Forecasting the Covolatility of Coffee Arabica and Crude Oil Prices: A Multivariate GARCH Approach with High-Frequency Data

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Series</td><td class="align_center"><span class="nowrap"><svg height="8.02022pt" id="M115" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g></svg>-</span>statistic</td><td class="align_center">MacKinnon approximate <span class="nowrap"><svg height="10.2124pt" id="M116" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" 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="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g></svg>-</span>value</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Crude oil</td><td class="align_center">−1.675</td><td class="align_center">0.4562</td></tr><tr><td class="align_left">Arabica coffee</td><td class="align_center">−2.053</td><td class="align_center">0.3896</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>DF unit root test of stationarity for level prices, with trend.</div>

Journal of Probability and Statistics

tab1

Table 1

Table 1: Forecasting the Covolatility of Coffee Arabica and Crude Oil Prices: A Multivariate GARCH Approach with High-Frequency Data 