Without knowing the rest of your profile, it's impossible to gauge the marginal signal value of taking analysis for a grade. I'd suggest posting that to get better feedback.
I plan to apply to the top 10 Finance PhD programs and to the HBS BusEcon program this December. I have not taken Real Analysis for a grade (Audited). Which one of the following would you recommend for me to take this summer?
Advanced Econometrics at LSE: Module 1: Main Regression. Topics to include: Principles of Estimation (Ordinary Least Squares, Generalized Least Squares and Maximum Likelihood Estimation with Micro-Econometric applications); Principles of Testing (t- and F-test; Wald, Likelihood Ratio, Lagrange Multiplier Testing Principles). Time Series: Basic Time Series Processes; Stationarity and Nonstationarity - Unit roots and Cointegration; Vector Autoregressions. Module 2: Estimation Methodology. Topics to include: Endogeneity in linear regression models; Instruments; 2SLS estimator and Generalized IV estimator; Simultaneous equations. Motivation, definition and asymptotic properties of GMM estimator; Efficient GMM estimation; Over-identifying restrictions. Introduction to Panel Data Models: Fixed effect and random effect models. Dynamic Panel Data Model. Arellano-Bond Estimator. Introduction to Quantile Estimation
Mathematics for Economists PhD level course at top 20 US B-School: Linear algebra, Differential calculus, The implicit function theorem, Quadratic forms Convex sets and concave functions, Unconstrained optimization, Method of Lagrangian Multipliers, Kuhn-Tucker Theorem, Parametric analysis: envelope theorem and comparative statics, Quasiconcavity and pseudoconcavity, Lagrange and Kuhn-Tucker revisited, Homogeneity and Homotheticity
OR pick two of the following Stanford Summer Courses:
MATH 115 Functions of a Real Variable: The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology.Thanks!
STATS 217 Introduction to Stochastic Processes: Discrete and continuous time Markov chains, poisson processes, random walks, branching processes, first passage times, recurrence and transience, stationary distributions. Non-Statistics masters students may want to consider taking STATS 215 instead.
STATS 242 Algorithmic Trading and Quantitative Strategies: An introduction to financial trading strategies based on methods of statistical arbitrage that can be automated. Methodologies related to high frequency data and stylized facts on asset returns; models of order book dynamics and order placement, dynamic trade planning with feedback; momentum strategies, pairs trading. Emphasis on developing and implementing models that reflect the market and behavioral patterns.
I agree with OneArmed. All three options are good. For me, it would mostly be a question of where I wanted to spend my summer. Academically I would rate 1>3>2, but it all really comes down to how your profile looks, what your research interests are, and how these courses can complement that...
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