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@ChadFulton
Last active September 25, 2017 17:24
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UCSV - Core PCE
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/fulton/projects/statsmodels/statsmodels/compat/pandas.py:62: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
" from pandas.core import datetools\n",
"/Users/fulton/.virtualenvs/default/lib/python2.7/site-packages/urllib3/util/ssl_.py:339: SNIMissingWarning: An HTTPS request has been made, but the SNI (Subject Name Indication) extension to TLS is not available on this platform. This may cause the server to present an incorrect TLS certificate, which can cause validation failures. You can upgrade to a newer version of Python to solve this. For more information, see https://urllib3.readthedocs.io/en/latest/advanced-usage.html#ssl-warnings\n",
" SNIMissingWarning\n",
"/Users/fulton/.virtualenvs/default/lib/python2.7/site-packages/urllib3/util/ssl_.py:137: InsecurePlatformWarning: A true SSLContext object is not available. This prevents urllib3 from configuring SSL appropriately and may cause certain SSL connections to fail. You can upgrade to a newer version of Python to solve this. For more information, see https://urllib3.readthedocs.io/en/latest/advanced-usage.html#ssl-warnings\n",
" InsecurePlatformWarning\n"
]
}
],
"source": [
"%matplotlib inline\n",
"from __future__ import division\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import statsmodels.api as sm\n",
"import matplotlib.pyplot as plt\n",
"# import seaborn as sn\n",
"\n",
"import ucsvo, tools\n",
"np.set_printoptions(suppress=True, precision=5, linewidth=150)\n",
"\n",
"# dta = pd.read_csv('data/p_pce_m59.csv')\n",
"# dta.index = pd.DatetimeIndex(start='1959-01', periods=len(dta), freq='M')\n",
"# dta.drop('Unnamed: 0', axis=1, inplace=True)\n",
"from pandas_datareader.data import DataReader\n",
"dta = DataReader('PCEPILFE', 'fred', start='1960-01-01', end='2017-07-01')\n",
"pce = np.log(dta['PCEPILFE'].resample('Q').last()).diff().iloc[4:-1] * 400\n",
"# pce = (np.log(dta['PCEPILFE'].resample('Q').last()).diff(4).iloc[4:] * 100).loc[:'2017-06-30']"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10ce1f350>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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kO54bV2Txlx2n+cz5+aSPEDDT1O3rphVnmKnr7KWr10VOeGeHj6ip247b6+v8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\nTorLq3l7dv9Wz2lKnyAWbs1m5b78Fr8L2nr/uXcNYtvhU+zJKWFPbjH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gRmstv/tEA6WU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\n+VUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cc897d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pce.plot(figsize=(15, 3), legend=True) \n",
"# pce_xfe.plot(legend=True);"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000\n",
"2000\n",
"3000\n",
"4000\n",
"5000\n",
"6000\n",
"7000\n",
"8000\n",
"9000\n",
"10000\n"
]
}
],
"source": [
"reload(tools)\n",
"reload(ucsvo)\n",
"\n",
"# Parameters\n",
"niter = 10000\n",
"nburn = 5000\n",
"nthin = 10\n",
"\n",
"# Scale the endog data\n",
"scale = pce.diff().std() / 5\n",
"endog = pce.values.copy() / scale\n",
"\n",
"# Create the model objects\n",
"mod = ucsvo.InflationLocalLevel(endog)\n",
"sim = mod.simulation_smoother()\n",
"obs_model = ucsvo.VolatilityLocalLevel(endog)\n",
"obs_sim = obs_model.simulation_smoother()\n",
"state_model = ucsvo.VolatilityLocalLevel(endog)\n",
"state_sim = state_model.simulation_smoother()\n",
"\n",
"# Initialize the priors\n",
"prior_grid_static_std = np.linspace(1e-3, 0.4 / 2, 5)\n",
"prior_grid_outliers = np.linspace(2, 10, 9)\n",
"# prior_outlier_prob = (1, 1)\n",
