{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Vector Error Correction Model (VECM): Applications In Finance"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](\"https://img.shields.io/badge/R-v3.5.0-green.svg\")
\n",
"
\n",
"\n",
"### Notebook by [Marco Tavora](https://marcotavora.me/)\n",
"\n",
"## Table of contents\n",
"\n",
"1. [Introduction](#Introduction)\n",
"2. [Installing Packages](#Installing-Packages)\n",
"3. [Johansen Test for Cointegration](#Johansen-Test-for-Cointegration)\n",
"3. [Fitting the VECM](#Fitting-the-VECM)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"[[go back to the top]](#Table-of-contents)\n",
"\n",
"From [Wikipedia](https://en.wikipedia.org/wiki/Error_correction_model#VECM):\n",
"\n",
"> The Engle–Granger approach as described above suffers from a number of weaknesses. Namely it is restricted to only a single equation with one variable designated as the dependent variable, explained by another variable that is assumed to be weakly exogeneous for the parameters of interest. It also relies on pretesting the time series to find out whether variables are I(0) or I(1). These weaknesses can be addressed through the use of Johansen's procedure. Its advantages include that pretesting is not necessary, there can be numerous cointegrating relationships, all variables are treated as endogenous and tests relating to the long-run parameters are possible. \n",
"\n",
"VECM models add error correction terms to the vector autoregression (VAR) model. Using simple matrix algebra,\n",
"the model can be written as follows:\n",
"\n",
"$$\\,\\left[ {\\begin{array}{*{20}{c}}\n",
"{\\Delta {y_{1,t}}}\\\\\n",
"{\\Delta {y_{2t}}}\n",
"\\end{array}} \\right] = \\left[ {\\begin{array}{*{20}{c}}\n",
"{{\\gamma _{01}}}\\\\\n",
"{{\\gamma _{02}}}\n",
"\\end{array}} \\right] + \\left[ {\\begin{array}{*{20}{c}}\n",
"{{\\alpha _1}}\\\\\n",
"{{\\alpha _2}}\n",
"\\end{array}} \\right]\\left[ {{\\beta _0}\\,\\,\\,{\\beta _1}\\,\\,\\,{\\beta _2}} \\right]\\left[ {\\begin{array}{*{20}{c}}\n",
"1\\\\\n",
"{{y_{1,t - 1}}}\\\\\n",
"{{y_{2,t - 1}}}\n",
"\\end{array}} \\right] + \\left[ {\\begin{array}{*{20}{c}}\n",
"{{\\gamma _{11}}}&{{\\gamma _{21}}}\\\\\n",
"{{\\gamma _{12}}}&{{\\gamma _{22}}}\n",
"\\end{array}} \\right]\\,\\,\\left[ {\\begin{array}{*{20}{c}}\n",
"{\\Delta {y_{1,t - 1}}}\\\\\n",
"{\\Delta {y_{2,t - 1}}}\n",
"\\end{array}} \\right] + \\left[ {\\begin{array}{*{20}{c}}\n",
"{{\\gamma _{31}}}&{{\\gamma _{41}}}\\\\\n",
"{{\\gamma _{32}}}&{{\\gamma _{42}}}\n",
"\\end{array}} \\right]\\,\\,\\left[ {\\begin{array}{*{20}{c}}\n",
"{\\Delta {y_{1,t - 2}}}\\\\\n",
"{\\Delta {y_{2,t - 2}}}\n",
"\\end{array}} \\right] + \\left[ {\\begin{array}{*{20}{c}}\n",
"{{\\nu _{1,t}}}\\\\\n",
"{{\\nu _{2,t}}}\n",
"\\end{array}} \\right]$$\n",
"\n",
"Following [this excellent blog post](http://blog.mindymallory.com/2018/02/basic-time-series-analysis-a-drunk-and-her-dog-explain-cointegration-and-the-vecm-model/) I will choose $y_1$ and $y_2$ to be the following time series:\n",
"\n",
"- SPY (the S&P 500 exchange traded fund)\n",
"- SHY (iShares 1-3 year Treasury Bond) prices. \n",
"\n",
"If both series are cointegrated, this information must included in the model. This is done introducing, as mentioned above, error correction terms:\n",
"\n",
"$${\\alpha _i}({\\beta _0}\\, + {\\beta _1}{y_{1,t - 1}}\\, + {\\beta _2}{y_{2,t - 1}}),\\,\\,\\,\\,\\,i = 1,2$$\n",
"\n",
"where \n",
"\n",
"$$({\\beta _0}\\, + {\\beta _1}{y_{1,t - 1}}\\, + {\\beta _2}{y_{2,t - 1}}),\\,\\,\\,\\,\\,i = 1,2$$\n",
"\n",
"corresponds to the long-run. If in the long-run the last equation is zero we have the folowing relation:\n",
"\n",
"$$\\,{y_{2,t - 1}} = - ({\\beta _0}/{\\beta _2})\\, - ({\\beta _1}/{\\beta _2}){y_{1,t - 1}}$$\n",
"\n",
