 0.225463
Tempt_2_lag15 6.767e-01 7.859e-01 0.861 0.389212
Tempt_2_lag16 -9.644e-01 7.855e-01 -1.228 0.219588
Tempt_2_lag17 6.427e-01 7.854e-01 0.818 0.413198
Tempt_2_lag18 2.169e-01 7.848e-01 0.276 0.782239
Tempt_2_lag19 -5.999e-01 7.848e-01 -0.764 0.444655
Tempt_2_lag20 1.836e-01 7.848e-01 0.234 0.815063
Tempt_2_lag21 -4.925e-02 7.848e-01 -0.063 0.949966
Tempt_2_lag22 1.257e+00 7.843e-01 1.602 0.109126
Tempt_2_lag23 -6.817e-01 7.845e-01 -0.869 0.384877
Tempt_2_lag24 -1.333e-01 5.590e-01 -0.239 0.811487
Interaction_W_lag1 -2.149e-07 8.117e-06 -0.026 0.978878
Interaction_W_lag2 2.474e-05 9.122e-06 2.712 0.006698
Interaction_W_lag3 -2.819e-05 9.173e-06 -3.073 0.002129
Interaction_W_lag4 1.566e-05 9.180e-06 1.706 0.087983
Interaction_W_lag5 -2.003e-06 9.185e-06 -0.218 0.827371
Interaction_W_lag6 -3.547e-06 9.200e-06 -0.386 0.699867
Interaction_W_lag7 9.896e-07 9.205e-06 0.108 0.914394
Interaction_W_lag8 5.554e-06 9.210e-06 0.603 0.546519
Interaction_W_lag9 -1.262e-05 9.207e-06 -1.370 0.170695
Interaction_W_lag10 1.388e-05 9.224e-06 1.504 0.132524
Interaction_W_lag11 -2.827e-06 9.235e-06 -0.306 0.759562
Interaction_W_lag12 -8.629e-06 9.238e-06 -0.934 0.350318
Interaction_W_lag13 2.950e-06 9.239e-06 0.319 0.749492
Interaction_W_lag14 4.842e-06 9.227e-06 0.525 0.599754
Interaction_W_lag15 -3.071e-06 9.217e-06 -0.333 0.739032
Interaction_W_lag16 5.111e-06 9.220e-06 0.554 0.579336
Interaction_W_lag17 -1.630e-05 9.221e-06 -1.768 0.077078
Interaction_W_lag18 2.197e-05 9.236e-06 2.379 0.017381
Interaction_W_lag19 -1.639e-05 9.262e-06 -1.770 0.076767
Interaction_W_lag20 6.391e-06 9.283e-06 0.688 0.491232
Interaction_W_lag21 -2.678e-06 9.285e-06 -0.288 0.773064
Interaction_W_lag22 1.212e-05 9.233e-06 1.312 0.189460
Interaction_W_lag23 -1.558e-05 8.185e-06 -1.903 0.057034
Interaction_W_lag24 6.169e-06 3.957e-06 1.559 0.118999
Interaction_S_lag1 -4.563e-06 7.396e-06 -0.617 0.537309
Interaction_S_lag2 1.461e-05 8.245e-06 1.772 0.076370
Interaction_S_lag3 -6.249e-06 8.293e-06 -0.753 0.451173
Interaction_S_lag4 2.800e-06 8.298e-06 0.337 0.735750
Interaction_S_lag5 2.097e-06 8.328e-06 0.252 0.801221
Interaction_S_lag6 8.460e-07 8.356e-06 0.101 0.919358
Interaction_S_lag7 -1.370e-05 8.363e-06 -1.638 0.101425
Interaction_S_lag8 2.595e-05 8.363e-06 3.103 0.001925
Interaction_S_lag9 -1.930e-05 8.353e-06 -2.311 0.020867
Interaction_S_lag10 -3.601e-06 8.348e-06 -0.431 0.666219
Interaction_S_lag11 1.531e-05 8.350e-06 1.834 0.066713
Interaction_S_lag12 -2.722e-06 8.348e-06 -0.326 0.744355
Interaction_S_lag13 -2.884e-06 8.357e-06 -0.345 0.730060
Interaction_S_lag14 -7.532e-06 8.350e-06 -0.902 0.367054
Interaction_S_lag15 9.548e-06 8.324e-06 1.147 0.251384
Interaction_S_lag16 -1.070e-05 8.303e-06 -1.289 0.197525
Interaction_S_lag17 1.356e-05 8.298e-06 1.634 0.102385
