{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Levy Stable models of Stochastic Volatility\n", "\n", "This tutorial demonstrates inference using the Levy [Stable](http://docs.pyro.ai/en/stable/distributions.html#stable) distribution through a motivating example of a non-Gaussian stochastic volatilty model.\n", "\n", "Inference with stable distribution is tricky because the density Stable.log_prob() is not defined. In this tutorial we demonstrate two approaches to inference: (i) using the [poutine.reparam](http://docs.pyro.ai/en/latest/poutine.html#pyro.poutine.handlers.reparam) effect to transform models in to a tractable form, and (ii) using the likelihood-free loss [EnergyDistance](http://docs.pyro.ai/en/latest/inference_algos.html#pyro.infer.energy_distance.EnergyDistance) with SVI.\n", "\n", "\n", "#### Summary\n", "\n", "- [Stable.log_prob()](http://docs.pyro.ai/en/stable/distributions.html#stable) is undefined.\n", "- Stable inference requires either reparameterization or a likelihood-free loss.\n", "- Reparameterization:\n", " - The [poutine.reparam()](http://docs.pyro.ai/en/latest/poutine.html#pyro.poutine.handlers.reparam) handler can transform models using various [strategies](http://docs.pyro.ai/en/latest/infer.reparam.html).\n", " - The [StableReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.stable.StableReparam) strategy can be used for Stable distributions in SVI or HMC.\n", " - The [LatentStableReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.stable.LatentStableReparam) strategy is a little cheaper, but cannot be used for likelihoods.\n", " - The [DiscreteCosineReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.discrete_cosine.DiscreteCosine) strategy improves geometry in batched latent time series models.\n", "- Likelihood-free loss with SVI:\n", " - The [EnergyDistance](http://docs.pyro.ai/en/latest/inference_algos.html#pyro.infer.energy_distance.EnergyDistance) loss allows stable distributions in the guide and in model likelihoods.\n", "\n", "#### Table of contents\n", "\n", "- [Daily S&P data](#data)\n", "- [Fitting a single distribution to log returns](#fitting) using EnergyDistance\n", "- [Modeling stochastic volatility](#modeling) using poutine.reparam" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Daily S&P 500 data \n", "\n", "The following daily closing prices for the S&P 500 were loaded from [Yahoo finance](https://finance.yahoo.com/quote/%5EGSPC/history/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import math\n", "import os\n", "import torch\n", "import pyro\n", "import pyro.distributions as dist\n", "from matplotlib import pyplot\n", "from torch.distributions import constraints\n", "\n", "from pyro import poutine\n", "from pyro.contrib.examples.finance import load_snp500\n", "from pyro.infer import EnergyDistance, Predictive, SVI, Trace_ELBO\n", "from pyro.infer.autoguide import AutoDiagonalNormal\n", "from pyro.infer.reparam import DiscreteCosineReparam, StableReparam\n", "from pyro.optim import ClippedAdam\n", "from pyro.ops.tensor_utils import convolve\n", "\n", "%matplotlib inline\n", "assert pyro.__version__.startswith('1.8.6')\n", "smoke_test = ('CI' in os.environ)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "torch.Size([23116])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = load_snp500()\n", "dates = df.Date.to_numpy()\n", "x = torch.tensor(df[\"Close\"]).float()\n", "x.shape" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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