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mmcky committed Mar 14, 2024
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62,157 changes: 0 additions & 62,157 deletions _downloads/4f20f803f2e6f2bfce589941ae46788a/life-expectancy-vs-gdp-per-capita.csv

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10 changes: 5 additions & 5 deletions _notebooks/about.ipynb
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"cells": [
{
"cell_type": "markdown",
"id": "56e4c3a1",
"id": "fb7d0182",
"metadata": {},
"source": [
"# About These Lectures"
]
},
{
"cell_type": "markdown",
"id": "c2645896",
"id": "4b718fca",
"metadata": {},
"source": [
"## About\n",
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},
{
"cell_type": "markdown",
"id": "ce515190",
"id": "d177994f",
"metadata": {},
"source": [
"## Level\n",
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},
{
"cell_type": "markdown",
"id": "6feb2eb6",
"id": "493486c3",
"metadata": {},
"source": [
"## Credits\n",
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}
],
"metadata": {
"date": 1708382802.5772257,
"date": 1710456262.8889675,
"filename": "about.md",
"kernelspec": {
"display_name": "Python",
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78 changes: 39 additions & 39 deletions _notebooks/ar1_processes.ipynb
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"cells": [
{
"cell_type": "markdown",
"id": "7186a21e",
"id": "b3e9146d",
"metadata": {},
"source": [
"\n",
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},
{
"cell_type": "markdown",
"id": "7fec624d",
"id": "88d435e3",
"metadata": {},
"source": [
"# AR1 Processes"
]
},
{
"cell_type": "markdown",
"id": "b97ec7a5",
"id": "99c97ec1",
"metadata": {},
"source": [
"# Migrated lecture\n",
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},
{
"cell_type": "markdown",
"id": "b1c31ff0",
"id": "b98652e7",
"metadata": {},
"source": [
"## Overview\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "207d60bd",
"id": "f0dc935e",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "ed3af388",
"id": "631c29fb",
"metadata": {},
"source": [
"## The AR(1) Model\n",
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},
{
"cell_type": "markdown",
"id": "c528a6f2",
"id": "22dbd358",
"metadata": {},
"source": [
"### Moving Average Representation\n",
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},
{
"cell_type": "markdown",
"id": "277d20bb",
"id": "4eb80a98",
"metadata": {},
"source": [
"### Distribution Dynamics\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "e05ea31e",
"id": "e640632b",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "ca6e6fea",
"id": "d55a64b7",
"metadata": {},
"source": [
"Here’s the sequence of distributions:"
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{
"cell_type": "code",
"execution_count": null,
"id": "cc3faadd",
"id": "35516720",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "2e0f90ab",
"id": "9a982913",
"metadata": {},
"source": [
"## Stationarity and Asymptotic Stability\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "7abd9539",
"id": "8654d80f",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "3ba0f8ab",
"id": "8072994d",
"metadata": {},
"source": [
"Moreover, the limit does not depend on the initial condition.\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "4db8edd3",
"id": "d33a071f",
"metadata": {
"hide-output": false
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},
{
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"metadata": {},
"source": [
"In fact it’s easy to show that such convergence will occur, regardless of the initial condition, whenever $ |a| < 1 $.\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "d667440c",
"id": "1465b7ce",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "a672a9f7",
"id": "56f8aa97",
"metadata": {},
"source": [
"As claimed, the sequence $ \\{ \\psi_t \\} $ converges to $ \\psi^* $."
]
},
{
"cell_type": "markdown",
"id": "11de976b",
"id": "419ff0f7",
"metadata": {},
"source": [
"### Stationary Distributions\n",
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},
{
"cell_type": "markdown",
"id": "da89a830",
"id": "d08a109e",
"metadata": {},
"source": [
"## Ergodicity\n",
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},
{
"cell_type": "markdown",
"id": "b18a290c",
"id": "03228695",
"metadata": {},
"source": [
"## Exercises"
]
},
{
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"id": "8d39cedf",
"id": "3dd39599",
"metadata": {},
"source": [
"## Exercise 26.1\n",
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},
{
"cell_type": "markdown",
"id": "7942356d",
"id": "ece576c3",
"metadata": {},
"source": [
"## Solution to[ Exercise 26.1](https://intro.quantecon.org/#ar1p_ex1)\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "3c3d6126",
"id": "6cc2b893",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "2cefbc01",
"id": "16c8926d",
"metadata": {},
"source": [
"## Exercise 26.2\n",
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},
{
"cell_type": "markdown",
"id": "3d5eb0c5",
"id": "12dc24d0",
"metadata": {},
"source": [
"## Solution to[ Exercise 26.2](https://intro.quantecon.org/#ar1p_ex2)\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "41269364",
"id": "69b59133",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "efc03a57",
"id": "aee63870",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "838ce883",
"id": "880b851b",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "50276878",
"id": "4df317fa",
"metadata": {},
"source": [
"We see that the kernel density estimator is effective when the underlying\n",
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},
{
"cell_type": "markdown",
"id": "dbe1113a",
"id": "84951c9e",
"metadata": {},
"source": [
"## Exercise 26.3\n",
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},
{
"cell_type": "markdown",
"id": "b9bceb72",
"id": "40c1be92",
"metadata": {},
"source": [
"## Solution to[ Exercise 26.3](https://intro.quantecon.org/#ar1p_ex3)\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "72f0770f",
"id": "ea118b92",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "e61998c9",
"id": "e35d22bd",
"metadata": {
"hide-output": false
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{
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"id": "1ab7416a",
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"metadata": {
"hide-output": false
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{
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"execution_count": null,
"id": "5f35ad79",
"id": "9fc0676a",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "34589a22",
"id": "a9cffa58",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "77492175",
"id": "b584678a",
"metadata": {},
"source": [
"The simulated distribution approximately coincides with the theoretical\n",
Expand All @@ -833,7 +833,7 @@
}
],
"metadata": {
"date": 1708382802.6020732,
"date": 1710456262.91425,
"filename": "ar1_processes.md",
"kernelspec": {
"display_name": "Python",
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