Electric Load Forecast Using Combined Models with HP Filter-SARIMA and ARMAX Optimized by Regression Analysis Algorithm

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Variable</td><td align="center">Dependent variable</td><td align="center">Parameter estimates</td><td align="center"><svg height="7.94193pt" id="M145" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.73553 4.62753 7.94193" width="4.62753pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g></svg>-value</td><td align="center">Pr &gt; <svg height="11.4781pt" id="M146" style="vertical-align:-2.18977pt" version="1.1" viewbox="-0.0498162 -9.28833 11.6477 11.4781" width="11.6477pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M167 -163V704H102V-163H167Z" id="g50-9"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="269" vert-adv-y="269"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,3.497,0)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.008,0)"><path d="M167 -163V704H102V-163H167Z" id="g50-9"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="269" vert-adv-y="269"></glyph.data></g></svg></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left"><span style="width: 7.75923ptpx;"><svg height="12.6917pt" id="M147" style="vertical-align:-3.40335pt" version="1.1" viewbox="-0.0498162 -9.28835 7.75923 12.6917" width="7.75923pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.742,-.222)"><path d="M490 563C409 598 330 631 258 673H233C161 631 81 597 0 563L14 533C89 551 168 576 245 598C320 575 400 551 476 533L490 563Z" id="g56-17"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="490" vert-adv-y="490"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M563 395C563 428 543 451 519 451C500 451 480 438 472 423C468 415 465 403 470 394C477 381 482 368 482 347C482 272 386 136 342 74H340C334 163 323 257 312 337C302 410 290 451 257 451C214 451 160 385 127 338L145 310C169 341 203 373 209 373C219 373 225 369 232 325C249 215 269 62 271 -15C220 -80 135 -165 18 -231L26 -257L142 -230C254 -105 279 -74 342 13C394 85 484 211 526 286C553 334 563 365 563 395Z" id="g50-122"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g></svg></span></td><td align="center"><span style="width: 7.52437ptpx;"><svg height="9.49474pt" id="M148" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.28835 7.52437 9.49474" width="7.52437pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.364,-.222)"><path d="M490 563C409 598 330 631 258 673H233C161 631 81 597 0 563L14 533C89 551 168 576 245 598C320 575 400 551 476 533L490 563Z" id="g56-17"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="490" vert-adv-y="490"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z" id="g50-121"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="569" vert-adv-y="569"></glyph.data></g></svg></span></td><td align="center">0.62871</td><td align="center">6.75</td><td align="center">
                    &lt;0.0001</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab6

Table 6

Table 6: Electric Load Forecast Using Combined Models with HP Filter-SARIMA and ARMAX Optimized by Regression Analysis Algorithm 