# Predictive Modeling of Photovoltaic Energy Yield Using an ARIMA Approach
## 2 Methods and Design
### Methods
This contrasts with the other popular way of predicting--making a forecast for only one period ahead, then appending the \"real\" value to the time series, making another one-period prognosis, and so on. One of the advantages of ARIMA methods is that they are capable of quality multi-period forecasts. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Year** & **January** & **February** & **March** & **April** & **May** & **June** & **July** & **August** & **September** & **October** & **November** & **December** \\ \hline
2013 & & & & & & 817.58 & 961.42 & 905.64 & 743.00 & 620.91 & 325.01 & 344.36 \\
2014 & 177.22 & 490.14 & 666.29 & 609.96 & 773.29 & 848.83 & 898.51 & 873.63 & 587.67 & 432.02 & 255.55 & 190.98 \\
2015 & 351.14 & 482.22 & 464.71 & 788.78 & 859.81 & 864.58 & 969.64 & 845.29 & 525.04 & 417.73 & 165.03 & 0.00 \\
2016 & 222.82 & 373.67 & 497.22 & 630.06 & 654.5 & 728.41 & 779.47 & 729.98 & 563.51 & 394.18 & 273.23 & 323.47 \\
2017 & 199.13 & 348.38 & 511.65 & 617.71 & 652.43 & 703.02 & 741.12 & 711.13 & 545.04 & 529.75 & 241.83 & 225.71 \\
2018 & 283.18 & 234.37 & 402.32 & 669.49 & 719.09 & 634.6 & 778.75 & 751.75 & 700.9 & 582.03 & 308.54 & 220.77 \\
2019 & 228.41 & 477.54 & 756.91 & 702 & 776.62 & 866.31 & 937.91 & 920.12 & 750.26 & 511.53 & 260.84 & 134.36 \\
2020 & 372.46 & 488.77 & 595.61 & 754.28 & 787.44 & 786.25 & 920.89 & 845.27 & 744.34 & 533 & 388.94 & 194.62 \\
2021 & 278.9 & 442.76 & 645.24 & 710 & 824.29 & 875.77 & 940.21 & 837.7 & 687.7 & 488.65 & 302.18 & 219.98 \\
2022 & 403.58 & 413.02 & 662.92 & 704.27 & 880.86 & 885.9 & 599.46 & 770.75 & 714.26 & 623.74 & 343.94 & 287.89 \\
2023 & 229.34 & 483.53 & 400.82 & 606.85 & 609.16 & 805.22 & 932.01 & 932.01 & 675.17 & 513.35 & 286.51 & 214.21 \\ Mean & 274.62 & 423.44 & 560.37 & 679.34 & 753.74 & 801.50 & 892.67 & 819.12 & 656.17 & 513.35 & 286.51 & 214.21 \\ Year & & & & & & & & & & & & \\ portion & 3.99\% & 6.16\% & 8.15\% & 9.88\% & 10.96\% & 11.66\% & 12.98\% & 11.91\% & 9.54\% & 7.47\% & 4.17\% & 3.12\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Values of the total energy generated by the 5 kW photovoltaic system—“Chikalov”—located in the town of Simitli, Blagoevgrad, southwestern Bulgaria. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Year** & **January** & **February** & **March** & **April** & **May** & **June** & **July** & **August** & **September** & **October** & **November** & **December** \\ \hline
2013 & & & & & & 146.00 & 171.68 & 161.72 & 132.68 & 110.88 & 58.04 & 61.49 \\
2014 & 31.65 & 87.52 & 118.98 & 108.92 & 138.09 & 151.58 & 160.45 & 156.00 & 104.94 & 77.15 & 45.63 & 34.10 \\
2015 & 62.70 & 86.11 & 82.99 & 140.85 & 153.54 & 154.39 & 173.15 & 150.95 & 93.76 & 74.60 & 29.47 & 0.00 \\
2016 & 39.79 & 66.73 & 88.79 & 112.51 & 116.88 & 130.07 & 139.19 & 130.35 & 100.63 & 70.39 & 48.79 & 57.76 \\
2017 & 35.56 & 62.21 & 91.37 & 110.31 & 116.50 & 125.54 & 132.34 & 126.99 & 97.33 & 94.60 & 43.19 & 40.31 \\
2018 & 50.57 & 41.85 & 71.84 & 119.55 & 128.41 & 113.32 & 139.06 & 134.24 & 125.16 & 103.93 & 55.10 & 39.42 \\
2019 & 40.79 & 85.28 & 135.16 & 125.36 & 138.68 & 154.70 & 167.48 & 164.31 & 133.98 & 91.34 & 46.58 & 23.99 \\
2020 & 66.51 & 87.28 & 106.36 & 134.69 & 140.61 & 140.40 & 164.45 & 150.94 & 132.92 & 95.18 & 69.45 & 34.75 \\
2021 & 49.80 & 79.06 & 115.22 & 126.79 & 147.20 & 156.39 & 167.90 & 149.59 & 122.80 & 87.26 & 53.96 & 39.28 \\
2022 & 72.07 & 73.75 & 118.38 & 125.76 & 157.30 & 158.20 & 171.33 & 137.63 &