Spatial Statistics and Spatial Econometrics

By Prof. Gaurav Arora   |   IIIT Delhi
Learners enrolled: 537
The purpose of this course is to introduce the analytical framework for analyzing spatial data and its target audience are students from social sciences (specifically, economics, political science and cognitive psychology), engineers, earth and geosciences, and applied physics. In the past decade or so, much interest has grown in the area due to readily-available spatially-delineated data, particularly when in 2008 the U.S. Geological Survey stopped charging for its high-resolution LANDSAT archive. However, modeling spatial data and spatial relationships necessitate the use of analytic tools beyond the standard statistical methods such as the ordinary least squares. Characterisation of spatial autocorrelation in spatial datasets for the purpose of statistical inference and statistical prediction is a focus of this course. In addition, we will ask: how and why does spatial autocorrelation arise; how is it measured and understood; how does it relate to issues of spatial heterogeneity and spatial dependence; and how these factors inform the specification and estimation of regression models. Specific modeling techniques include spatial autocorrelation measures (Moran's I, Geary's C, Variogram and Kriging estiators) and spatial regression models.

INTENDED AUDIENCE: Students of physical, computation and social sciences who are interested in characterizing and modeling the spatial dimension in modern datasets and conduct statistical inference for real-world applications, including (but not restricted to) natural resource management, LULC change models, inventory management,

PREREQUISITES: Students should have the knowledge of basic probability and statistics, linear algebra and differential calculus

INDUSTRY SUPPORT: Major consulting firms like Deloitte, PwC, McKinsey and Co. etc., specifically for the purpose of risk analysis and management. In addition, the IT sector, Geospatial industry, and several other industrial sectors value the knowledge of spatial data analysis.
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Humanities and Social Sciences
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 25 Jul 2022
End Date : 14 Oct 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 29 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Introduction to spatial data and spatial models: Geostatistical data; Lattice sata; and Point data.
Week 2: Stationarity and Ergodicity of spatial random process.  
Week 3: Characterising Spatial Autocorrelation: Variaogram, Semi-variaogram; Covariogram and Correlogram. Fitting a Variogram: Miminum Norm Quadratic Estimation; Generalized Least Squares Estimation; Maximum-likelihood and Restricted Maximum-Likelihood Estimation.
Week 4: Characterising Spatial Autocorrelation: Variaogram, Semi-variaogram; Covariogram and Correlogram. Fitting a Variogram: Miminum Norm Quadratic Estimation; Generalized Least Squares Estimation; Maximum-likelihood and Restricted Maximum-Likelihood Estimation - Cont.
Week 5: Spatial Prediction: Stochastic approach and decision-theoretic considerations. Spatial Interpolation: Ordinary Kirging; Kriging with Spatial Covariance.
Week 6: Spatial Econometrics and Regional Science: Moving from characterization of spatial pattens to deducing explanatory factors and  inference. Spatial Dependence and Spatial Heterogeneity. 
Week 7: The formal expression of spatial dependence structures: Spatial contiguity matrix, generalized spatial weight matrix; and spatial lag operators.
Week 8: Spatial externalities: Spatial multipliers and spatial regression; Global and Local Moran's-I Statistics.
Week 9: Estimation and hypothesis testing: Maximum likelihood estimation with spatial dependece in the dependent variable and the model errors. Likelihood ratio test and Lagrange multiplier tests for spatial process models.
Week 10: Applications on ArcGIS (incl. ArcPy - Python for ArcGIS)
Week 11: Applications on ArcGIS (incl. ArcPy - Python for ArcGIS) - Cont.
Week 12: Applications on R.

Books and references

  1. Statistics for Spatial Data by Noel A. C. Cressie (Wiley-Interscience Publication)
  2. Sptaial Econometrics: Methods and Models by Luc Anselin (Kluwer Academic Press)
  3. Le Sage J. and Pace K. (2009) Introduction to Spatial Econometrics, Taylor and Francis/CRC.

Instructor bio

Prof. Gaurav Arora

IIIT Delhi
Gaurav Arora is an applied microeconomist with specialization in natural resource economics, agricultural economics, applied econometrics and remote sensing. As an empiricist, he enjoys developing and applying econometric models to tease out causal mechanisms that are rooted in the microeconomic theory for decision problems at the intersection of agricultural production and natural resource management. He is also keenly interested in the integration of social sciences and natural sciences, more particularly economics among the social science disciplines, and agronomy and earth sciences among the natural science disciplines. He is a recipient of the Faculty Research Fellowship (2020-2022) at IIIT-Delhi; the James R. Prescott scholarship (2016) for outstanding creativity in research at Iowa State University (ISU); and the Earl O. Heady Fellowship (2012) for academic excellence at ISU. He obtained PhD in Economics from Iowa State University, M.S. in Agricultural and Resource Economics from the University of Arizona, and Bachelor of Technology in Environmental Engineering from Indian School of Mines, Dhanbad

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 29 October 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIIT Delhi .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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