State Space Models

All state space models are written and estimated in the R programming language. The models are available here with instructions and R procedures for manipulating the models here here.

Sunday, October 20, 2013

A Random Walk Through Old Stockholm


On October 14, 2013 Eugene Fama, Lars Peter Hansen and Robert Shiller were jointly awarded the Nobel Prize in Economics. Each recipient's award was given for topics of interest to the Random Stock Walker: Fama for his work on the Efficient Market Hypothesis (EMH) which is closely related to the Random Walk Model; Hansen for his work on the Generalized Method of Moments (GMM) estimator (a semi-parametric model related to the non-parametric bootstrap); Shiller for his work on economic bubbles (his approach is closely related to Attractor Theory). The 2013 Nobel Prize in Economics is also interesting because the work of Fama and Shiller seem, on the surface, to contradict each other. In future posts, I'll discuss each researcher's work in detail (also see John Cochrane's blog, here, and the Noah Opinion blog, here, here, here, here, here and here). For right now, here is the Random Walker summary:
  • The strong-form of EMH asserts that all stock prices are a random walk because all information is immediately reflected in the stock price. The random walk is one of the models that is always tested by the Random Stock Walker, essentially as a null-model. Fama has been particularly critical of economic bubbles and Technical Analysis, arguing that in the short-run active management and fundamental analysis add nothing that isn't immediately available in the stock price.
  • The GMM estimator is semi-parametric in that normal theory is not required for every part of the model. The bootstrap is non-parametric and makes no assumptions about the mathematical form of the model error distribution.
  • Shiller used the ex-post rational price (the discounted sum of actual dividends) as the assumed attractor for a stock price. Shiller shows that the actual price varies a lot more than the ex-post rational price. This is a form of fundamental analysis which not only contradicts the EMH but also begs the question of what drives the ex-post rational price. The Random Stock Walker submits a collection of other fundamental models (business-as-usual, US economy, World System, Market Index, etc. along with the Random Walk) to multi-model inference using the Akaike Information Criteria rather than using probabilities drawn from the normal distribution.
From the Random Stock Walker perspective, this is the most interesting Nobel Prize in Economics. The implications for investing (favor low-fee index funds, invest for the long run) are important to understand but incomplete (how does the buy-and-hold strategy relate to stock market bubbles, particularly when the bubble pops just when you need retirement funds). The implications for economic theory are profound (are consumers and investors really profit maximizers or are they just trying to survive in a very uncertain world). The purpose of the Nobel Prize in Economics should be not just to reward achievement but also to draw our attention to a body of work that has important implications for the future development of economics. From the perspective of the Random Stock Walker, the 2013 Nobel Prize did all these things.

The title of this post is derived from a book by Burton Malkiel title A Random Walk Down Wall Street. The Nobel Museum is located in Old Stockholm at Stortorget 2, 103 16 in Stockholm, Sweden. Here's an appropriate if somewhat nerdy question: How long would it take you to find the Nobel Museum if you started at the Myntgatan bridge in Old Stockholm, flipped a coin and used the result to decide which way to turn at each interaction, that is, took a random walk through Old Stockholm?