title: GARCH MODEL with Exogenous Variables in the conditional mean and variance
body: <p>I need help writing a GARCH equation with exogenous variables by hand. I can write conditional mean and conditional variance equations, but not with exogenous variables. The fitted GARCH model is a AR(1)-GARCH(1,1) model. This is what I have so far:</p>
  
  <p><img src="https://i.stack.imgur.com/xHkaK.jpg" alt="enter image description here"></p>
  
  <p>I need  help adding mxreg1 and mxreg2 (the significant exogenous variables) in the conditional mean equation. Thanks!</p>
  
  <p>If it is hard for you to answer the question because it is like a hand written equation, you could do your best and upload a picture of a readable version of the conditional mean equation. Thanks!</p>
  
  <pre class="lang-r prettyprint-override"><code>*---------------------------------*
  *          GARCH Model Fit        *
  *---------------------------------*
  
  Conditional Variance Dynamics   
  -----------------------------------
  GARCH Model : fGARCH(1,1)
  fGARCH Sub-Model    : GARCH
  Mean Model  : ARFIMA(1,0,0)
  Distribution    : norm 
  
  Optimal Parameters
  ------------------------------------
          Estimate  Std. Error  t value Pr(&gt;|t|)
  mu     -0.006505    0.009810 -0.66311 0.507258
  ar1     0.149542    0.044502  3.36030 0.000779
  mxreg1  0.372466    0.054183  6.87422 0.000000
  mxreg2 -0.000754    0.000249 -3.02629 0.002476
  mxreg3  0.000749    0.000514  1.45800 0.144840
  mxreg4  0.000003    0.000006  0.50995 0.610085
  mxreg5  0.062401    0.080066  0.77937 0.435760
  omega   0.000276    0.000017 15.95469 0.000000
  alpha1  0.119026    0.023418  5.08266 0.000000
  beta1   0.785459    0.032615 24.08273 0.000000
  vxreg1  0.000000    0.001602  0.00000 1.000000
  vxreg2  0.000000    0.000010  0.00000 1.000000
  vxreg3  0.000000    0.000021  0.00000 1.000000
  vxreg4  0.000000    0.000000  0.00000 1.000000
  vxreg5  0.001912    0.003569  0.53563 0.592212
  </code></pre>