\n",
"Mandelbrot-Van Ness
\n",
"\n",
"\n",
"
\n",
"\n",
"$$\n",
"W^H_t ={C_H}\\,\\left\\{\\int_{-\\infty}^{t} (t-s)^{H-\\frac{1}{2}}dW_s - \\int_{-\\infty}^{0} (-s)^{H-\\frac{1}{2}}dW_s\\right\\}.\n",
"$$\n",
"
\n",
"\n",
"
\n",
"\n",
"
\n",
"\n",
"where the choice\n",
"\n",
"$$\n",
"C_H = \\sqrt{ \\frac{2\\,H\\,\\Gamma(3/2-H)}{\\Gamma(H+1/2)\\,\\Gamma(2-2\\,H)}}\n",
"$$\n",
"\n",
"ensures that\n",
"\n",
"$$\n",
"\\mathbb{E}\\left[W^H_t W^H_s\\right] = \\frac{1}{2}\\,\\left\\{t^{2 H} + s^{2 H} - |t-s|^{2 H}\\right\\}.\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"zanadu": {}
},
"source": [
"# Forecasting"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"zanadu": {
"code_type": ""
}
},
"outputs": [],
"source": [
"import scipy.special as scsp"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"zanadu": {
"is_abstract": false,
"is_hidden": false
}
},
"outputs": [],
"source": [
"def c_tilde(h):\n",
" return scsp.gamma(1.5-h) / (scsp.gamma(h+0.5) * scsp.gamma(2.-2.*h))\n",
"\n",
"def forecast_XTS(rvdata, h, date, nLags, delta, nu):\n",
" nLagsRa = np.arange(nLags)\n",
" cf = 1./((nLagsRa+0.5) ** (h+0.5) * (nLagsRa+0.5+delta))\n",
" ldata = rvdata.truncate(after=date)\n",
" ldata = np.log(ldata.iloc[-nLags:])\n",
" ldata['cf'] = np.fliplr([cf])[0]\n",
" ldata = ldata.dropna()\n",
" fcst = (ldata.iloc[:, 0] * ldata['cf']).sum() / sum(ldata['cf']) ## Riemann sum approximation\n",
" return np.exp(fcst + 2.*nu**2. *c_tilde(h)*delta**(2.*h))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"zanadu": {
"code_type": ""
}
},
"outputs": [],
"source": [
"idCol = 0\n",
"rvdata = pd.DataFrame(rv1[rv1.columns[idCol]])\n",
"nu = Coefdf[\"nu\"][idCol] # Vol of vol estimate for index idCol\n",
"h = Coefdf[\"H\"][idCol] # H estimate for index idCol\n",
"delta = 1\n",
"nLags = 600\n",
"dates = rvdata.iloc[nLags:-delta].index\n",
"rv_predict = [forecast_XTS(rvdata, h=h, date=d, nLags=nLags, delta=delta, nu=nu) for d in dates]\n",
"rv_actual = rvdata.iloc[nLags+delta:].values"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"zanadu": {
"code_type": "",
"is_hidden": true
}
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"