Determinants of price fluctuations in the electricity market: a study with PCA and NARDL models

Figures & data

Figure 1. Histogram for the occurrence of negative and spike LMPs.

Table 1. Descriptive statistics of LMPs.

Variable	Negative LMP	Spike LMP	Overall
Number of Occurrence	2,067,194	3,943,996	392,216,015
mean	−26.22	326.21	35.62
Std. Dev.	47.37	240.14	42.61
skewness	−7.06	4.05	17.15
kurtosis	135.88	22.99	545.14
min	−2240.30	175.96	−2240.30
p5	−107.05	179.70	14.88
p25	−30.48	202.72	23.43
p50	−9.54	250.75	28.46
p75	−2.7	351.66	36.45
p95	0	689.57	72.68
max	0	4643.74	4643.74

Table 2. Covariates of PCA.

variable	Negative LMPs	Spike LMPs	Overall
Percentage of Occurrence	Neg_Per	Peak_Per
mean	Neg_Mean	Peak_Mean	Mean
Std. Dev.	Neg_Std	Peak_Std
skewness	Neg_Sku	Peak_Sku	Skewness
kurtosis	Neg_Kur	Peak_Kur	Kurtosis
min	Neg_Min	Peak_Min
max		Peak_Max

Table 3. Variations explained by the eigenvalues of PCA.

Component	Eigenvalue	Difference	Proportion	Cumulative
PC1	5.67	2.31	0.35	35%
PC2	3.36	0.28	0.21	56%
PC3	3.08	1.11	0.19	76%
PC4	1.98	1.10	0.12	88%
PC5	0.88	0.22	0.06	94%
PC6	0.67	0.55	0.04	98%
PC7	0.12	0.03	0.01	99%
PC8	0.09	0.04	0.01	99%
PC9	0.05	0.01	0.00	99%
PC10	0.04	0.02	0.00	100%
PC11	0.02	0.01	0.00	100%
PC12	0.01	0.00	0.00	100%
PC13	0.01	0.00	0.00	100%
PC14	0.01	0.00	0.00	100%
PC15	0.00	0.00	0.00	100%
PC16	0.00	.	0	100%

Table 4. Covariate coefficients of six PCs.

Covariate	PC1	PC2	PC3	PC4	PC5	PC6
Mean	0.3697	0.1928	0.0934	0.0365	0.2326	−0.0640
Skewness	−0.3410	0.2816	0.1046	0.0804	−0.0714	−0.0012
Kurtosis	−0.3700	0.1999	0.1216	0.0742	−0.0197	−0.0134
Neg_Per	−0.0947	−0.3074	0.1834	−0.0022	0.1819	0.8583
Neg_Min	−0.0347	0.2896	−0.4527	0.1104	0.0767	0.0454
Neg_Mean	−0.0925	0.2929	−0.3811	−0.2543	0.2246	0.1397
Neg_Std	0.0926	−0.2810	0.4240	0.1003	−0.2452	−0.2561
Neg_Sku	0.0639	−0.0759	−0.1459	0.6509	−0.0667	0.1845
Neg_Kur	−0.0810	−0.0217	0.2285	−0.6219	0.1353	0.0175
Peak_Per	0.3177	0.0361	0.1899	0.1168	0.5363	0.0058
Peak_Min	0.3704	0.1905	0.0920	0.0368	0.2328	−0.0624
Peak_Mean	0.3742	0.2081	0.0676	−0.0577	−0.1353	0.1449
Peak_Std	0.1286	0.4198	0.1842	−0.0573	−0.4019	0.2727
Peak_Sku	−0.3020	0.2032	0.2681	0.1658	0.2431	−0.0696
Peak_Kur	−0.2868	0.1511	0.2822	0.1924	0.3669	−0.0996
Peak_Max	0.0641	0.4160	0.3064	0.0565	−0.2298	0.1533

Table 5. NARDL results.

${\mathit{STD}}_{\mathit{t}}$	Coefficient	Standard Deviation	t
${\mathit{STD}}_{\mathit{t}-1}$	0.3758	0.0262	14.35
${\mathit{MEAN}}_{\mathit{t}}$	0.8608	0.0264	32.62
${\mathit{MEAN}}_{\mathit{t}-1}$	−0.3922	0.0342	−11.47
${\mathit{Neg}\_\mathit{Per}}_t^{-}$	0.5347	0.0001	8.75
${\mathit{Neg}\_\mathit{Per}}_{t-1}^{-}$	−0.1848	0.0001	−2.97
${\mathit{Peak}\_\mathit{Per}}_t^{+}$	0.1194	0.0001	2.34
${\mathit{Peak}\_\mathit{Per}}_{t-1}^{+}$	−0.0011	0.0001	−0.02
constant	−11.5231	1.2389	−9.3

Figure 2. Distribution of negative and spike LMPs in one day.