Semi‐Parametric Generalized Additive Vector Autoregressive Models of Spatial Basis Dynamics

An extensive empirical literature addressing the behavior of prices over time and across spatially distinct markets has grown substantially over time. A fundamental axiom of economics--the "Law of One Price"--underlies the arbitrage behavior thought to characterize such relationships. This literature has progressed from a simple consideration of correlation coecents and linear regression models to classes of models that address particular time series properties of price data and consider nonlinear price linkages. In recent years, this literature has focused on models capable of accommodating structural change and regime switching behavior. This regime switching behavior has been addressed through the application of nonlinear time series models such smooth and discrete threshold autoregressive models. The regime switching behavior arises because of unobservable transactions costs which may result in discrete trade/no trade regimes or smooth, continuous transitions among different states of the market. As the empirical literature has evolved, it has applied increasingly exible models of regime switching. For example, Goodwin, Holt, and Prestemon (2012) applied smooth transition autoregressive models to consider regional linkages in markets for oriented strand board lumber products. Enders and Holt (2012) examined commodity price relationships using a series of overlapping smooth transition functions to capture structural changes and mean shifting behavior. This literature has also involved an evolution in the methods for statistically testing structural change and regime switching behaviors. Chow tests with known break points have evolved into tests of discrete and gradual mean shifting with unknown break points and variable speeds of adjustment among regimes. These tests address the widely recognized problems associated with nonstandard test statistics and parameters that may be unidentified under null hypotheses. In this paper, we propose a new class of semi-parametric models that accommodate mean shifting behavior in a vector autoregressive modeling framework. We view this approach as a natural next step in the evolution of nonlinear time series models of spatial and regional price behavior. To this end, we consider recent advances in semiparametric modeling that have developed methods for additive models that consist of a mixture of parametric and nonparametric components. Our vector autoregressive models adopt the "Generalized Additive Models" (GAM) estimation procedures Hastie and Tibshirani (1986) and Linton (2000). In particular, we use the backfitting and integration algorithms developed for GAM model estimation to incorporate a non-parametric mean shift in the linkages describing individual pairs and larger groups of market prices. Our empirical specification involves simple and vector error correction models that relate price differences to lagged values of prices and price differentials. Our application is to daily data collected from a number of important corn and soybean markets at spatially distinct markets in North Carolina. These data have been previously utilized to evaluate regional price linkages and spatial market integration (see, for example, Goodwin and Piggott (2001)). We use generalized impulse response functions to evaluate the dynamics of regional price adjustments to localized shocks in individual markets. Implications for regional price adjustments and, in particular, adjustments during recent periods of high volatility, are discussed in the paper. Finally, we offer suggestions for further extensions of the semi-parametric analysis of regime switching behavior.