The world that we live in, including our financial market place, is to a large extent non-linear in nature. Ironically, when we analyze financial data we often find ourselves reaching for a set of statistical tools that tend to be linear in scope. This is not surprising given the low signal to noise ratios found in financial data, as well as the single history of data we have to work with. Concerns over “data-snooping” and “over fitting” of data are well founded and this is especially true when it comes to the task of analyzing potential relationships between asset returns and possible market indicators. Although these concerns are well justified, they can also be crippling as valid signals may be hiding within one or more market indicators in systematic yet highly non-linear ways that standard statistical techniques simply cannot uncover.
This paper describes a set of statistical and graphical tools that can be used to identify statistically valid market signals in terms of arbitrarily complex and smooth functions of one to five indicator variables. By combining a particular type of non-parametric regression analysis with Newey-West style variance estimators, it is possible to construct valid t-statistic functions that can be used as market timing trading signals or as inputs into larger models. A Windows based statistical and graphical analysis package known as GlassBox is introduced as a feasible way to quickly conduct the type of analysis described in the paper. Given the voluminous output created by high dimensional smoothing, the ability to represent and quickly graph 1,000's of data points in a high dimensional space is of critical importance. GlassBox is capable of creating 5-D graphs that can be used to identify complex yet systematic patterns in the data. GlassBox also allows the user to graphically “drill down” into lower dimensional plots to assess levels of smoothness in terms of conditional 2-D and 3-D graphs. Taken together, the tools and methods described in this paper represent a powerful alternative to simple linear models, or models requiring other pre-imposed parametric assumptions.
Back