BrozOnBonds: Academic Corner — “Spatially” Biased Forecasting Models

Michael Williams
November 24, 2013

As noted by famed statistician and time-series econometrician George E.P. Box: "...all models are wrong, but some are useful".

This is certainly true when trying to formulate trading rules and prediction models that necessarily require us to assume that certain factors are held fixed. Our assumptions and compromises explicitly or implicitly defined within our models decimate their ability to predict in an absolute sense. Yet, by building better models, we are able to increase these models' relative prediction power and profit potential.   A recent paper by authors Hossein Asgharian, Wolfgang Hess, and Lu Liu (A Spatial Analysis of International Stock Market Linkages; Journal of Banking and Finance: 2013, Vol. 37-12, pg. 4738-4754) is an example of how using unique and innovative statistical techniques can lead to a new understanding of cross-market linkages. In this paper, Asgharian et al. study the contemporaneous dependence among 41 international equity market returns. While their paper is certainly not the first to explore issues of cross-market dependence, contagion, and avenues of potentially profitable arbitrage, they are some of the first to use "spatial analysis" techniques to account for non-linear interactions among financial markets.   Prior literature studying financial market dependence made use of "gravity models" which allow for a bilateral connection between two markets. Yet, the global financial system is made up of more than just two markets. Rather, it is a network of pair-wise interconnections among all the markets. This collection of bilateral interconnections among markets could lead to systemic behavior where a shock in one market has system-wide effects. These non-linear, multiple-path impacts make models of simple pair-wise interactions incomplete, likely biased, and hence unsuitable for use in developing profitable trading strategies.   Models accounting for the above-mentioned interconnectivity were originally developed for use in geographical statistical analysis. According to Tobler's First Law of Geography "Everything is related to everything else, but near things are more related than distant things" (W.R. Tobler A Computer Movie Simulating Urban Growth in the Detroit Region; Economic Geography: 1970, Vol. 46, pg. 234-240). An example of this law in practice would be in real estate where houses located next to each other are more likely (on average) to be more like another than two houses separated by great distance. To account for this effect, geographical statisticians construct and employ "weights matrices" that explicitly account for whether two objects are co-located in space (e.g. whether they are "neighbors"). Failing to do so would render traditional, non-spatial statistics invalid.   Back to the context of finance, the fact that global financial markets are interconnected in a vast web of interrelationships means that traditional statistical models, especially econometric forecasting models, may not be fully taking into account these interconnections. Further, any trading strategies from these inadequate models may be misspecified and potentially quite costly. It is with relief that Asgharian et al. point to a way that these shortfalls can be remedied.   Specifically, one should determine what exogenous "forces" may link a network of markets together. This link may be a description of a market's relative spatial location but could also include economic linkages (e.g. bilateral trade flows, cross-holdings of sovereign debt, common currency usage, etc.), and even generalized notions of financial market "distance" (e.g. cross-market transactions expenses, order execution latencies, and other forms of trading frictions). The only caveat on what could be considered as a "linkage" is governed by Tobler's Law. That is, any linkage is valid so long as "more distant" markets are "less related" and that the model makes good economic sense*. From there, spatial statistics can be estimated and be used to determine whether the "distance" among the markets plays any role in how those markets function and behave. Further, spatial econometrics models may be estimated that attempt to explain or predict future returns after, of course, accounting for these "distance" effects.   For a good primer on spatial statistics and econometrics, please refer to the E-Slides presented by Luc Anselin available from the Arizona State University's GeoDa Center for Geospatial Analysis and Computation.   Thus, very complex market interrelationships may be modeled and accounted for in time-series returns forecasting models using spatial statistical techniques. The benefit of doing so may be more accurate returns predictions and more profitable resulting trades.       * Note that some spatial econometricians suggest that using non-location-based weighting matrices may lead to biased results. These biases mainly arise from unintended non-linearities being incorporated into the model as well as an "endogeneity" issue where the dependent variable and the weight matrices are simultaneously determined (see, e.g. Steve Gibbons and Henry G. Overman's Mostly Pointless Spatial Econometrics?; Spatial Economics Research Centre: 2010, Discussion Paper no. 61). Thus, one should always be aware that more complicated models may actually be less parsimonious and worse at predicting future events than smaller, less sophisticated models.   1 The BrozOnBonds: Academic Corner is a periodic, educational piece intended to highlight recent academic work to the trading and investing community. These articles are authored by Dr. Michael Williams, an Assistant Finance Professor in the College of Business and Public Administration at Governors State University. Dr. Williams both teaches courses and conducts research on derivative assets and their markets. For more information, please contact Dr. Williams at or visit