Interaction_S_lag18 -4.104e-06 8.295e-06 -0.495 0.620816
Interaction_S_lag19 -8.450e-06 8.262e-06 -1.023 0.306457
Interaction_S_lag20 1.485e-05 8.240e-06 1.803 0.071486
Interaction_S_lag21 -1.812e-05 8.236e-06 -2.200 0.027868
Interaction_S_lag22 1.767e-05 8.131e-06 2.173 0.029823
Interaction_S_lag23 -9.935e-06 7.242e-06 -1.372 0.170148
Interaction_S_lag24 5.637e-06 3.671e-06 1.536 0.124698
Wind2_lag1 1.575e-05 1.208e-05 1.304 0.192363
Wind2_lag2 -3.172e-05 1.325e-05 -2.394 0.016677
Wind2_lag3 1.853e-05 1.334e-05 1.389 0.164934
Wind2_lag4 5.872e-06 1.336e-05 0.440 0.660285
Wind2_lag5 -1.165e-05 1.339e-05 -0.870 0.384064
Wind2_lag6 -3.222e-06 1.339e-05 -0.241 0.809894
Wind2_lag7 4.032e-06 1.340e-05 0.301 0.763476
Wind2_lag8 4.284e-06 1.341e-05 0.320 0.749308
Wind2_lag9 1.313e-05 1.341e-05 0.979 0.327611
Wind2_lag10 -1.417e-05 1.344e-05 -1.055 0.291462
Wind2_lag11 -5.070e-06 1.344e-05 -0.377 0.706054
Wind2_lag12 2.111e-05 1.344e-05 1.570 0.116368
Wind2_lag13 -1.930e-05 1.345e-05 -1.435 0.151195
Wind2_lag14 4.764e-07 1.344e-05 0.035 0.971731
Wind2_lag15 -1.563e-06 1.345e-05 -0.116 0.907513
Wind2_lag16 1.552e-05 1.346e-05 1.153 0.249142
Wind2_lag17 -1.267e-05 1.346e-05 -0.941 0.346579
Wind2_lag18 7.244e-06 1.346e-05 0.538 0.590515
Wind2_lag19 -1.225e-05 1.350e-05 -0.907 0.364341
Wind2_lag20 1.895e-05 1.353e-05 1.400 0.161430
Wind2_lag21 -4.322e-06 1.351e-05 -0.320 0.749049
Wind2_lag22 -1.285e-05 1.339e-05 -0.960 0.337262
Wind2_lag23 1.153e-05 1.218e-05 0.946 0.343942
Wind2_lag24 -3.861e-06 6.248e-06 -0.618 0.536608
Solar2_lag1 -1.685e-06 5.001e-06 -0.337 0.736172
Solar2_lag2 -2.456e-06 5.790e-06 -0.424 0.671483
Solar2_lag3 -6.191e-06 6.002e-06 -1.031 0.302372
Solar2_lag4 2.491e-06 6.040e-06 0.412 0.680024
Solar2_lag5 4.596e-06 6.042e-06 0.761 0.446936
Solar2_lag6 -4.876e-06 6.042e-06 -0.807 0.419660
Solar2_lag7 8.946e-06 6.043e-06 1.480 0.138784
Solar2_lag8 -1.560e-05 6.046e-06 -2.580 0.009901
Solar2_lag9 1.349e-05 6.054e-06 2.229 0.025844
Solar2_lag10 3.926e-06 6.057e-06 0.648 0.516903
Solar2_lag11 -1.068e-05 6.058e-06 -1.762 0.078028
Solar2_lag12 9.270e-06 6.061e-06 1.529 0.126195
Solar2_lag13 -1.394e-05 6.064e-06 -2.298 0.021562
Solar2_lag14 1.433e-05 6.066e-06 2.362 0.018204
Solar2_lag15 -9.401e-06 6.071e-06 -1.549 0.121537
Solar2_lag16 5.630e-06 6.070e-06 0.928 0.353654
Solar2_lag17 -2.253e-06 6.066e-06 -0.371 0.710332
Solar2_lag18 -5.067e-07 6.064e-06 -0.084 0.933415
Solar2_lag19 1.028e-05 6.064e-06 1.695 0.090073
Solar2_lag20 -1.250e-05 6.066e-06 -2.061 0.039362
Solar2_lag21 4.986e-06 6.044e-06 0.825 0.409424
Solar2_lag22 2.809e-07 5.857e-06 0.048 0.961747
Solar2_lag23 -7.105e-07 5.109e-06 -0.139 0.889389
Solar2_lag24 3.796e-06 2.775e-06 1.368 0.171347
Wind **
Solar ***
Wind2
Solar2 .
