profile truncation order

Author: ulf1

examples/profile-find-truncation-order.ipynb

@@ -0,0 +1,180 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Load Packages"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "#!pip install memory_profiler\n",
+    "import memory_profiler\n",
+    "%load_ext memory_profiler"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Load Data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with np.load('data/demo1.npz') as data:\n",
+    "    x = data['px'][:, 0]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Find truncation order m\n",
+    "The task is to find the first $m^*$ whereas \n",
+    "\n",
+    "$$\n",
+    "|w_{m^*}| \\geq \\tau \\; \\wedge \\; |w_{m^*+1}| < \\tau\n",
+    "$$\n",
+    "\n",
+    "(see \"Fixed-Width Window Fracdiff\" in Lopez, 2018, pp. 80--84)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# numpy version\n",
+    "def find_truncation_order1(d, tau=1e-5, mmax=20000):\n",
+    "    w = np.empty((mmax+1,))\n",
+    "    w[0] = 1\n",
+    "    for k in range(1, mmax+1):\n",
+    "        w[k] = -w[k-1] * ((d - k + 1) / k)\n",
+    "        if np.abs(w[k]) < tau:\n",
+    "            break\n",
+    "    return k-1, w[:k]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# list version\n",
+    "def find_truncation_order2(d, tau=1e-5, mmax=20000):\n",
+    "    w = [1]\n",
+    "    for k in range(1, mmax+1):\n",
+    "        wk = -w[-1] * ((d - k + 1) / k)\n",
+    "        if abs(wk) < tau:\n",
+    "            break\n",
+    "        w.append(wk)\n",
+    "    return k-1, w"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Speed\n",
+    "The `list` version is much faster"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "8.01 ms ± 1.97 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
+      "936 µs ± 129 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "d = 0.345\n",
+    "%timeit mstar, w = find_truncation_order1(d)\n",
+    "%timeit mstar, w = find_truncation_order2(d)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Memory"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "peak memory: 62.33 MiB, increment: -0.14 MiB\n",
+      "peak memory: 62.11 MiB, increment: 0.01 MiB\n"
+     ]
+    }
+   ],
+   "source": [
+    "d = 0.345\n",
+    "%memit mstar, w = find_truncation_order1(d)\n",
+    "%memit mstar, w = find_truncation_order2(d)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# References\n",
+    "* Prado, M.L. de, 2018. Advances in Financial Machine Learning, 1st ed. Wiley."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "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": "3.7.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}