China Total Energy Consumption Forecast with Optimized Continuous Conformable Fractional Grey Model

<span style="color: rgb(17, 17, 17); font-family: Poppins; font-size: 14px;">One of the methods used for forecasting of the time series is the fractional grey modeling approach. In this paper, the OCCFGM(1,1) model is utilized to forecasting of the total energy consumption data of China. The optimal values of&nbsp;</span><span class="MathJax_Preview" style="color: inherit; font-family: Poppins; font-size: 14px;"></span><span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>&amp;#x03B1;</mi></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 17.22px; font-size-adjust: none; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgb(17, 17, 17); font-family: Poppins; position: relative;"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-2" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-3" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.235em; padding-bottom: 0.293em; box-sizing: content-box !important;">α</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><span style="color: rgb(17, 17, 17); font-family: Poppins; font-size: 14px;">&nbsp;and&nbsp;</span><span class="MathJax_Preview" style="color: inherit; font-family: Poppins; font-size: 14px;"></span><span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>r</mi></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 17.22px; font-size-adjust: none; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgb(17, 17, 17); font-family: Poppins; position: relative;"><span id="MJXc-Node-4" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-5" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-6" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.235em; padding-bottom: 0.293em; box-sizing: content-box !important;">r</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></span></span><span style="color: rgb(17, 17, 17); font-family: Poppins; font-size: 14px;">, which are fractional parameters in the model, are calculated using the Brute Force algorithm. Data collected from official sources from 2013 to 2022 are used to build the forecasting model, while data from 2013 to 2020 are employed to evaluate the accuracy at the model. The obtained results indicate that the OCCFGM(1,1) model exhibits superior forecasting performance compared to the other models under consideration.</span>