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mmcky committed Apr 13, 2024
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10 changes: 5 additions & 5 deletions _notebooks/about.ipynb
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"cells": [
{
"cell_type": "markdown",
"id": "ca17ea17",
"id": "a41110f4",
"metadata": {},
"source": [
"# About These Lectures"
]
},
{
"cell_type": "markdown",
"id": "5387edbc",
"id": "67c0a355",
"metadata": {},
"source": [
"## About\n",
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},
{
"cell_type": "markdown",
"id": "db295b9c",
"id": "3be293ca",
"metadata": {},
"source": [
"## Level\n",
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},
{
"cell_type": "markdown",
"id": "34ce644a",
"id": "9550fccb",
"metadata": {},
"source": [
"## Credits\n",
Expand All @@ -96,7 +96,7 @@
}
],
"metadata": {
"date": 1712122261.9337194,
"date": 1712983675.5954692,
"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": "a764f923",
"id": "5dbf5954",
"metadata": {},
"source": [
"\n",
Expand All @@ -13,15 +13,15 @@
},
{
"cell_type": "markdown",
"id": "952824e5",
"id": "0e13d9b2",
"metadata": {},
"source": [
"# AR1 Processes"
]
},
{
"cell_type": "markdown",
"id": "3f1ee208",
"id": "37105763",
"metadata": {},
"source": [
"# Migrated lecture\n",
Expand All @@ -34,7 +34,7 @@
},
{
"cell_type": "markdown",
"id": "7ff94b33",
"id": "d54b7465",
"metadata": {},
"source": [
"## Overview\n",
Expand All @@ -60,7 +60,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "000022c0",
"id": "1bb63311",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "5018d858",
"id": "340a930b",
"metadata": {},
"source": [
"## The AR(1) Model\n",
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},
{
"cell_type": "markdown",
"id": "e23e8b01",
"id": "3bea7f64",
"metadata": {},
"source": [
"### Moving Average Representation\n",
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},
{
"cell_type": "markdown",
"id": "34d008c3",
"id": "1055eb58",
"metadata": {},
"source": [
"### Distribution Dynamics\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "f45eac2d",
"id": "39e246c0",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "dbb403e4",
"id": "e43099c2",
"metadata": {},
"source": [
"Here’s the sequence of distributions:"
Expand All @@ -213,7 +213,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "1aa3874a",
"id": "97581636",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "3544e411",
"id": "14bcdf4f",
"metadata": {},
"source": [
"## Stationarity and Asymptotic Stability\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "53aac33f",
"id": "c951ba9d",
"metadata": {
"hide-output": false
},
Expand All @@ -275,7 +275,7 @@
},
{
"cell_type": "markdown",
"id": "5a78814a",
"id": "88c44aa2",
"metadata": {},
"source": [
"Moreover, the limit does not depend on the initial condition.\n",
Expand All @@ -286,7 +286,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "7705fb79",
"id": "73946f07",
"metadata": {
"hide-output": false
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},
{
"cell_type": "markdown",
"id": "d9dfb78a",
"id": "9be76970",
"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": "c612f52d",
"id": "0e128d7b",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "1e815dad",
"id": "6c2c4736",
"metadata": {},
"source": [
"As claimed, the sequence $ \\{ \\psi_t \\} $ converges to $ \\psi^* $."
]
},
{
"cell_type": "markdown",
"id": "b29ff6f0",
"id": "cebe0578",
"metadata": {},
"source": [
"### Stationary Distributions\n",
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},
{
"cell_type": "markdown",
"id": "3d4c26fe",
"id": "50fb9963",
"metadata": {},
"source": [
"## Ergodicity\n",
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},
{
"cell_type": "markdown",
"id": "f3972adb",
"id": "7872beef",
"metadata": {},
"source": [
"## Exercises"
]
},
{
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"id": "65b7e09b",
"id": "d213e15c",
"metadata": {},
"source": [
"## Exercise 30.1\n",
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},
{
"cell_type": "markdown",
"id": "ef365fa8",
"id": "b6bbbe27",
"metadata": {},
"source": [
"## Solution to[ Exercise 30.1](https://intro.quantecon.org/#ar1p_ex1)\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "b3d8f6e9",
"id": "a20693b9",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "cf7ba7ff",
"id": "2150c235",
"metadata": {},
"source": [
"## Exercise 30.2\n",
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},
{
"cell_type": "markdown",
"id": "6457ee6a",
"id": "75290ce2",
"metadata": {},
"source": [
"## Solution to[ Exercise 30.2](https://intro.quantecon.org/#ar1p_ex2)\n",
Expand All @@ -608,7 +608,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "70200314",
"id": "95d62e07",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "6712558c",
"id": "2f576419",
"metadata": {
"hide-output": false
},
Expand All @@ -661,7 +661,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "44e1ba41",
"id": "3e7b1118",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "fda40784",
"id": "505b3455",
"metadata": {},
"source": [
"We see that the kernel density estimator is effective when the underlying\n",
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},
{
"cell_type": "markdown",
"id": "a07a2d56",
"id": "3c199784",
"metadata": {},
"source": [
"## Exercise 30.3\n",
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},
{
"cell_type": "markdown",
"id": "ac2d97bc",
"id": "0a7105ce",
"metadata": {},
"source": [
"## Solution to[ Exercise 30.3](https://intro.quantecon.org/#ar1p_ex3)\n",
Expand All @@ -745,7 +745,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "4b5c4a1a",
"id": "a91e167d",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "648239b6",
"id": "a2e5a2e7",
"metadata": {
"hide-output": false
},
Expand All @@ -774,7 +774,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "7053d0bf",
"id": "fd568c27",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "96d02b2c",
"id": "62cd87d3",
"metadata": {
"hide-output": false
},
Expand All @@ -800,7 +800,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "e092b8e2",
"id": "7fd45286",
"metadata": {
"hide-output": false
},
Expand All @@ -824,7 +824,7 @@
},
{
"cell_type": "markdown",
"id": "8aacd8d0",
"id": "8f2b438f",
"metadata": {},
"source": [
"The simulated distribution approximately coincides with the theoretical\n",
Expand All @@ -833,7 +833,7 @@
}
],
"metadata": {
"date": 1712122261.9617279,
"date": 1712983675.6213908,
"filename": "ar1_processes.md",
"kernelspec": {
"display_name": "Python",
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