Advanced Econometric Modeling

Advanced Econometric Modeling

Advanced Econometric Modeling is an online and instructor led course by Muhammad Anees, Assistant Professor and Senior Econometrician at An Economist. The course aims at introducing the recent and recently appearing trends in Econometrics Methods and Application with real world examples to enable our young PhD scholars and faculty members to adopt and apply the methods.

Apply For AdmissionSee Course Contents

Course Objectives

Econometric Modeling

Understanding the mathematical theory behind modern econometric methods
Problems Solving

Identification of issues and problems in traditional econometric methods
Skills Development

Developing a research skill set to apply advanced econometric modeling
Writing Effectively

Writing effective research reports based on the evidence from world data analysis.
Statistical Softwares

Learning new software beyond conventional econometric tools like RATS, GAUSS and JMulti.
Independent Research

Become independent researchers in the area of Economics and Finance

Learning Outcomes

Understand Econometric Models

Application and Understanding of complex econometric methods to real world cases
Apply Econometrics Theory

Develop independent research skills based on application of relevant econometric modeling.
Estimation without Help

Estimate models with complexity without needs for further guidance and notes
Effective and High Impact Writing

Write effective research reports based on the estimated econometric models
Research Publication

Learn best practices in publication of high impact research and policy papers
Softwares Use and Programming

Predict and forecast economic and financial with any software using any data

Selected Topics Covered In the Course

The following is a tentative list of the topics covered in the course. You can add your own topics to the course contents when you enroll in the private mode of the course to ensure you learn and apply your desired topics to analyse your data and write your reports.
Selected Topics in Advanced Econometric Modeling
Unit Root, Structural Breaks, VAR, VECM, Structural VAR, Structural VECM and Structural Cointegration.
Nonlinear Unit Roots, Cointegration with Multiple Known Breaks, Nonlinear Cointegration
Asymmetric Unit Root, Causality with I(2) Variables and Causality and Causality with Structural VAR
Cointegration with Multiple Unknown Breaks, Causality Test with Multiple Unknown Breaks
Add you desired topics to the list here.
Wavelet Analysis of Economic and Financial Time Series and Economic Variables with High Frequency
Frequency Domain Analysis of Financial and Economic Time Series Data
Generalized SEM for Panel Data, Nonlinear SUREG, 3SLS Models and Nonlinear Equations and DSFE using Stata

Who Should Attend This Course?

If you need further information about our course, please click here


Master and PhD Students in Economics, Finance and Social Sciences

Faculty Members

All faculty members in Economics, Finance and Social Sciences


All business professionals who are using predictive models for decision making


Econometrics Research that can be included on their LinkedIn profiles directly from the certificate validation link. The certificates will be published through a private link as well on An Economist to help you add your research skills developed during the class projects to showcase the quality of work and assessment.

Registration Details

Register for the course in Advanced Econometric Modeling today. Read the auto-response and wait for the customized email from Professor Anees. You will be assisted in person to proceed and confirm your admission.

Apply For Admission HereCheck Course Contents

Examination and Assessment of Econometric Modeling Course

Each candidate of the course will be evaluated based on writing a high impact research article or thesis. At the end of the course, it is expected that each student would have been able to write a high quality publishable research papers to be submitted for high quality and higher ranked journals on top ranked publishers only.
Apply for AdmissionCourse Contents

Econometrics Modeling

Feedback and Sample Video Tutorial

Read how our students feel about our courses and see a small video tutorial of the course delivery
I was not confident to select and apply any econometric model. AEM helped me confide in my skills in Econ. Modeling.
Daniel Soberson - PhD Finance, Germany

Submit Application For Admission Now

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Cointegration Test Including Multiple Breaks Using GAUSS

In this tutorial on Cointegration Test Including Multiple Breaks Using GAUSS, we will show usng GUASS how to estimate cointegration tests with multiple breaks. Abdulnasser Hatemi-J has written an excellent paper titled: Tests for cointegration with two unknown regime shifts with an application to financial market integration which describes the methodology of Cointegration Test Including Multiple Breaks and we have used his written code available here. The abstract of the paper is quoted here:

It is widely agreed in empirical studies that allowing for potential structural change in economic processes is an important issue. In existing literature, tests for cointegration between time series data allow for one regime shift. This paper extends three residual-based test statistics for cointegration to the cases that take into account two possible regime shifts. The timing of each shift is unknown a priori and it is determined endogenously. The distributions of the tests are non-standard. We generate new critical values via simulation methods. The size and power properties of these test statistics are evaluated through Monte Carlo simulations, which show the tests have small size distortions and very good power properties. The test methods introduced in this paper are applied to determine whether the financial markets in the US and the UK are integrated.

Cointegration Test Including Multiple Breaks Using GAUSS can be replicated using the following video tutorial or simply follow the steps:

Congratulations on running your Cointegration Test Including Multiple Breaks Using GAUSS. For learning specific module in Applied Econometrics Research using GAUSS, please enroll for a course here.

Video on Cointegration Test Including Multiple Breaks Using GAUSS

Download Economic Data using Excel

In this video tutorial, we will explain how to Download Economic Data using Excel in one minute. The data can be downloaded from various sources like World Bank, International Monetary Fund and other data providers through Knoema Addin in Excel. The Knoema addin is one of the best and most easy tool to Download Economic Data using Excel. You can download economic, financial, trade, political and data on other related topics.

Download Economic Data using Excel

Follow these steps to Download Economic Data using Excel from Knoema using Excel.

The following video tutorial is only recorded to help you do the above practical in simple sessions. You can request us for custom download of any Economic and Financial data. We are happy to provide both free and paid support in making data availability from different sources. Watch the video tutorial now.

To request private courses in Data Analysis, click here.

Phillips-Ouliaris Cointegration Test

In this short tutorial in Eviews, we would explain the basic steps of conduting Phillips-Ouliaris Cointegration Test. To run Phillips-Ouliaris Cointegration Test in Eviews, we will need to ender the data as dated frequency and panel structure. Theoretically, the Phillips-Ouliaris Cointegration Test can found well explained in P. C. B. Phillips and S. Ouliaris (1990): Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica 58, 165–193 which can be downloaded here.

Phillips-Ouliaris Cointegration Test

To run Phillips-Ouliaris Cointegration Test in Eviews, open Eviews and follow the steps below:

The following video tutorial explains the above steps to help replication be more convenient. If you would like to learn more about Applied Econometrics Research using Eviews, check our private and instructor led courses here.

Structural VAR using JMulti

Structural VAR using JMulti is A Video Tutorial By Econometrician during the online course in Applied Econometrics Research. In this video tutorial, we demonstrate the key steps in running Structural VAR using JMulti. The estimation and setting up of structural var is one of the main problem for all who wish to explore VAR models with structural changes in the system. Before following the steps, download JMulti here.

Structural VAR using JMulti

To estimate Structural VAR using JMulti, follow the steps:

It is assumed that basic theory of SVAR is clear to the users. To learn more and details of theory, one can request a complete Instructor Led Private Course in Applied Econometrics Research Here.

Free Sample Freelance Project Proposal

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I would be happy help you get a 100% satisfaction through the following process of our working:
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I am professionally trained and the highly recogized online course provider in Stata, Eviews, SPSS, Nvivo10/11, WinRATS, SAS, GAUSS, Gretl, Minitab, C++, JavaScript and Python. I helped more than 300 clients from around the world in applied econometrics and statistics for corporate governance, financial performance, economics research, business evaluation, Value at Risk, Options Pricing, Stock Evaluation, Pairs Trading and Backtesting through the use of above statistical softwares. It is backed by my education in economics, statistics and econometrics from The University of Sheffield, UK.
I have a teaching and academic research experience of more than 11 years at a QS Ranked University. I teach modules in Economics, Statistics, Econometrics and Quantitative Analysis. Key themes and topics of my teaching are Qualitative Data Analysis, Factor Analysis, Principle Component Analysis, Power and Sample Size determination for Survival Studies, Analysis of Open ended surveys and interviews, Multivariate Time Series techniques in VAR/VECM, VARX, SVAR, Multivariate GARCH, ARDL and Bayesian Multivariate Time Series Methods. So far, more than 70 PhD and MS/MRes candidates completed their courses in Applied Econometrics and Applied Statistics under my supervision.
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Assistant Professor
Founder Econometricians Club
Founder AnEconomist
Founder Stata Pro Help

Tests for Autocorrelated Errors

In ordinary least square regression model, we specify the equation as
y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + ut
and we can test the assumption of autocorrelation or we can test whether the disturbances are autocorrelated.
To test the autocorrelation, we can follow the steps below:
(i) Estimate the regression model above using ordinary least square approach/OLS:
sysuse auto, clear
gen t=_n
tsset t
reg price rep78 trunk length
. reg price rep78 trunk length
Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(3, 65)        =      6.42
Model |   131790806         3  43930268.8   Prob > F        =    0.0007
Residual |   445006152        65   6846248.5   R-squared       =    0.2285
-------------+----------------------------------   Adj R-squared   =    0.1929
Total |   576796959        68  8482308.22   Root MSE        =    2616.5
price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
rep78 |   578.7949   348.6211     1.66   0.102    -117.4495    1275.039
trunk |  -31.78264   108.8869    -0.29   0.771    -249.2447    185.6794
length |   70.17701   22.01136     3.19   0.002     26.21729    114.1367
_cons |  -8596.181   3840.351    -2.24   0.029    -16265.89   -926.4697

(ii)  Now calculate the residuals from the above regression:
predict errors, res
(iii)  Run another regression by inserting lagged residuals or the lag values of error terms, (errors) as predicted from above regression model into a regression model of the residuals as a dependent variable. Our regression model will be estimated through the following regression code in Stata: reg errors rep78 trunk length l.errors. We can consider this regression as auxiliary regression. The results from this auxiliary regression is given below
. reg errors rep78 trunk length l.errors
Source |       SS           df       MS      Number of obs   =        63
-------------+----------------------------------   F(4, 58)        =      4.66
Model |   104717963         4  26179490.9   Prob > F        =    0.0025
Residual |   325759819        58   5616548.6   R-squared       =    0.2433
-------------+----------------------------------   Adj R-squared   =    0.1911
Total |   430477782        62  6943190.04   Root MSE        =    2369.9
errors |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
rep78 |  -47.23696   332.1243    -0.14   0.887    -712.0559     617.582
trunk |   62.68025   103.8779     0.60   0.549    -145.2539    270.6144
length |   9.373147   20.97416     0.45   0.657     -32.6112    51.35749
errors |
L1. |   .5273932   .1225638     4.30   0.000      .282055    .7727313
_cons |  -2375.671   3741.339    -0.63   0.528    -9864.774    5113.432

(iv) Using the estimated results from auxiliary regression above, note the the R-squared value and multiply it by the number of included observations:
scalar N=_result(1)
scalar R2=_result(7)
scalar NR2= N*R2
scalar list N  R2  NR2
N =         63
R2 =  .24325986
NR2 =  15.325371

(v)  Now, the null hypothesis of BP test is that there is no autocorrelation, we can use the standard Chi-Square distribution to find the tabulated values of the Chi-Square to check if the null hypothesis of no autocorrelation needs to be rejected. According to theory, the Chi-Square statistic calculated using the NRSquare approach above, the test statistic NR2 converges asymptotically where degrees of freedom for the test is s which the number of lags of the residuals included in the auxiliary regression and we have included 1 lagged value of errors/residuals so degrees of freedom in this case is 1. We can use Stata conventional functions for distribution to determine the tabulated values at 5% level of significance using the following code:
scalar chi151=invchi2tail(1, .05)
scalar list chi151
chi15 =  3.8414598
We got from the above tutorial in tests for autocorrelation, NR2 = 15.325371 > 3.84 = Chi-Square (1, 5%). As the calculated value of Chi2 is greater than tabulated values of Chi2, so we reject the null hypothesis of no autocorrelation on the disturbances.

Selected Resources to Learn Economics and Econometrics In Short Time

The selected resources to learn economics and econometrics in short time is presented here. These are the resources which we will have to refer most of the times when we begin learning economics or economics. The selection of resources to begin the study of economics and economists matters a lot and hence selecting the best set of books, software manuals, blogs and tutorials and related materials provides a strong foundation towards understanding of economics and economics in a recommended level. Welcome to An Economist selected resources to learn Economics and Econometrics in short time.


Micro Economics

Consumers, firms, and general equilibrium:
Arne Hallam (Iowa State), Microeconomics
Nolan Miller (Harvard), Lecture Notes on Microeconomic Theory
Robert Nau (Duke), Seminar in Choice Theory
Sten Nyberg (SSE), Advanced Microeconomics
Ariel Rubinstein (Tel Aviv), Lecture Notes in Microeconomic Theory: The Economic Agent
Max Stinchcombe (Texas), Single-Person and Multi-Person Decision Theory
Guoqiang Tian (Texas A&M), Microeconomic Theory
Nicholas Yannelis (Illinois), Lecture Notes in General Equilibrium Theory

Game theory and mechanism design:

Wayne Bialas (SUNY Buffalo), Game Theory
Bernard Caillaud (ENPC) / Benjamin Hermalin (Berkeley), Hidden Action and Incentives
Bernard Caillaud (ENPC) / Benjamin Hermalin (Berkeley), Hidden-Information Agency
Yongmin Chen (Colorado), Microeconomic Theory II
Peter Cramton (Maryland), Advanced Microeconomics
Christian Ewald (St Andrews), Games, Fixed Points and Mathematical Economics
Douglas Gale (NYU), Strategic Foundations of General Equilibrium
Benjamin Hermalin (Berkeley), Lecture Notes for Economics
Paul Klemperer (Oxford), Auctions: Theory and Practice
Levent Koçkesen (Columbia), Advanced Microeconomic Analysis I
Martin Osborne (Toronto) / Ariel Rubinstein (Tel Aviv), Bargaining and Markets
Jim Ratliff (prev. Arizona), Graduate-Level Course in Game Theory
Francesco Squintani (UCL), Notes for Non-Cooperative Game Theory
Max Stinchcombe (Texas), Dynamics and Learning
Max Stinchcombe (Texas), Notes for a Course in Game Theory

International trade:

Pol Antras (Harvard), Advanced Topics in International Trade
Donald Davis (Columbia), Notes on Competitive Trade Theory
István Kónya (Boston College), Lecture Notes in International Trade
Edward Leamer (UCLA), Sources of International Comparative Advantage
James Markusen et al. (Colorado), International Trade: Theory and Evidence
Applied and computational micro / other topics in micro:
Daron Acemoglu (MIT), Lecture Notes in Graduate Labor Economics
Ted Bergstrom (UC Santa Barbara), The Theory of Public Goods and Externalities
Christopher Carroll (JHU), Solution Methods for Microeconomic Dynamic Stochastic Optimization Problems
Alan Duncan (Nottingham), Labour Economics I & II
Bryan Ellickson (UCLA), General Equilibrium and Finance
Ariel Rubinstein (Tel Aviv), Economics and Language
Ariel Rubinstein (Tel Aviv), Modelling Bounded Rationality
David Zilberman (Berkeley), Economics & Policy of Production, Technology and Risk in Agricultural & Natural Resources


Various models:

Willem Buiter (Cambridge), Lectures on Really Useful Ad Hoc Macroeconomics
John Driscoll (Fed), Lecture Notes in Macroeconomics
Brian Krauth (Simon Fraser), Macroeconomic Theory
Roland Meeks (Oxford), Economic Growth
Gregor Smith (Queen's), Macroeconomics Lecture Notes
Paul Söderlind (St Gallen), Macro II
Stephen Williamson (WUSTL), Notes on Macroeconomic Theory
Recursive (dynamic programming) treatments and dynamic methods:
Chris Edmond (NYU), Advanced Macroeconomic Techniques
Jeremy Greenwood (Rochester), Lecture Notes on Dynamic Competitive Analysis
Nezih Guner (Penn State), Advanced Macroeconomic Theory
Lars-Peter Hansen (Chicago) / Thomas Sargent (NYU), Recursive Models of Dynamic Linear Economies
Lars-Peter Hansen (Chicago) / Thomas Sargent (NYU), Robustness
John Hassler (Stockholm U), Math II (Dynamic Systems)
Christopher House (Michigan), Macroeconomics II
David Kendrick (Texas), Stochastic Control for Economic Models
Miles Kimball (Michigan), Advanced Mathematical Methods for Macroeconomics .doc
Ian King (Auckland), A Simple Introduction to Dynamic Programming in Macroeconomic Models
Paul Klein (Western Ontario), Solving the Growth Model by Linearizing the Euler Equations
Dirk Krüger (Frankfurt), Macroeconomic Theory
Dirk Krüger (Frankfurt), Quantitative Macroeconomics: An Introduction
Per Krusell (Princeton), Lecture Notes for Macroeconomics I
Lars Ljungqvist (SSE) / Thomas Sargent (NYU), Recursive Macroeconomic Theory .ps
Rody Manuelli (Wisconsin), Notes on Discrete Time Economic Models: The Growth Model
Rody Manuelli (Wisconsin), Topics in Macroeconomics: An Introduction to Stochastic Calculus
Maurice Obstfeld (Berkeley), Dynamic Optimization in Continuous-Time Economic Models I & II
Nicola Pavoni (University College), Notes on Dynamic Methods in Macroeconomics
Shouyong Shi (Toronto), Macro Theory I
John Stachurski (Melbourne), Stochastic Economic Dynamics
Nancy Stokey (Chicago), Brownian Models in Economics
Stijn Van Nieuwenburg (NYU) / Pierre-Olivier Weill (NYU), Exercises in Recursive Macroeconomic Theory
Randall Wright (Penn), Macroeconomics
Asset pricing, financial economics and financial mathematics:
Christian Ewald (St Andrews), Discrete-Time Finance
Christian Ewald (St Andrews), Mathematical Finance: Introduction to Continuous-Time Financial Market Models
Robert Kohn (NYU), Continuous-Time Finance
Antonio Mele (LSE), Lecture Notes in Financial Economics
Steven Shreve (Carnegie Mellon), Stochastic Calculus and Finance
Tyler Shumway (Michigan), Introduction to Finance
Tyler Shumway (Michigan), Introduction to Continuous-Time Asset Pricing
Paul Söderlind (St. Gallen), Financial Theory I & II
A.W. van der Vaart (Vrije U), Financial Stochastics
A.W. van der Vaart (Vrije U), Martingales, Diffusions, and Financial Mathematics

Other macro and computational methods:

Miles Kimball (Michigan), Q-Theory and Real Business Cycle Analytics
Miles Kimball (Michigan), Real Business Cycle Theory: A Semiparametric Approach
Dirk Krüger (Frankfurt), Dynamic Fiscal Policy
Dirk Krüger (Frankfurt), Consumption and Saving: Theory and Evidence
Eric Leeper (Indiana), Bundesbank Mini-Course on Monetary Economics
Stephanie Schmitt-Grohe (Duke) / Martin Uribe (Duke), International Macroeconomics
Shouyong Shi (Toronto), Topics in Monetary Theory
Paul Söderlind (St Gallen), Macroeconomic and Financial Forecasting
Paul Söderlind (St Gallen), Empirical Macroeconomics
Paul Söderlind (St Gallen), Monetary Policy
Harald Uhlig (Humboldt U Berlin), A Toolkit for Analyzing Nonlinear Stochastic Models Easily
Martin Uribe (Duke), Lectures in Open Economy Macroeconomics


Probability and mathematical statistics:

Richard Bass (Connecticut), The Basics of Financial Mathematics
Graham Brightwell (LSE), Probability for Finance and Economics
Robert Gray (Stanford), Probability, Random Processes, and Ergodic Properties
Charles Grinstead (Swarthmore) / Laurie Snell (Dartmouth), Introduction to Probability
Rachel Fewster (Auckland), Statistical Theory
Arne Hallam (Iowa State), Econometrics I
Guido Imbens (UCLA), Probability and Statistics
Oliver Knill (Harvard), Probability
Daniel McFadden (Berkeley), Statistical Tools
D.S.G. Pollock (Queen Mary College), Lectures in Mathematical Statistics
S.R.S. Varadhan (NYU), Probability Theory
S.R.S. Varadhan (NYU), Stochastic Processes
Ivan Wilde (King's College London),  Measure, Integration & Probability
Robert Wolpert (Duke), Probability and Measure Theory

