{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import matplotlib as mpl\n",
"import numpy as np\n",
"import sympy as sy\n",
"sy.init_printing() "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def round_expr(expr, num_digits):\n",
" return expr.xreplace({n : round(n, num_digits) for n in expr.atoms(sy.Number)})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Systems of First-Order Equations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In time series analysis, we study difference equations by writing them into a linear system. For instance,\n",
"\n",
"$$\n",
"3y_{t+3} - 2y_{t+2} + 4y_{t+1} - y_t = 0\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We define \n",
"\n",
"$$\n",
"\\mathbf{x}_t = \n",
"\\left[\n",
"\\begin{matrix}\n",
"y_t\\\\\n",
"y_{t+1}\\\\\n",
"y_{t+2}\n",
"\\end{matrix}\n",
"\\right], \\qquad\n",
"\\mathbf{x}_{t+1} = \n",
"\\left[\n",
"\\begin{matrix}\n",
"y_{t+1}\\\\\n",
"y_{t+2}\\\\\n",
"y_{t+3}\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Rerrange the difference equation for better visual shape,\n",
"\n",
"$$\n",
"y_{t+3} = \\frac{2}{3}y_{t+2} - \\frac{4}{3}y_{t+1} + \\frac{1}{3}y_{t}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The difference equation can be rewritten as\n",
"\n",
"$$\n",
"\\mathbf{x}_{t+1} = A \\mathbf{x}_{t}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That is,\n",
"\n",
"$$\n",
"\\left[\n",
"\\begin{matrix}\n",
"y_{t+1}\\\\\n",
"y_{t+2}\\\\\n",
"y_{t+3}\n",
"\\end{matrix}\n",
"\\right] = \n",
"\\left[\n",
"\\begin{matrix}\n",
"0 & 1 & 0\\\\\n",
"0 & 0 & 1\\\\\n",
"\\frac{1}{3} & -\\frac{4}{3} & \\frac{2}{3}\n",
"\\end{matrix}\n",
"\\right]\n",
"\\left[\n",
"\\begin{matrix}\n",
"y_t\\\\\n",
"y_{t+1}\\\\\n",
"y_{t+2}\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In general, we make sure the difference equation look like:\n",
"\n",
"$$\n",
"y_{t+k} = a_1y_{t+k-1} + a_2y_{t+k-2} + ... + a_ky_{t}\n",
"$$\n",
"\n",
"then rewrite as $\\mathbf{x}_{t+1} = A \\mathbf{x}_{t}$, where\n",
"\n",
"$$\n",
"\\mathbf{x}_t = \n",
"\\left[\n",
"\\begin{matrix}\n",
"y_{t}\\\\\n",
"y_{t+1}\\\\\n",
"\\vdots\\\\\n",
"y_{t+k-1}\n",
"\\end{matrix}\n",
"\\right], \\quad\n",
"\\mathbf{x}_{t+1} = \n",
"\\left[\n",
"\\begin{matrix}\n",
"y_{t+1}\\\\\n",
"y_{t+2}\\\\\n",
"\\vdots\\\\\n",
"y_{t+k}\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And also\n",
"\n",
"$$A=\\left[\\begin{array}{ccccc}\n",
"0 & 1 & 0 & \\cdots & 0 \\\\\n",
"0 & 0 & 1 & & 0 \\\\\n",
"\\vdots & & & \\ddots & \\vdots \\\\\n",
"0 & 0 & 0 & & 1 \\\\\n",
"a_{k} & a_{k-1} & a_{k-2} & \\cdots & a_{1}\n",
"\\end{array}\\right]$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Markov Chains"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Markov chain is a type of stochastic process, commonly modeled by difference equation, we will be slightly touching the surface of this topic by walking through an example."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Markov chain is also described by the first-order difference equation $\\mathbf{x}_{t+1} = P\\mathbf{x}_t$, where $\\mathbf{x}_t$ is called state vector, $A$ is called stochastic matrix."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Suppose there are 3 cities $A$, $B$ and $C$, the proportion of population migration among cities are constructed in the stochastic matrix below"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"M = \n",
"\\left[\n",
"\\begin{matrix}\n",
".89 & .07 & .10\\\\\n",
".07 & .90 & .11\\\\\n",
".04 & .03 & .79\n",
"\\end{matrix}\n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For instance, the first column means that $89\\%$ of population will stay in city $A$, $7\\%$ will move to city $B$ and $4\\%$ will migrate to city $C$. The first row means $7\\%$ of city $B$'s population will immigrate into $A$, $10\\%$ of city $C$'s population will immigrate into $A$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Suppose the initial population of 3 cities are $(593000, 230000, 709000)$, convert the entries into percentage of total population."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.38707572, 0.15013055, 0.46279373])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.array([593000, 230000, 709000])\n",
"x = x/np.sum(x);x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Input the stochastic matrix"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"M = np.array([[.89, .07, .1], [.07, .9, .11], [.04, .03, .79]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After the first period, the population proportion among cities are"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.4012859 , 0.2131201 , 0.38559399])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x1 = M@x\n",
"x1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The second period"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.41062226, 0.26231345, 0.3270643 ])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x2 = M@x1\n",
"x2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The third period"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.41652218, 0.30080273, 0.28267509])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x3 = M@x2\n",
"x3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can construct a loop till $\\mathbf{x}_{100} = M\\mathbf{x}_{99}$, then plot the dynamic path. Notice that the curve is flattening after 20 periods, and we call it convergence to steady-state."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"k = 100\n",
"X = np.zeros((k, 3))\n",
"X[0] = M@x\n",
"i = 0\n",
"\n",
"while i+1 < 100:\n",
" X[i+1] = M@X[i]\n",
" i = i + 1"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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