Abstract. We consider a discrete time Heath--Jarrow--Morton type forward interest rate model, where the interest rate curves are driven by a geometric spatial autoregression field. Local asymptotic normality is proved for stable and unstable no-arbitrage models containing a simple stochastic discounting factor. Based on these results, asymptotically optimal tests are constructed for testing the autoregression parameter.

AMS Subject Classification (1991): 62F05

Received March 1, 2007, and in revised form June 29, 2007. (Registered under 6464/2009.)