Econometrics (general):

Herman Bierens (Penn State), Econometrics Lecture Notes
Erik Biorn (Oslo), Econometrics - Advanced
Michael Creel (Barcelona), Graduate Economics Lecture Notes
Bruce Hansen (Wisconsin), Econometrics
Daniel McFadden (Berkeley), Econometrics
Ariel Pakes (Harvard), Advanced Applied Econometrics
Ariel Pakes (Harvard) / Oliver Linton (LSE), Nonlinear Methods for Econometrics
D.S.G. Pollock (Queen Mary College), A Course of Econometrics
D.S.G. Pollock (Queen Mary College), Introductory Econometrics
D.S.G. Pollock (Queen Mary College), Topics in Econometric Theory
Paul Söderlind (St. Gallen), Lecture Notes for Econometrics

Macroeconometrics (time series) / financial econometrics:

John Cochrane (Chicago), Time Series for Macroeconomics and Finance
D.S.G. Pollock (Queen Mary College), The Methods of Time Series Analysis
Paul Söderlind (St. Gallen), Lecture Notes in Financial Econometrics
A.W. van der Vaart (Vrije U), Time Series
Microeconometrics and other econometrics:
Alan Duncan (Nottingham), Cross-Sectional and Panel Data Econometrics
Stepan Jurajda (Charles U), Econometrics of Panel Data and Limited Dependent Variable Models
James LeSage (Toledo), Spatial Econometrics
Charles Manski (Northwestern) / Daniel McFadden (Berkeley), Structural Analysis of Discrete Data and Econometric Applications
Kenneth Train (Berkeley), Discrete Choice Methods with Simulation
Melvyn Weeks (Cambridge), Advanced Econometrics: Microeconometrics


Mathematics for economists:

Julio Dávila (Penn), Mathematics for Economic Theory
Arne Hallam (Iowa State), Quantitative Methods in Economic Analysis
John Hillas / Dmitriy Kvasov (Auckland), Foundations of Economic Analysis
Michael Manove (Boston U), Mathematics for Micro
Markus Möbius (Harvard), Mathematics for Economists
Efe Ok (NYU), Real Analysis & Probability Theory with Economic Applications
Martin Osborne (Toronto), Mathematical Methods for Economic Theory
Guoqiang Tian (Texas A&M), Mathematical Economics
Viatcheslav Vinogradov (Charles U), A Cook-Book of Mathematics


Steve Alpern (LSE), Optimization Theory
Stephen Boyd (Stanford) / Lieven Vandenberghe (UCLA), Convex Optimization
Michael Burger (UCLA), Infinite-Dimensional Optimization and Optimal Design
Jan van den Heuvel (LSE) / Graham Brightwell (LSE), Optimization Theory
Robert Vanderbei (Princeton), Linear Programming: Foundations and Extensions
Pravin Varaiya (Berkeley), Lecture Notes on Optimization
Klaus Wälde (U Würzburg), Applied Intertemporal Optimization
Richard Woodward (Texas A&M), Dynamic Optimization