"nperiods = 4\n",
"prior_outlier_prob = (1 / (4 * nperiods) * 10 * nperiods,\n",
" (1 - 1 / (4 * nperiods)) * 10 * nperiods)\n",
"\n",
"# Storage\n",
"states = np.zeros((niter + 1, mod.nobs))\n",
"filtered_states = np.zeros((niter + 1, mod.nobs))\n",
"obs_mixing = np.zeros((niter + 1, mod.nobs), dtype=int)\n",
"state_mixing = np.zeros((niter + 1, mod.nobs), dtype=int)\n",
"obs_static_std = np.zeros(niter + 1)\n",
"obs_stochastic_std = np.zeros((niter + 1, mod.nobs))\n",
"state_static_std = np.zeros(niter + 1)\n",
"state_stochastic_std = np.zeros((niter + 1, mod.nobs))\n",
"outliers = np.zeros((niter + 1, mod.nobs))\n",
"outlier_prob = np.zeros(niter + 1)\n",
"\n",
"# Initial values\n",
"obs_stochastic_std[0, :] = 1\n",
"state_stochastic_std[0, :] = 1\n",
"outliers[0, :] = 1\n",
"outlier_prob[0] = 0.01\n",
"\n",
"# Iterate\n",
"# np.random.seed(1234)\n",
"for i in range(1, niter + 1):\n",
" if (i % 1000) == 0:\n",
" print i\n",
" # Sample states\n",
" states[i] = ucsvo.sample_inflation_states(\n",
" mod, obs_stochastic_std[i-1], outliers[i-1], state_stochastic_std[i-1], sim=sim)\n",
" \n",
" # Save filtered states\n",
" tmp1 = np.array(sim._simulation_smoother.simulated_kfilter.filtered_state[0], copy=True)\n",
" tmp2 = np.array(sim._simulation_smoother.generated_state[0, :-1], copy=True)\n",
" filtered_states[i] = tmp1 + tmp2\n",
" \n",
" # Intermediate computations\n",
" obs_disturbances = mod.endog.squeeze() - states[i]\n",
" state_disturbances = states[i] - np.r_[0, states[i, :-1]]\n",
" \n",
" # Sample mixing\n",
" obs_mixing[i] = ucsvo.sample_mixing(obs_disturbances / outliers[i-1], obs_stochastic_std[i-1])\n",
" state_mixing[i] = ucsvo.sample_mixing(state_disturbances, state_stochastic_std[i-1])\n",
" \n",
" # Sample variances\n",
" obs_static_std[i], obs_stochastic_std[i] = ucsvo.sample_volatilities(\n",
" obs_disturbances / outliers[i-1], obs_mixing[i], prior_grid_static_std,\n",
" model=obs_model, sim=obs_sim)\n",
" state_static_std[i], state_stochastic_std[i] = ucsvo.sample_volatilities(\n",
" state_disturbances, state_mixing[i], prior_grid_static_std,\n",
" model=state_model, sim=state_sim)\n",
" \n",
" # Sample outliers\n",
" outliers[i] = ucsvo.sample_outliers(\n",
" obs_disturbances, obs_mixing[i], obs_stochastic_std[i], outlier_prob[i-1], prior_grid_outliers)\n",
" outlier_prob[i] = ucsvo.sample_outlier_prob(outliers[i], prior_outlier_prob)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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k4Yw0ZyyexBg60HF0Siml0mfj/iaMgTn9rNDNS0yMot0ulVJpoAmd6iQcjeMj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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12664bcd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 2, figsize=(15, 9))\n",
"\n",
"axes[0, 0].plot(pce, label='PCEPILFE')\n",
"axes[0, 0].plot(pce.index, np.median(states[nburn::nthin], axis=0).T * scale, label='Estimated trend');\n",
"axes[0, 0].legend()\n",
"axes[0, 0].set(title='Core PCE and estimated trend')\n",
"\n",
"axes[1, 0].plot(pce.index, np.median(obs_stochastic_std[nburn::nthin], axis=0).T * scale);\n",
"axes[1, 0].set(title='Stochastic volatility: observation innovation')\n",
"\n",
"axes[0, 1].plot(pce.index, np.median(state_stochastic_std[nburn::nthin], axis=0).T * scale);\n",
"axes[0, 1].set(title='Stochastic volatility: trend innovation')\n",
"\n",
"axes[1, 1].plot(pce.index, np.median(outliers[nburn::nthin], axis=0))\n",
"axes[1, 1].set(title='Outliers');"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Filtered (one-sided) Smoothed (two-sided)\n",
"DATE \n",
"2011Q1 1.314095 1.562196\n",
"2011Q2 1.614048 1.643170\n",
"2011Q3 1.646849 1.661283\n",
"2011Q4 1.643255 1.676383\n",
"2012Q1 1.833549 1.686765\n",