Interaction_W **
Interaction_S *
coal.price..EUR.tn.
natural.gas.price..EUR.MwH. *
emission.allowance.price..EUR.Tn_CO2.
temperature..Celsius. *
Tempt_2 *
Demand..MwH. ***
Demand_2
Wind_lag1
Wind_lag2
Wind_lag3 .
Wind_lag4 .
Wind_lag5
Wind_lag6
Wind_lag7
Wind_lag8
Wind_lag9
Wind_lag10
Wind_lag11
Wind_lag12
Wind_lag13
Wind_lag14
Wind_lag15
Wind_lag16
Wind_lag17 .
Wind_lag18 *
Wind_lag19 *
Wind_lag20
Wind_lag21
Wind_lag22
Wind_lag23
Wind_lag24
Solar_lag1 *
Solar_lag2
Solar_lag3
Solar_lag4
Solar_lag5
Solar_lag6
Solar_lag7
Solar_lag8 .
Solar_lag9
Solar_lag10
Solar_lag11
Solar_lag12
Solar_lag13
Solar_lag14
Solar_lag15
Solar_lag16
Solar_lag17
Solar_lag18
Solar_lag19
Solar_lag20
Solar_lag21 .
Solar_lag22 .
Solar_lag23
Solar_lag24 .
Output_lag1 ***
Output_lag2 ***
Output_lag3 ***
Output_lag4
Output_lag5
Output_lag6
Output_lag7 .
Output_lag8
Output_lag9
Output_lag10 *
Output_lag11
Output_lag12 .
Output_lag13
Output_lag14 **
Output_lag15
Output_lag16 **
Output_lag17 .
Output_lag18
Output_lag19
Output_lag20
Output_lag21
Output_lag22
Output_lag23 *
Output_lag24 *
Demand..MwH._lag1 ***
Demand..MwH._lag2 ***
Demand..MwH._lag3
Demand..MwH._lag4
Demand..MwH._lag5
Demand..MwH._lag6
Demand..MwH._lag7
Demand..MwH._lag8 *
Demand..MwH._lag9
Demand..MwH._lag10
Demand..MwH._lag11
Demand..MwH._lag12 .
Demand..MwH._lag13
Demand..MwH._lag14
Demand..MwH._lag15
Demand..MwH._lag16
Demand..MwH._lag17
Demand..MwH._lag18 *
Demand..MwH._lag19 *
Demand..MwH._lag20 *
Demand..MwH._lag21
Demand..MwH._lag22 .
Demand..MwH._lag23 **
Demand..MwH._lag24 ***
temperature..Celsius._lag1
temperature..Celsius._lag2
temperature..Celsius._lag3
temperature..Celsius._lag4
temperature..Celsius._lag5
temperature..Celsius._lag6
temperature..Celsius._lag7
temperature..Celsius._lag8
temperature..Celsius._lag9
temperature..Celsius._lag10
temperature..Celsius._lag11
temperature..Celsius._lag12
temperature..Celsius._lag13
temperature..Celsius._lag14
temperature..Celsius._lag15
temperature..Celsius._lag16
temperature..Celsius._lag17
temperature..Celsius._lag18
temperature..Celsius._lag19
temperature..Celsius._lag20
temperature..Celsius._lag21
temperature..Celsius._lag22
temperature..Celsius._lag23
temperature..Celsius._lag24
Tempt_2_lag1
Tempt_2_lag2
Tempt_2_lag3
Tempt_2_lag4
Tempt_2_lag5
Tempt_2_lag6
Tempt_2_lag7
Tempt_2_lag8 *
Tempt_2_lag9
Tempt_2_lag10
Tempt_2_lag11
Tempt_2_lag12
Tempt_2_lag13
Tempt_2_lag14
Tempt_2_lag15
Tempt_2_lag16
Tempt_2_lag17
Tempt_2_lag18
Tempt_2_lag19
Tempt_2_lag20
Tempt_2_lag21
Tempt_2_lag22
Tempt_2_lag23
Tempt_2_lag24
Interaction_W_lag1
Interaction_W_lag2 **
Interaction_W_lag3 **
Interaction_W_lag4 .