Linear algebra / calculus / differential equations

Alan Bain (prev. Cambridge), Stochastic Calculus
Michael Berry (Tennessee) et al., Templates for the Solution of Linear Systems
George Cain (Georgia Tech) / James Herod (Georgia Tech), Multivariable Calculus
William Chen (Macquarie), First-Year Calculus
William Chen (Macquarie), Linear Algebra
Ian Craw (Aberdeen), Advanced Calculus and Analysis
Lawrence Evans (Berkeley), An Introduction to Stochastic Differential Equations
John Friedlander / Peter Rosenthal (Toronto), Calculus Lecture Notes
Jonathan Goodman (NYU), Stochastic Calculus
Jim Hefferon (St. Michael's College), Linear Algebra
Robert Kohn (NYU), Partial Differential Equations for Finance
Thomas Kurtz (Wisconsin), Lectures in Stochastic Analysis
Lee Lady (Hawaii), Topics in Calculus
Keith Matthews (Queensland), Elementary Linear Algebra
Kaare Petersen / Michael Petersen (Technical U Denmark), The Matrix Cookbook
Dinakar Ramakrishnan (Caltech), Calculus, Number Theory & Vector Calculus
Klaus Schmitt (Utah), Nonlinear Analysis and Differential Equations
Ruslan Shapirov (Bashkir State U, Russia), Course of Linear Algebra and Multidimensional Geometry
Dan Sloughter (Furman), Difference to Differential Equations
Dan Sloughter (Furman), The Calculus of Functions of Several Variables
Gerald Teschl (Vienna), Ordinary Differential Equations and Dynamical Systems
Sergei Treil (Brown), Linear Algebra Done Wrong

Analysis / measure theory / topology:

Robert Anderson (Berkeley), Measure Theory
Douglas Arnold (Penn State), Complex Analysis
Douglas Arnold (Penn State), Functional Analysis
George Cain (Georgia Tech), Complex Analysis
William Chen (Macquarie), Fundamentals of Analysis
William Chen (Macquarie), Introduction to Complex Analysis
William Chen (Macquarie), Introduction to Lebesgue Integration
William Chen (Macquarie), Linear Functional Analysis
William Chen (Macquarie), Multivariable and Vector Analysis
Paul Garrett (Minnesota), Functional Analysis
Lee Larson (Louisville), Real Analysis Lecture Notes
Vitali Liskevich (Bristol), Measure Theory and Functional Analysis
Aisling McCluskey (York, Ca.) / Brian McMaster (York, Ca.), Topology Course Notes
Sidney Morris (Ballarat), Topology without Tears
Sylvia Serfaty (NYU), Functional Analysis Notes
Bert Wachsmuth (Seton Hall), Interactive Real Analysis
Elias Zakon (Windsor), Mathematical Analysis I

Mathematical game theory and logic, other math:

Stefan Bilaniuk (Trent), A Problem Course in Mathematical Logic
William Chen (Macquarie), Discrete Mathematics
William Chen (Macquarie), Congruences, Polynomials, and Group Theory
George Collins, II (Case Western), Fundamental Numerical Methods and Data Analysis
Germund Dahlquist (prev. RIT Sweden) / Ake Bjork (Linkoping), Numerical Mathematics in Scientific Computation
Thomas Ferguson (UCLA), Game Theory
Steven Pav (UCSD), Numerical Methods Course Notes
Stephen Simpson (Penn State), Mathematical Logic
Steven Sugden (Bond U, Australia), Discrete Mathematics
Michal Walicki (Bergen), Introduction to Logic


Alexandre Stevanov's Listing of Math Lecture Notes
Eric Weissenstein's Mathworld



Ian Cavers (UBC), An Introductory Guide to Matlab
Paul Fackler (North Carolina State), Matlab Primer
Edward Neuman (Southern Illinois University), Matlab Tutorials
Christian Roessler (Melbourne), Matlab Basics
Kermit Sigmon (Florida), Matlab Primer
Kermit Sigmon (Florida), Matlab Tutorial
Matlab Summary and Tutorial at Florida


Marc Nerlove (Maryland), Notes on GAUSS
Felix Ritchie (Trig Consulting), Guide to Programming in GAUSS
Mark Watson (Princeton), GAUSS Basics
GAUSS 5.0 User Guide at Aptech


Robert Yaffee (NYU), Getting Started with STATA for MS Windows: A Brief Introduction
STATA Tutorial at Princeton


Peter Flynn (Silmaril Consultants), A Beginner's Introduction to Typesetting with LaTex

Unit Root Tests, Publication Style Tables in Stata

There is commonly a question on many forums as to how can one test unit root of several variables and export the results of all these tests into a single file in Word or Excel sheet. To demonstrate in this tutorials, we will use Unit Root Tests, Publication Style Tables in Stata.
To help these querries, I have written the following simplest do file which you can use after modifiying for the relevant places like file_paths and variables_names. The code will do the job to test the variable for unit root or stationarity and compile the results from all the individual tests into a single table and export it to your desired format like MS Word or MS Excel sheet for further use and modifications. The steps in this tutorial will help you extend this do file to include many other tests like summary statistics to be exported into the same files.