"2012Q2 1.784689 1.634882\n",
"2012Q3 1.602402 1.589092\n",
"2012Q4 1.619860 1.586136\n",
"2013Q1 1.648590 1.561965\n",
"2013Q2 1.549595 1.542252\n",
"2013Q3 1.477431 1.532722\n",
"2013Q4 1.584711 1.550276\n",
"2014Q1 1.601352 1.553385\n",
"2014Q2 1.673959 1.545422\n",
"2014Q3 1.607930 1.498917\n",
"2014Q4 1.441970 1.459553\n",
"2015Q1 1.389307 1.471360\n",
"2015Q2 1.432447 1.496563\n",
"2015Q3 1.473350 1.528910\n",
"2015Q4 1.402771 1.551077\n",
"2016Q1 1.603549 1.613728\n",
"2016Q2 1.696060 1.622007\n",
"2016Q3 1.741232 1.589930\n",
"2016Q4 1.601570 1.529238\n",
"2017Q1 1.491321 1.500356\n",
"2017Q2 1.514219 1.514219\n"
]
}
],
"source": [
"filtered_trend = pd.Series(np.median(filtered_states[nburn::nthin] * scale, axis=0), index=pce.index)\n",
"filtered_trend.index = pd.PeriodIndex(filtered_trend.index, freq='Q')\n",
"smoothed_trend = pd.Series(np.median(states[nburn::nthin] * scale, axis=0), index=pce.index)\n",
"smoothed_trend.index = pd.PeriodIndex(smoothed_trend.index, freq='Q')\n",
"trends = pd.concat([filtered_trend, smoothed_trend], axis=1).loc['2011':]\n",
"trends.columns = ['Filtered (one-sided)', 'Smoothed (two-sided)']\n",
"print trends"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Tc7nwGsdv3DycqtrpVNs2ESdJxs6cweIKJ562KTK7Abh41l9wybRLiFZuozPQ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\n5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KzqBDAbE7JJyCzkziEN91B3DbLS3teV+IzCJg97rPLwyEgq7Iple0+wYFsS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\nCwIYRcmgHnMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x127c2c290>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(15, 5))\n",
"\n",
"ax.plot(pce, label='PCE')\n",
"ax.plot(pce.index, np.median(states[nburn::nthin], axis=0).T * scale, label='Smoothed')\n",
"ax.plot(pce.index, np.median(filtered_states[nburn::nthin], axis=0).T * scale, label='Filtered')\n",
"ax.hlines(2, pce.index[0], pce.index[-1], linewidth=1, linestyle='--')\n",
"ax.hlines(0, pce.index[0], pce.index[-1], linewidth=1)\n",
"ax.legend();"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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tO84SN2OuaGYnXIntBdtmgccDPuWaC0ZERERERKRMlUvEEx7oR0zeaqjRHIKqnHE7Pj4W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\nhsYD4Kp3zqgQd4nbw8JtaUxfs4+f1+8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ev86t5Kk5FTwzfy0bm1spKSrgwNFljB/YmzED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\nSVIe+z80Sr8LMdAiwwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x127a8efd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(15, 5))\n",
"\n",
"# ax.plot(pce, label='PCE')\n",
"ax.plot(pce.index, np.median(states[nburn::nthin], axis=0).T * scale, label='Smoothed')\n",
"ax.plot(pce.index, np.median(filtered_states[nburn::nthin], axis=0).T * scale, label='Filtered')\n",
"ax.hlines(2, pce.index[0], pce.index[-1], linewidth=1, linestyle='--')\n",
"ax.hlines(0, pce.index[0], pce.index[-1], linewidth=1)\n",
"ax.set_xlim('1990', '2018')\n",
"ax.set_ylim(-1.5, 5.5)\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\pi_t & = \\tau_t + \\varepsilon_t \\\\\n",
"\\tau_t & = \\tau_{t-1} + \\sigma_{\\Delta \\tau, t} \\eta_{\\tau, t} \\\\\n",
"\\varepsilon_t & = \\sigma_{\\varepsilon, t} s_t \\eta_{\\varepsilon, t} \\\\\n",
"\\Delta \\ln(\\sigma_{\\varepsilon_t}^2) & = \\gamma_\\varepsilon v_{\\varepsilon, t} \\\\\n",
"\\Delta \\ln(\\sigma_{\\Delta \\tau}^2) & = \\gamma_{\\Delta \\tau} v_{\\Delta \\tau, t}\n",
"\\end{align}\n",
"$$\n",
"\n",
"where:\n",
"\n",
"- $\\eta_\\varepsilon, \\eta_\\tau, v_\\varepsilon, v_{\\Delta \\tau} \\sim N(0, 1)$\n",
