{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Monte Carlo Simulation of Time Series\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demqua10.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-23\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "Simulate time series using Monte Carlo Method.\n", "\n", "A commodity price is governed by weekly price movements\n", "\\begin{equation*}\n", "\\log(p_{t+1}) = \\log(p_t) + \\tilde \\epsilon_t\n", "\\end{equation*}\n", "where the $\\tilde \\epsilon_t$ are i.i.d. normal with mean $\\mu=0.005$ and standard deviation $\\sigma=0.02$.\n", "\n", "To simulate three time series of T=40 weekly price changes, starting from a price of 2, execute the script" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.stats import norm\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "m, T = 3, 40\n", "mu, sigma = 0.005, 0.02\n", "e = norm.rvs(mu,sigma,size=[T,m])\n", "logp = np.zeros([T+1,m])\n", "logp[0] = np.log(2)\n", "for t in range(T):\n", " logp[t+1] = logp[t] + e[t]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Make figure" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.set(xlabel='Week', ylabel='Price', xlim=[0,T])\n", "ax.plot(np.exp(logp));" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 4 }