"Hence, the $\\beta$s we obtain after fitting the VECM inform us about the equilibrium relationship between the time series. When the two series deviate from equilibrium, the $\\alpha$s \"push them back\".\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Installing Packages\n",
"[[go back to the top]](#Table-of-contents)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# install.packages('ggplot2')\n",
"# install.packages('xts')\n",
"# install.packages('quantmod')\n",
"# install.packages('broom')\n",
"# install.packages('tseries')\n",
"# install.packages(\"kableExtra\")\n",
"# install.packages(\"knitr\")\n",
"# install.packages(\"vars\")\n",
"# install.packages(\"urca\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To load the data we will use the library `quantmod` which contains the function `getSymbols`. From the [documents](https://www.rdocumentation.org/packages/quantmod/versions/0.4-13/topics/getSymbols)\n",
"\n",
"> getSymbols is a wrapper to load data from various sources, local or remote.\n",
"\n",
"In our case we will load data from Yahoo Finance."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"rm(list=ls()) \n",
"library(tseries)\n",
"library(dynlm)\n",
"library(vars)\n",
"library(nlWaldTest) \n",
"library(lmtest)\n",
"library(broom) \n",
"library(car)\n",
"library(sandwich)\n",
"library(knitr)\n",
"library(forecast) "
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\t- 'SHY'
\n",
"\t- 'SPY'
\n",
"
\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'SHY'\n",
"\\item 'SPY'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'SHY'\n",
"2. 'SPY'\n",
"\n",
"\n"
],
"text/plain": [
"[1] \"SHY\" \"SPY\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"library(quantmod)\n",
"setSymbolLookup(SHY='yahoo',SPY='yahoo')\n",
"getSymbols(c('SHY','SPY')) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Defining `y1` and `y2` as the adjusted prices and joining them:"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] \"Our dataframe is:\"\n"
]
},
{
"data": {
"text/plain": [
" SHY SPY\n",
"2007-01-03 111.6693 68.01018\n",
"2007-01-04 111.9062 68.07811\n",
"2007-01-05 111.0136 68.03567\n",
"2007-01-08 111.5271 67.99307\n",
"2007-01-09 111.4323 68.01858\n",
"2007-01-10 111.8035 68.00159"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"y1 <- SPY$SPY.Adjusted\n",
"y2 <- SHY$SHY.Adjusted\n",
"time_series <- cbind(y1, y2)\n",
"print('Our dataframe is:')\n",
"colnames(time_series) <- c('SHY', 'SPY') \n",
"head(time_series)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stationarity\n",
"[[go back to the top]](#Table-of-contents)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can check for stationary of the series individually:"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"\tAugmented Dickey-Fuller Test\n",
"\n",
"data: time_series$SHY\n",
"Dickey-Fuller = -1.5363, Lag order = 14, p-value = 0.7747\n",
"alternative hypothesis: stationary\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\n",
"\tAugmented Dickey-Fuller Test\n",
"\n",
"data: time_series$SPY\n",
"Dickey-Fuller = -3.7478, Lag order = 14, p-value = 0.02158\n",
"alternative hypothesis: stationary\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"adf.test(time_series$SHY)\n",
"adf.test(time_series$SPY)"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] \"p-values:\"\n"
]
},
{
"data": {
"text/html": [
"0.774665887814869"
],
"text/latex": [
"0.774665887814869"
],
"text/markdown": [
"0.774665887814869"
],
"text/plain": [
"[1] 0.7746659"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"0.0215848302364735"
],
"text/latex": [
"0.0215848302364735"
],
"text/markdown": [
"0.0215848302364735"
],
"text/plain": [
"[1] 0.02158483"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"print('p-values:')\n",
"adf.test(time_series$SHY)$p.value\n",