"- $s_t \\sim \\text{iid}$ and independent of the error terms above s.t. $$s_t = \\begin{cases} 1 & \\text{w/ prob} ~ 1 - p \\\\ U[2, 10] & \\text{w/ prob} ~ p \\end{cases}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Priors\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\gamma_\\varepsilon & \\sim U[0, 0.4 / \\sqrt{np}] \\\\\n",
"\\gamma_{\\Delta \\tau} & \\sim U[0, 0.4 / \\sqrt{np}] \\\\\n",
"p & \\sim \\text{Beta}(\\alpha, \\beta) \\\\\n",
"\\tau_0 & \\sim N(0, \\kappa) \\\\\n",
"\\ln(\\sigma_{\\varepsilon, 0}) & \\sim N(0, \\kappa) \\\\\n",
"\\ln(\\sigma_{\\Delta \\tau, 0}) & \\sim N(0, \\kappa) \\\\\n",
"\\end{align}\n",
"$$\n",
"\n",
"and the uniform distributions are approximated by equally spaced grids; 9 points in the grids for $s_t$, and 5 points for the $\\gamma_\\cdot$ parameters."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stochastic volatility approximation\n",
"\n",
"Let $x_t = \\sigma_t \\eta_t$ and $\\ln(\\sigma_t^2) = \\ln(\\sigma_{t-1}^2) + \\gamma v_t$ with $(\\eta_t, v_t) \\sim N(0, 1)$. Then:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\ln(x_t^2) & = \\ln(\\sigma_t^2) + \\ln(\\eta_t^2) \\\\\n",
"\\ln(\\sigma_t^2) & = \\ln(\\sigma_{t-1}^2) + \\gamma v_t\n",
"\\end{align}\n",
"$$\n",
"\n",
"and this is a linear state space model with non-Gaussian measurement errors. i.e. writing $y_t \\equiv \\ln (x_t^2)$ and $\\alpha_t = \\ln(\\sigma_t^2)$ and $z_t = \\ln(\\eta_t^2)$, then we have:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"y_t & = \\alpha_t + z_t \\\\\n",
"\\alpha_t & = \\alpha_{t-1} + \\gamma v_t\n",
"\\end{align}\n",
"$$\n",
"\n",
"i.e. we have a local level model where the unobserved level is the stochastic volatility.\n",
"\n",
"Now, $z_t \\sim \\ln(\\chi_1^2)$. The approximation replaces this distribution with a mixture of normals distribution, such that:\n",
"\n",
"$$z_t \\approx \\sum_{i=1}^n I(w_{t} = i) a_{it}, \\qquad a_{it} \\sim N(\\mu_i, \\sigma_i^2)$$\n",
"\n",
"where $w_t = i$ with probability $p(w_t = i) = p_i$. The values $\\{p_i, \\mu_i, \\sigma_i^2 \\}$ that define the approximation are given in Kim, Shephard, and Chib (1998) for a 7-component approximation and in Omori, Chib, Shephard, and Nakajima (2007) for a more accurate 10-component approximation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Posterior simulation\n",
"\n",
"Block the parameters into six blocks (Stock and Watson actually describe this three blocks; they combine the first two together, and the next two together):\n",
"\n",
"$$\\theta = \\left ( \\{\\tau_t \\}_t, \\{w_{\\varepsilon, t}, w_{\\Delta \\tau, t} \\}_t, \\{ \\gamma_\\varepsilon, \\gamma_{\\Delta \\tau} \\}, \\{\\sigma_{\\varepsilon, t}, \\sigma_{\\Delta \\tau, t} \\}_t, \\{s_t \\}_t, \\{ p \\} \\right )$$"
]
},
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"### Drawing $\\tau_t | \\cdot$ (the states)\n",
"\n",
"Conditional on all the other parameters, this is a state space model with time-varying covariances. We draw the vector $\\{ \\tau_t \\}_t$ using the simulation smoother. In particular, the time-varying state covariance is given by $\\{\\sigma_{\\Delta \\tau, t}^2 \\}_t$ and the time-varying state measurement covariance is constructed as $\\{ (s_t \\sigma_{\\varepsilon_t})^2 \\}_t$.\n",
"\n",
"Practically:\n",
"\n",
"- Replace `obs_cov` and `state_cov` with the newly drawn values.\n",
"- Perform simulation smoothing to get the drawn $\\{ \\tau_t | \\cdot \\}_t$\n",
"\n",
"### Drawing $w_{\\varepsilon, t}, w_{\\Delta \\tau, t} | \\cdot$ (the s.v. mixing variates)\n",
"\n",
"The idea here is that the $w_{\\cdot, t}$ are multinomial, representing the component selected at time $t$. Thus conditional on the values of $\\ln(\\eta_{\\cdot, t}^2)$ (the \"observations\" of the mixture process), the posterior is available as the set of $i=1, \\dots, 10$ probabilities:\n",