***Step 1. Load the data, I have used the example location folder and files. You can change the path to your desired detination of the file/folder where your data exists.
use "E:\Dropbox\data.dta", clear

***Step 2. Now create a temporary files using
tempname anees_uroot
tempfile unitroots

***Step 3. Then you need to write to the temporary files as to what should be the names of the headers of the table. Also you need to specify which file to use and what to add to the file as headers.
postfile `anees_uroot' str12 name dfuller_statistic dfuller_pvalue dfuller_lags perron_statistic pperron_rho pperron_pvalue pperron_lags using `unitroots'

***Step 4. Load the variables. You can add as many variables as you wish or that you would like to use in reports. Replace the var_i with your real variables here.
foreach var of varlist var_1 var_2 var_3 var_4 {

***Step 5. This section conducts the tests. I have added simple ADF and PP tests for unit root. Please note, you should make sure the tests stores the r() to be exported.
dfuller `var'
local dfuller_statistic = r(Zt)
dfuller `var'
local dfuller_pvalue = r(p)
dfuller `var'
local dfuller_lags = r(lags)
pperron `var'
local perron_statistic = r(Zt)
pperron `var'
local pperron_rho = r(Zrho)
pperron `var'
local pperron_pvalue = r(p)
pperron `var'
local pperron_lags = r(lags)

***Step 6. Write theresults into the temporary files and close the section code.
post `anees_uroot' ("`var'") (`dfuller_statistic') (`dfuller_pvalue') (`dfuller_lags') (`perron_statistic') (`pperron_rho') (`pperron_pvalue') (`pperron_lags')

***Step 7. Close the post file as started above. You can now see the produced results in a tabular format to be copied right from Stata output window or use the next line of code to export the stored results into Excel etc.
postclose `anees_uroot'
use `unitroots'

***Step 8. Export the results to Excel and keep the the stored names for tests_values as variables headers. The first column named; Name will contain variable names.
export excel using "E:\Dropbox\Stata Unit Root Tests.xls", firstrow(variables) replace
***Step 9 Optional. Use the list command in Stata to see the results produced by above tutorial.

The full code should look like the following.
This tutorial was written for a online course in Time Series Econometrics. I have edited just the names of the variables from the output and codes. You can book your and get your Stata code as neat and clean as it should be possible.

Econometric Models Selection

In this simple outline on the issue of commonly raised douts on how to select an economic model, I would like to sum the issue in this 300 words article. Econometric Models Selection is one key problem for all. The model selection is based on the type of data and type of variables. Here, we mention an order following which helps an econometric model strategy development for us. We assume to use Panel data to develop econometric model selection strategy. Initially, to determine the right set of models, the nature of data structure for the panel data follows like this: A. Check data structure. 1. if N>T, then follows B series of steps. 2. If T>N, then follow the steps in C series.

If we assume the panel data has N sufficiently greater than T, then simple panel data or instrumental/GMM models for panel data can be achieved using the following order. This helps in Econometric Models selection looking into the key steps of the econometric analysis of the given panel data.

For Case 1, follow these steps.
B1. The first stepOLS
B3. Hausman
B4. Assumptions of RE or FE from B3.
B5. Endogeneity Tests
B6. Instrumental Regression
B7. GMM if seens dynamics/autocorrelation in B4.

If the data at hands is such that T is sufficiently larger than N, the panel time series structure will be evidenced and hence our econometric models selection strategy will follow the following procedures. The unit roots and cointegration is for panel time series data which are also sometimes considered as longer time panel data or longer panel data. In such cases, the time series properties in estimators are heavily observed and hence the steps to select an econometric models selection strategy will include these.
For Case 2, follow these steps
C1. Unit Root
C2. Cointegration