"adf.test(time_series$SPY)$p.value"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
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bVZ6BqSw+p+Q15LcpW8NLbuIdYECdiD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\ngg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(2,1))\n",
"plot.ts(time_series$SHY,\n",
" type='l')\n",
"plot.ts(time_series$SPY, \n",
" type='l')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Johansen Test for Cointegration\n",
"[[go back to the top]](#Table-of-contents)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The most well known cointegration test is the Johansen test which estimates the VECM parameters and determines whether the determinant of \n",
"\n",
"$$\\alpha \\beta = \\left[ {\\begin{array}{*{20}{c}}\n",
"{{\\alpha _1}}\\\\\n",
"{{\\alpha _2}}\n",
"\\end{array}} \\right]\\left[ {{\\beta _0}\\,\\,\\,{\\beta _1}\\,\\,\\,{\\beta _2}} \\right]$$\n",
"\n",
"\n",
"is zero or not. If $\\alpha \\beta\\neq 0$, the series are cointegrated."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"library(urca)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"###################### \n",
"# Johansen-Procedure # \n",
"###################### \n",
"\n",
"Test type: trace statistic , without linear trend and constant in cointegration \n",
"\n",
"Eigenvalues (lambda):\n",
"[1] 2.248927e-02 3.620157e-03 4.437196e-18\n",
"\n",
"Values of teststatistic and critical values of test:\n",
"\n",
" test 10pct 5pct 1pct\n",
"r <= 1 | 10.65 7.52 9.24 12.97\n",
"r = 0 | 77.46 17.85 19.96 24.60\n",
"\n",
"Eigenvectors, normalised to first column:\n",
"(These are the cointegration relations)\n",
"\n",
" SHY.l3 SPY.l3 constant\n",
"SHY.l3 1.00000 1.0000 1.00000\n",
"SPY.l3 -84.59851 163.3147 -8.78908\n",
"constant 6927.78683 -12622.5372 543.67420\n",
"\n",
"Weights W:\n",
"(This is the loading matrix)\n",
"\n",
" SHY.l3 SPY.l3 constant\n",
"SHY.d 2.147229e-05 1.049741e-04 -1.531138e-17\n",
"SPY.d 2.088562e-05 -1.870590e-06 1.148836e-17\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"johansentest <- ca.jo(time_series, type = \"trace\", ecdet = \"const\", K = 3)\n",
"summary(johansentest)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The lines $r=0$ and $r\\le 1$ are the results of the test. More specifically:\n",
"\n",
"- line $r=0$: these are the results of the hypothesis test with null hypothesis $r=0$. More concretely, this test checks if the matrix has zero rank. In the present case the hypothesis is rejected since the test variable is well above the $1\\%$ value;\n",
"- line $r\\le 1$: these are the results of the hypothesis test $r\\le 1$. Now since the test value is below the $1\\%$ value value we fail to reject the null hypothesis. Hence we conclude that the rank of $\\alpha \\beta$ is 1 and therefore the two series are cointegrated and we can use the VECM model.\n",
"\n",
"Note that if hypotheses were reject we would have $r=2$ corresponding to two stationary series."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting the VECM\n",
"[[go back to the top]](#Table-of-contents)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"$rlm\n",
"\n",
"Call:\n",
"lm(formula = substitute(form1), data = data.mat)\n",
"\n",
"Coefficients:\n",
" SHY.d SPY.d \n",
"ect1 2.147e-05 2.089e-05\n",
"SHY.dl1 -4.754e-02 6.806e-04\n",
"SPY.dl1 5.658e-01 -1.192e-01\n",
"SHY.dl2 -6.092e-02 4.440e-04\n",
"SPY.dl2 3.243e-02 -6.055e-02\n",
"\n",
"\n",
"$beta\n",
" ect1\n",
"SHY.l3 1.00000\n",
"SPY.l3 -84.59851\n",
"constant 6927.78683\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t <- cajorls(johansentest, r = 1)\n",
"t"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $\\beta$ coefficients are given above. The $\\gamma$ coefficients are above the $beta$s in the output."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}