"\n",
"$$\n",
"P[w_t = i | \\cdot] \\propto p_i f_N(\\ln(\\eta_{\\cdot, t}^2 + c) | \\ln (\\sigma_{\\cdot, t}^2) + m_i - 1.2704, v_i^2)\n",
"$$\n",
"\n",
"Conditional on $\\{ \\tau_t \\}_t$, $\\{ s_t \\}$, we can construct the two s.v. \"observation\" series:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"x_{\\varepsilon, t} & = \\sigma_{\\varepsilon, t} \\eta_{\\varepsilon, t} \\\\\n",
"& = (\\pi_t - \\tau_t) / s_t\n",
"\\end{align}\n",
"$$\n",
"\n",
"and\n",
"\n",
"$$\n",
"\\begin{align}\n",
"x_{\\Delta \\tau, t} & = \\sigma_{\\Delta \\tau, t} \\eta_{\\tau, t} \\\\\n",
"& = (\\tau_t - \\tau_{t-1})\n",
"\\end{align}\n",
"$$\n",
"\n",
"From this series, and conditional on the values of the stochastic volatilities $\\{ \\sigma_{\\cdot, t} \\}$, we can compute the realized disturbances:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\eta_{\\varepsilon, t} & = x_{\\varepsilon, t} / \\sigma_{\\varepsilon, t} \\\\\n",
"& = (\\pi_t - \\tau_t) / (s_t \\sigma_{\\varepsilon, t})\n",
"\\end{align}\n",
"$$\n",
"\n",
"and\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\eta_{\\tau, t} & = x_{\\Delta \\tau, t} / \\sigma_{\\Delta \\tau, t} \\\\\n",
"& = (\\tau_t - \\tau_{t-1}) / \\sigma_{\\Delta \\tau, t}\n",
"\\end{align}\n",
"$$\n",
"\n",
"Then the densities $f_N(\\ln(\\eta_{\\cdot, t}^2 + c) | \\ln (\\sigma_{\\cdot, t}^2) + m_i - 1.2704, v_i^2)$ can be computed and the mixing variates $w_{\\cdot, t}$ can be drawn from the normalized probabilities.\n",
"\n",
"Note, each $w_{\\cdot, t}$ will be one of $1, 2, \\dots, 10$ indicating which component is active at time $t$.\n",
"\n",
"### Drawing $\\gamma_\\varepsilon, \\gamma_{\\Delta \\tau} | \\cdot$ (the s.v. std. devs.)\n",
"\n",
"Recall the state space model for the volatilities:\n",
"\n",
"$$\n",
"\\begin{align}\n",
"y_{\\cdot, t} & = \\alpha_{\\cdot, t} + \\sum_{i=1}^{10} w_{\\cdot, i, t} a_{\\cdot, i, t} \\\\\n",
"\\alpha_{\\cdot, t} & = \\alpha_{\\cdot, t-1} + \\gamma_\\cdot v_{\\cdot, t} \\\\\n",
"\\end{align}\n",
"$$\n",
"\n",
"and recall that the posterior is proportional to the likelihood times the prior. Since the prior is a probability mass function, the posterior is also a probability mass function on the same points, where the probabilities are proportional to the likelihood times the prior. Thus the posterior probabilities can be contructed by computing the likelihood at each of the prior $\\gamma_\\cdot$ values, multiplying by the prior, and then normalizing so that they sum to one.\n",
"\n",
"### Drawing $\\sigma_{\\varepsilon, t}, \\sigma_{\\Delta \\tau, t} | \\cdot$ (the s.v. states)\n",
"\n",
"Draws of $\\{ \\alpha_{\\cdot, t} \\}$ can be computed using a simulation smoother on the state space model for volatilities. The \"observed data\" $\\{y_{\\cdot, t}\\}$ is computable from $\\{ x_{\\cdot, t} \\}$.\n",
"\n",
"### Drawing $s_t | \\cdot$ (the outlier multipliers)\n",
"\n",
"Since the prior is a probability mass function, the posterior is also a probability mass function on the same points, where the probabilities are proportional to the likelihood times the prior. Thus the posterior probabilities can be contructed by computing the likelihood at each of the prior $s_t$ values, multiplying by the prior (and actually the prior is the same for each $s_t$), and then normalizing so that they sum to one.\n",
"\n",
"### Drawing $p | \\cdot$ (the prob. of outliers)\n",
"\n",
"Given the series of outliers, the number of outliers is binomial with probability $p$, and the Beta distribution is conjugate for this model. Thus the posterior is Beta with computable hyperparameters and can be sampled from directly."
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