Interaction_W_lag5
Interaction_W_lag6
Interaction_W_lag7
Interaction_W_lag8
Interaction_W_lag9
Interaction_W_lag10
Interaction_W_lag11
Interaction_W_lag12
Interaction_W_lag13
Interaction_W_lag14
Interaction_W_lag15
Interaction_W_lag16
Interaction_W_lag17 .
Interaction_W_lag18 *
Interaction_W_lag19 .
Interaction_W_lag20
Interaction_W_lag21
Interaction_W_lag22
Interaction_W_lag23 .
Interaction_W_lag24
Interaction_S_lag1
Interaction_S_lag2 .
Interaction_S_lag3
Interaction_S_lag4
Interaction_S_lag5
Interaction_S_lag6
Interaction_S_lag7
Interaction_S_lag8 **
Interaction_S_lag9 *
Interaction_S_lag10
Interaction_S_lag11 .
Interaction_S_lag12
Interaction_S_lag13
Interaction_S_lag14
Interaction_S_lag15
Interaction_S_lag16
Interaction_S_lag17
Interaction_S_lag18
Interaction_S_lag19
Interaction_S_lag20 .
Interaction_S_lag21 *
Interaction_S_lag22 *
Interaction_S_lag23
Interaction_S_lag24
Wind2_lag1
Wind2_lag2 *
Wind2_lag3
Wind2_lag4
Wind2_lag5
Wind2_lag6
Wind2_lag7
Wind2_lag8
Wind2_lag9
Wind2_lag10
Wind2_lag11
Wind2_lag12
Wind2_lag13
Wind2_lag14
Wind2_lag15
Wind2_lag16
Wind2_lag17
Wind2_lag18
Wind2_lag19
Wind2_lag20
Wind2_lag21
Wind2_lag22
Wind2_lag23
Wind2_lag24
Solar2_lag1
Solar2_lag2
Solar2_lag3
Solar2_lag4
Solar2_lag5
Solar2_lag6
Solar2_lag7
Solar2_lag8 **
Solar2_lag9 *
Solar2_lag10
Solar2_lag11 .
Solar2_lag12
Solar2_lag13 *
Solar2_lag14 *
Solar2_lag15
Solar2_lag16
Solar2_lag17
Solar2_lag18
Solar2_lag19 .
Solar2_lag20 *
Solar2_lag21
Solar2_lag22
Solar2_lag23
Solar2_lag24
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 402.6 on 8458 degrees of freedom
(49 observations deleted due to missingness)
Multiple R-squared(full model): 0.9826 Adjusted R-squared: 0.982
Multiple R-squared(proj model): 0.9788 Adjusted R-squared: 0.9781
F-statistic(full model): 1726 on 276 and 8458 DF, p-value: < 2.2e-16
F-statistic(proj model): 133.3 on 253 and 8458 DF, p-value: < 2.2e-16
#Model1 (old): #Wind -2.784e-01 8.751e-02 -3.181 0.001471 ** #Solar -4.408e-01 8.187e-02 -5.385 7.45e-08 *** #Wind2 -3.168e-06 6.228e-06 -0.509 0.610966 #Solar2 5.885e-06 2.679e-06 2.196 0.028087 * #Interaction_W -9.612e-06 3.942e-06 -2.438 0.014770 * #Model 1 (new): #Wind -2.685e-01 8.735e-02 -3.074 0.002119 ** #Solar -3.125e-01 8.471e-02 -3.688 0.000227 *** #Wind2 -2.565e-06 6.205e-06 -0.413 0.679373 #Solar2 4.528e-06 2.722e-06 1.664 0.096241 . #Interaction_W -1.069e-05 3.940e-06 -2.712 0.006691 ** #Interaction_S -9.797e-06 3.836e-06 -2.554 0.010681 * #Model 2 with hours: <- felm ( Day.ahead.Price..EUR.MWh. ~ + Solar + Wind2 + Solar2 + Interaction_W + Interaction_S + Demand..MwH. + Demand_2 + coal.price..EUR.tn. + natural.gas.price..EUR.MwH. + emission.allowance.price..EUR.Tn_CO2.| hour, data= data)summary (model_felm2)
Call:
felm(formula = Day.ahead.Price..EUR.MWh. ~ Wind + Solar + Wind2 + Solar2 + Interaction_W + Interaction_S + Demand..MwH. + Demand_2 + coal.price..EUR.tn. + natural.gas.price..EUR.MwH. + emission.allowance.price..EUR.Tn_CO2. | hour, data = data)
Residuals:
Min 1Q Median 3Q Max
-95.70 -17.73 -2.17 13.25 445.35
Coefficients:
Estimate Std. Error t value Pr(>|t|)
Wind -1.157e-02 1.095e-03 -10.566 < 2e-16
Solar -2.231e-02 1.355e-03 -16.464 < 2e-16
Wind2 1.452e-07 7.598e-08 1.911 0.0561
Solar2 -2.624e-07 5.622e-08 -4.668 3.09e-06
Interaction_W 5.190e-08 5.225e-08 0.993 0.3206
Interaction_S 9.075e-07 5.992e-08 15.143 < 2e-16
Demand..MwH. 1.167e-02 1.310e-03 8.907 < 2e-16
Demand_2 -1.972e-07 3.402e-08 -5.798 6.96e-09
coal.price..EUR.tn. 1.026e-01 7.690e-02 1.335 0.1820
natural.gas.price..EUR.MwH. 1.253e+00 9.152e-02 13.695 < 2e-16
emission.allowance.price..EUR.Tn_CO2. 1.071e+00 8.845e-02 12.112 < 2e-16
Wind ***
Solar ***
Wind2 .
Solar2 ***
Interaction_W
Interaction_S ***
Demand..MwH. ***
Demand_2 ***
coal.price..EUR.tn.
natural.gas.price..EUR.MwH. ***
emission.allowance.price..EUR.Tn_CO2. ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 32.03 on 8748 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared(full model): 0.5848 Adjusted R-squared: 0.5832
Multiple R-squared(proj model): 0.4587 Adjusted R-squared: 0.4566
F-statistic(full model):362.4 on 34 and 8748 DF, p-value: < 2.2e-16
F-statistic(proj model): 673.9 on 11 and 8748 DF, p-value: < 2.2e-16
#Model 2 (new) #Wind -1.157e-02 1.095e-03 -10.566 < 2e-16 *** #Solar -2.231e-02 1.355e-03 -16.464 < 2e-16 *** #Wind2 1.452e-07 7.598e-08 1.911 0.0561 . #Solar2 -2.624e-07 5.622e-08 -4.668 3.09e-06 *** #Interaction_W 5.190e-08 5.225e-08 0.993 0.3206 #Interaction_S 9.075e-07 5.992e-08 15.143 < 2e-16 *** #Model2 (Old) #Wind -1.156e-02 1.184e-03 -9.757 < 2e-16 *** #Solar -1.181e-02 1.165e-03 -10.140 < 2e-16 *** #Wind2 1.125e-07 8.215e-08 1.369 0.171 #Solar2 -4.238e-07 4.982e-08 -8.507 < 2e-16 *** #Interaction_W 5.068e-08 5.647e-08 0.898 0.369 #Interaction_S 3.527e-07
I would say the results are pretty robust as there are pretty minor differences between the original and new model. You could still argue there issues with robustness with more tests as there are still noticable differences.
Lets still calculate the offsets
#1.04 (lignite), 0.95 (coal) and 0.4 (natural gas) <- 1.04 * Wind_replacement2<- 1.04 * Solar_replacement2<- 0.95 * Wind_replacement2<- 0.95 * Solar_replacement2<- 0.4 * Wind_replacement2<- 0.4 * Solar_replacement2<- data.frame (Ignite_W = Ignite_W,Ignite_S = Ignite_S,Coal_W = Coal_W,Coal_S = Coal_S,NaturalGas_W = naturalgas_W,NaturalGas_S = naturalgas_Sprint (replacement_table)
Ignite_W Ignite_S Coal_W Coal_S NaturalGas_W NaturalGas_S
1 -0.4827462 -0.4919068 -0.44097 -0.4493379 -0.1856716 -0.1891949
