{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 確率過程のシミュレーション\n", "\n", "## システム\n", "\n", "Klein (2000) の方法を使うと, 合理的期待モデルから線形システム\n", "\n", "\\begin{align}\n", " x^1_{t+1} &= \\Omega_x x_t^1 + \\Omega_u u_t + \\Omega_y y^u_{t+1} + \\xi_{t+1} \\\\\n", " x^2_t &= \\Psi_x x_t^1 + \\Psi_y y^u_t\n", "\\end{align}\n", "\n", "を導出できる. [16ED07](http://www.kenjisato.jp/teaching/16ED07.pdf) を参照. 有限長の $u$ に対するシミュレーションであればこの表現を用いて分析ができる.\n", "\n", "有限でない $u$ に対するシミュレーションを行う場合には, $u_{t+1} = \\Phi u_t + \\epsilon_{t+1}$ と特定化するのが便利である. 次の状態空間方程式を得る. \n", "\n", "\\begin{align*}\n", "&\\begin{array}{rcl}\n", " x_{t+1} &=& \n", " \\Omega_{x}x_{t} +(\\Omega_{u}+\\Omega_{y}M\\Phi)u_{t}+\\xi_{t+1}\\\\\n", " y_t &=&\n", " \\Psi_{x}x_{t}+\\Psi_{y}Mu_{t}. \n", "\\end{array}& (\\Sigma)\n", "\\end{align*}\n", "\n", "$x_t := x^1_t$, $y_t := x^2_t$ と定義しなおした.　ただし, $M$ はシルベスタ方程式 $M-T_{uu}^{-1}S_{uu}M\\Phi=-T_{uu}^{-1}C_{u}$ の解である. \n", "\n", "簡単化のため $\\xi_t = 0$ として (Blanchard-Kahn の仮定), 線形確率システム $(\\Sigma)$ のシミュレーションをしてみよう. \n", "\n", "\\begin{align*}\n", " u_0 &= 0.01 \\\\\n", " \\Phi &= 0.5\n", "\\end{align*}\n", "\n", "とし, $\\epsilon_{t+1}$ は $[-0.001,0.001]$ 上の一様分布に従う iid 確率過程とする. \n", "\n", "まずは利用するライブラリをインポートする. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import scipy.linalg as la\n", "import scipy.stats as st\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline \n", "# Jupyter Notebook で図をノート内に表示" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "前回のデータを再利用する. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with np.load('coeff.npz') as data:\n", " Omega_x = data['Omega_x']\n", " Omega_y = data['Omega_y']\n", " Omega_u = data['Omega_u']\n", " Psi_x = data['Psi_x']\n", " Psi_y = data['Psi_y']\n", " Tuu = data['Tuu']\n", " Suu = data['Suu']\n", " Cu = data['Cu']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $u$ のシミュレーション\n", "\n", "#### 一様乱数\n", "\n", "今回は, シミュレーションに[ジェネレータ](https://wiki.python.org/moin/Generators)を用いよう. 入力項の生成も逐次的に行う. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def u_gen(u0, phi, e):\n", " u0 = u0\n", " while True:\n", " u1 = phi * u0 + e.rvs()\n", " yield u0\n", " u0 = u1" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = u_gen(u0=0.01, phi=0.5, e=st.uniform(-0.001, 0.001))\n", "ut = []\n", "for _ in range(100):\n", " ut.append(next(u))\n", "plt.plot(ut)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "システム $(\\Sigma)$ のシミュレーションコードは次のように書ける. scipy.linalg.solve_sylvester でシルベスタ方程式を解いている." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def gen_path(x0, u0, phi, e):\n", " x0 = np.asarray(x0).reshape((2,1))\n", " M = la.solve_sylvester(-la.solve(Tuu,Suu), \n", " np.array([[1/phi]]), \n", " -la.solve(Tuu, Cu)/phi)\n", " u = u_gen(u0, phi, e)\n", " \n", " while True:\n", " u0 = next(u)\n", " x1 = (Omega_x.dot(x0) +\n", " (Omega_u + Omega_y.dot(M) * phi) * u0)\n", " y0 = Psi_x.dot(x0) + Psi_y.dot(M) * u0\n", " \n", " yield (x0, y0)\n", " \n", " x0 = x1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "シミュレーション結果は for t in range(steps) という標準的なループを用いれば取り出せる. next 関数を使わずに書くと次のように書ける. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "k, z, n, c = [], [], [], []\n", "\n", "path = gen_path(x0=[0.0, 0.0], u0=0.01, \n", " phi=0.5, e=st.uniform(-0.001, 0.001))\n", "\n", "for (x, y), _ in zip(path, range(200)):\n", " k.append(x[0, 0])\n", " z.append(x[1, 0])\n", " n.append(y[0, 0])\n", " c.append(y[1, 0])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "決定論的定常状態: " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cb, kb = (0.5511920622464518, 2.772987427012156)\n", "nb, zb = (0.29583592293349903, 1.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "シミュレーション結果を繰り返し出力できるように, 関数として抽象化しよう." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def simulate(x0, u0, phi, e, steps):\n", " \"\"\"simulate Hansen's RBC model\n", " \n", " Parameters\n", " ----------\n", " \n", " x0: 2d array of float\n", " Initial values for K and Z, typically x0 = [0., 0.]\n", " \n", " u0: float\n", " Initial value for u\n", " \n", " phi: float\n", " u1 = phi * u0 + e\n", " \n", " e: (distribution object with\n", " attribute method rvs)\n", " \n", " steps: int\n", " length of simulation \n", " \n", " \"\"\"\n", " \n", " k, z, n, c = [], [], [], []\n", "\n", " path = gen_path(x0, u0, phi, e)\n", " for (x, y), t in zip(path, range(steps)):\n", " k.append(x[0, 0])\n", " z.append(x[1, 0])\n", " n.append(y[0, 0])\n", " c.append(y[1, 0])\n", "\n", " fig, ax = plt.subplots(2, 2)\n", " fig.set_size_inches(10,8)\n", "\n", "\n", " ax[0, 0].set_title('$K$')\n", " ax[0, 0].plot(kb + kb*np.array(k))\n", " ax[0, 0].axhline(kb, color='black', linestyle='dotted')\n", "\n", " ax[0, 1].set_title('$Z$')\n", " ax[0, 1].plot(zb + zb*np.array(z))\n", " ax[0, 1].axhline(zb, color='black', linestyle='dotted')\n", "\n", " ax[1, 0].set_title('$N$')\n", " ax[1, 0].plot(nb + nb*np.array(n))\n", " ax[1, 0].axhline(nb, color='black', linestyle='dotted')\n", "\n", " ax[1, 1].set_title('$C$')\n", " ax[1, 1].plot(cb + cb*np.array(c))\n", " ax[1, 1].axhline(cb, color='black', linestyle='dotted')" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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p0ijOi5tZM+AxYGjUclbe20Bbd19hZgOAkcBOma5TWlr67eOSkhJKSkpiiTcJ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\nvX4lTYvZli1Qu3b4/bzFzDmXCk4/HV57Ld5ROOe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Wq6b6+++lPzZVZWSo1qypCqpVq9rX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\n1r27lbgor1Wr4IADwu/nnHN5BgywOo8TJ8Y7EuccRJaYHQCsCHm8kvz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "simulate(x0=[0.0, 0.0], u0=0.01, \n", " phi=0.9, e=st.uniform(-0.001, 0.001), steps=300)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HIiKFauRI6N4dHn447khEpCGJTMDWri29BAzg5z+H//ov2LAh7khEpFBddRXc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\ntGnS0YgUDvWAiYhIozn4YNhhB3jyyaQjESktSsBERKROZnD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "simulate(x0=[0.0, 0.0], u0=0.1, \n", " phi=0.5, e=st.uniform(-0.001, 0.001), steps=200)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### ショックの一般化\n", "\n", "上の例では $u$ がゼロの周りを変動するケースを紹介した. ゼロでない定数の周りを変動する $u \\in \\mathbb R^m$ を扱うためには工夫が必要である. 以下ではその方法を紹介する. \n", "\n", "$$\n", "\\mathbb{E} u_t = \\mu \\in \\mathbb R^m\n", "$$\n", "\n", "として, 平均からの乖離 $u_{t} - \\mu$ が\n", "\n", "$$\n", "u_{t+1} - \\mu = \\Phi (u_t - \\mu) + \\epsilon_{t+1} \n", "$$\n", "\n", "に従うと考えればよい. これを, \n", "\n", "$$\n", "u_{t+1} = \\Phi u_t + (I - \\Phi) \\mu + \\epsilon_{t+1} \n", "$$\n", "\n", "と書き換えると, 次の方程式を得る.\n", "\n", "$$\n", "\\begin{bmatrix}\n", " \\mu \\\\\n", " u_{t+1}\n", "\\end{bmatrix}\n", "=\n", "\\begin{bmatrix}\n", " \\mu\\\\\n", " \\Phi u_t + \\epsilon_{t+1}\n", "\\end{bmatrix} \n", "=\n", "\\begin{bmatrix}\n", " I & 0\\\\\n", " I-\\Phi & \\Phi\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", " \\mu \\\\\n", " u_t\n", "\\end{bmatrix}\n", "+\n", "\\begin{bmatrix}\n", " 0 \\\\\n", " \\epsilon_{t+1}\n", "\\end{bmatrix}.\n", "$$\n", "\n", "拡大した変数\n", "\n", "$$\n", "\\bar{u}_t = \n", "\\begin{bmatrix}\n", " \\mu \\\\\n", " u_t\n", "\\end{bmatrix}\n", "$$\n", "\n", "についてシステム $\n", "E \\mathbb E_t x_{t+1} = A x_t + B u_t\n", "$ を書き直すには、\n", "\n", "\\begin{align}\n", " B \\to \\bar B = \n", " \\begin{bmatrix}\n", " 0 & B\n", " \\end{bmatrix}\n", "\\end{align}\n", "\n", "とすればよい. 最終的に\n", "\n", "$$\n", " E \\mathbb E_t x_{t+1} = A x_t + \\bar B \\bar u_t\n", "$$\n", "\n", "が分析すべきシステムである. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }