Python Guide to Accompany Introductory Econometrics for Finance

175 Pages·2019·10.502 MB·English

by  Ran Tao, Chris Brooks

Electronic copy available at: https://ssrn.com/abstract=3475303
© RanTaoandChrisBrooks2019
TheICMACentre,HenleyBusinessSchool,UniversityofReading
Allrightsreserved.
This guide draws on material from ‘Introductory Econometrics for Finance’, published by Cam-
bridge University Press, © Chris Brooks (2019). The Guide is intended to be used alongside the
book,andpagenumbersfromthebookaregivenaftereachsectionandsubsectionheading.
The authors accept no responsibility for the persistence or accuracy of URLs for external or third-
party internet websites referred to in this work, and nor do we guarantee that any content on such
websitesis,orwillremain,accurateorappropriate.
i
Electronic copy available at: https://ssrn.com/abstract=3475303
Contents
1 Gettingstarted 1
1.1 WhatisPython? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 DifferentwaystorunPythoncode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 WhatdoesaJupyterNoteBooklooklike? . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Gettinghelp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 DatamanagementinPython 12
2.1 Variablesandnamerules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Whitespace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Mathematicaloperations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Twolibraries: PandasandNumPy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Datainputandsaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Datadescriptionandcalculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Anexample: calculatingsummarystatisticsforhouseprices . . . . . . . . . . . . . . . 20
2.9 Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.10 Savingdataandresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Simplelinearregression-estimationofanoptimalhedgeratio 27
4 Hypothesistesting-Example1: hedgingrevisited 31
5 Estimationandhypothesistesting-Example2: theCAPM 33
6 Sampleoutputformultiplehypothesistests 39
7 MultipleregressionusinganAPT-stylemodel 41
7.1 Stepwiseregression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
8 Quantileregression 49
9 Calculatingprincipalcomponents 57
10 Diagnostictesting 60
10.1 Testingforheteroscedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
10.2 UsingWhite’smodifiedstandarderrorestimates . . . . . . . . . . . . . . . . . . . . . . 62
10.3 TheNewey-Westprocedureforestimatingstandarderrors . . . . . . . . . . . . . . . . 64
10.4 Autocorrelationanddynamicmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
10.5 Testingfornon-normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
10.6 Dummyvariableconstructionanduse . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
10.7 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
10.8 TheRESETtestforfunctionalform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
10.9 Stabilitytests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
11 ConstructingARMAmodels 80
12 ForecastingusingARMAmodels 85
13 Estimatingexponentialsmoothingmodels 89
ii
Electronic copy available at: https://ssrn.com/abstract=3475303
14 Simultaneousequationsmodelling 91
15 TheGeneralisedmethodofmomentsforinstrumentalvariables 94
16 VARestimation 97
17 Testingforunitroots 106
18 Cointegrationtestsandmodellingcointegratedsystems 109
19 Volatilitymodelling 121
19.1 Testingfor’ARCHeffects’inexchangeratereturns . . . . . . . . . . . . . . . . . . . . . 121
19.2 EstimatingGARCHmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
19.3 GJRandEGARCHmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
19.4 ForecastingfromGARCHmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
20 Modellingseasonalityinfinancialdata 132
20.1 Dummyvariablesforseasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
20.2 EstimatingMarkovswitchingmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
21 Paneldatamodels 137
22 Limiteddependentvariablemodels 142
23 Simulationmethods 150
23.1 DerivingcriticalvaluesforaDickey-Fullertestusingsimulation . . . . . . . . . . . . . 150
23.2 PricingAsianoptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
23.3 VaRestimationusingbootstrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
24 TheFama-MacBethprocedure 160
25 UsingextremevaluetheoryforVaRcalculation 164
iii
Electronic copy available at: https://ssrn.com/abstract=3475303
List of Figures
1 OpeningthePythonConsole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 RunningCodefromtheConsole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 OpeningtheAnacondaNavigator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 OpeningaJupyterNoteBook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 TheInterfaceofaJupyterNoteBook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 RenamingJupyterNoteBook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7 FileMenuOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
8 EditMenuOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
9 ViewMenuOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
10 CellMenuOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
11 KernelMenuOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
12 HelpMenuOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
13 TheCellEditandCommandMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
14 LineplotoftheAverageHousePriceSeries . . . . . . . . . . . . . . . . . . . . . . . . . 24
15 HistogramoftheAverageHousePriceSeries . . . . . . . . . . . . . . . . . . . . . . . . 25
16 Time-SeriesPlotofTwoSeries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
17 ScatterPlotoftwoSeries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
18 LinearRegressionforDifferentQuantiles . . . . . . . . . . . . . . . . . . . . . . . . . . 56
19 PercentageofEigenvaluesAttributabletoEachComponent . . . . . . . . . . . . . . . 59
20 Time-seriesPlotofResiduals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
21 HistogramofResiduals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
22 RegressionResidualsandFittedSeries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
23 PlotoftheParameterStabilityTest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
24 GraphComparingtheStaticForecastswiththeActualSeries . . . . . . . . . . . . . . . 87
25 GraphComparingtheDynamicForecastswiththeActualSeries . . . . . . . . . . . . . 87
26 In-sample,Out-of-sampleandSimpleExponentialSmoothing . . . . . . . . . . . . . . 90
27 ImpulseResponses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
28 VarianceDecompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
29 VarianceDecompositionsforDifferentOrderings . . . . . . . . . . . . . . . . . . . . . 105
30 Actual,FittedandResidualPlot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
31 GraphoftheSixUSTreasuryInterestRatesSeries . . . . . . . . . . . . . . . . . . . . . 114
32 DynamicandStaticForecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
33 SmoothedStateProbabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
34 GraphoftheFittedValuesfromtheFailureProbitRegression . . . . . . . . . . . . . . 147
35 HistogramandtheProbabilityDensityFunctionoftheStandardNormalDistribution 165
36 HillPlot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
iv
Electronic copy available at: https://ssrn.com/abstract=3475303
List of Tables
1 GrangerCausalityWaldtests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
2 SimulatedAsianOptionPriceValues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
v
Electronic copy available at: https://ssrn.com/abstract=3475303
1 Getting started
1.1 What is Python?
Python is an open-source, high-level and interpreted programming language for various purposes.
Several libraries it provides have proved particularly useful for both financial industry practitioners
and academic researchers, and therefore the programming language has become increasingly popu-
lar.
Python has several strengths: first, it is user-friendly for programming beginners. Learners do
not need to spend too much time on its syntax because the language is simple and very concise,
meaningthatthecodeishighlyefficientandmuchcanbeachievedinjustafewlinescomparedwith
otherlanguages. Second,itprovidesextensivesupportlibraries,webservicetools,stringoperations,
panel data analysis, etc. Most frequently used programming tasks have already been scripted and
users can easily import them for their own purposes. Finally, it is free of charge and thus open to
everyone. UserscaneasilystepintostatisticalanalysisbyimplementingcodeinPython.
Mostrelevantforourpurposes,Pythoncanalsoimplementmanydifferentstatisticalandecono-
metric tests. StatsModels is a powerful Python library to conduct many statistical tests, and in this
guideitwillbeusedfrequently.
NotethatthisguideisbasedonPythonversion3.6. However,therearesignificantdifferencesbe-
tweenversion2.7andversions3.5andabove. IfyouusetheearlierversionofPython(2.7),thesyntax
aswellascertainmodulesitprovidesaredifferent. Moreover,asPythonisanopen-sourceprogram-
ming language and has many libraries or packages updated frequently, some functions might no
longerbesupportedormayhavemovedtoothermodulesinfutureversions.
This section assumes that readers have successfully set up an environment and downloaded the
Pythonsoftwareontoanavailablecomputer. ThereareanumberofwaystoimplementPythoncode.
NotethatthisbookimplementsallexamplecodeinJupyterNoteBookviaAnaconda.1 Alternatively,
youcanchoosePyCharm,Spyderandetc. dependentonyourownpreferences. Spyder,forexample,
is also a popular Python environment that is available through Anaconda, but it is not interactive,
meaning that you write the code and then run it with the output appearing in a different window.
Therearenodifferencesbetweentheseenvironmentsintermsofthesyntaxitself,however.
Agood wayof familiarisingyourself withPython isto learnabout itssyntax andgo throughthe
examples given in this guide. There now follows a presentation of the fundamentals of the Python
package, together with instructions on how to achieve standard tasks and sample output. All ex-
ample code is given, with different colours highlighting different parts of the code. A number of
comments and explanations along with this code will hopefully make it easier to understand. Ad-
ditionally, it is noteworthy that Python has a strict rule for naming variables. For example, variable
names must start with a letter or underscore, any phrase variable must be integrated by an under-
score instead of adding blank in between, and it is also CASE-SENSITIVE. Thus, it is important to
entercommandsexactlyastheexampleshowsinordertoavoidunnecessaryerrors.
Finally,itisworthmentioningthattheaimofthisbookistohelpfinancestudentsandresearchers
who are new to Python to quickly master the basic syntax and knowledge to enable them to imple-
ment various applications of econometric tests. Since the core of Python is not a specialist econo-
metricprogramminglanguagelikeRorSTATA,somestatisticaloutputlooksverypreliminaryanda
number of econometric tests are not yet developed or tested in Python. To cover as many examples
from Introductory Econometrics for Finance as possible, we attempt to design some functions to com-
pletethesetests. Undoubtedly,thereisstillconsiderableroomtoimprovethecodeandnodoubtthe
outcomescouldhavebeenachievedindifferentways.
1Jupyterisanopen-source,web-based,interactivetoolforimplementingthePythonlanguage. Youcaneitherdown-
loadJupyterdirectlyoraccessitbyinstallingtheAnacondaplatform.
1
Electronic copy available at: https://ssrn.com/abstract=3475303
1.2 Different ways to run Python code
Unlike other statistic software, there are a number of ways to run Python code. The simplest way
to write and execute Python code is via the Python console. Assuming that the reader has installed
Python on a Windows-based computer, to open the console/terminal, we click on Start and type
’cmd’inthesearchengine. ThenhittingENTERleadstheWindowssystemtolaunchanewinterface
(Figure 1). Next, we type ’Python’ and press ENTER, in which case the Python console opens. We
cannowdirectlywriteandexecutecodehere.
Figure1: OpeningthePythonConsole
Alternatively,youcanwriteyourcodeinaneditorandexecuteitfromtheconsole. Forexample,we
can first open a Notepad++ file and write the command line print("Hello World"), saving the file as
name of program.py. Then we repeat the procedure as stated above. Click Start, search for ’cmd’
and press ENTER. You need to navigate the Python console to where you have saved the file (in
thiscase,wehavesavedthefileontheDesktop). Writethefollowinglinetoexecutetheprogramme
(Figure2).
Figure2: RunningCodefromtheConsole
However, it is usually more convenient to implement Python code using an IDE (Integrated Devel-
opment Environment). In this book, we use ’Anaconda’, which will first need to be downloaded.2
Oncethesoftwareisonthecomputer,clickonStart,searchfor’Anaconda’andopentheprogramme
’Anaconda Navigator’. As you can see in Figure 3, Anaconda is a collection of software packages.
There are several applications that can be launched such as the Jupyter NoteBook, Spyder, etc. For
2Anacondacanbedownloadedfromhttps://www.anaconda.com/download/
2
Electronic copy available at: https://ssrn.com/abstract=3475303
the purpose of better presenting code in this book, we choose the Jupyter NoteBook because it is
designedasanopen-sourceWeb-based,interactivecomputingapplication.3
Figure3: OpeningtheAnacondaNavigator
We now step into how to use Jupyter NoteBook. To launch this application, click the Launch button
below the icon (highlighted by a red circle). Anaconda then takes a few seconds to open a web page
(Figure 4). You can see a number of folders on the main screen. Choose a folder as the directory for
the Python code. For instance, we can click on the folder Desktop and then create a new script by
clicking the button New. In the drop-down menu, click Python 3. Jupyter then creates a new web
pagewherethecodecanbewrittenandexecuted. ThedetailofhowtouseJupyterwillbepresented
inthenextsection.
3NotethatreadersneedtodownloadAnacondawithcautionsince,asstatedabove,therearetwodifferentversions.
OneisforPython2.7,andtheotherisforPython3.x. WewillmainlyfocusonthePython3.xversion.
3
Electronic copy available at: https://ssrn.com/abstract=3475303
Figure4: OpeningaJupyterNoteBook
4
Electronic copy available at: https://ssrn.com/abstract=3475303