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mschauer/AR1.ipynb

Created March 5, 2018 16:44
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Coefficients of AR1 process
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AR1.ipynb
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"cell_type": "code",
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"metadata": {},
"outputs": [
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"name": "stdout",
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"text": [
"(b, bhat) = (2.0, 2.0500515007848965)\n",
"(ρ, ρhat) = (0.6, 0.5164152557046513)\n",
"(q, qhat) = (3.5, 3.4220194291625035)\n"
]
}
],
"source": [
"ρ = 0.6\n",
"n = 2000\n",
"q = 3.5\n",
"\n",
"ϵ = √(q)*randn(n)\n",
"b = 2.0\n",
"\n",
"dy = zeros(n)\n",
"dy0 = b\n",
"for i in 2:n\n",
" dy[i] = ρ*dy[i-1] + (1-ρ)*b + ϵ[i]\n",
"end\n",
"\n",
"\n",
"bhat = mean(dy)\n",
"@show b, bhat\n",
"\n",
"ρhat = cov(dy[1:end-1],dy[2:end])/var(dy)\n",
"@show ρ, ρhat\n",
"\n",
"qhat = var(dy)*(1-ρhat^2)\n",
"@show q, qhat;"
]
},
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"cell_type": "code",
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"metadata": {},
"outputs": [
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"name": "stdout",
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"text": [
"(b, bhat) = (2.0, 3.136071249999999)\n",
"(ρ, ρhat) = (0.6, 0.5695279198418081)\n",
"(q, qhat) = (3.5, 0.10473112351007102)\n"
]
}
],
"source": [
"dy = [2.12318\n",
" 2.74068\n",
" 2.83197\n",
" 3.09359\n",
" 3.1262 \n",
" 3.12673\n",
" 3.05937\n",
" 2.69639\n",
" 2.86075\n",
" 2.71875\n",
" 2.97134\n",
" 2.82393\n",
" 3.12892\n",
" 3.57996\n",
" 3.79306\n",
" 3.61577\n",
" 3.39027\n",
" 3.78913\n",
" 3.15499\n",
" 3.48236\n",
" 3.17111\n",
" 3.51603\n",
" 3.43454\n",
" 3.03669]\n",
"\n",
"\n",
"bhat = mean(dy)\n",
"@show b, bhat\n",
"\n",
"ρhat = cov(dy[1:end-1],dy[2:end])/var(dy)\n",
"@show ρ, ρhat\n",
"\n",
"qhat = var(dy)*(1-ρhat^2)\n",
"@show q, qhat;"
]
},
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"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"ConjugatePriors.NormalInverseChisq{Float64}(μ=0.2, σ2=10.0, κ=2.0, ν=3.0)"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Distributions, ConjugatePriors\n",
"nix = ConjugatePriors.NormalInverseChisq(0.2, 10., 2., 3.)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.2, 5.0)"
]
},
"execution_count": 49,
"metadata": {},
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}
],
"source": [
"mode2(d::ConjugatePriors.NormalInverseChisq) = (d.μ, d.ν * d.σ2 / (d.ν + 3))\n",
"μ, σ2 = mode2(nix)"
]
},
{
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