1 Statistical problems in a discrete time random field HJM type interest rate model Erika Fülöp Department of Applied Mathematics and Probability Theory, Faculty of Informatics, University of Debrecen, Hungary Keywords: HJM type forward interest rate model, strong consistency, LAN Abstract We consider a discrete time Heath-Jarrow-Morton (HJM) type forward interest rate model, where the interest rate curves are driven by a geometric spatial autoregression field. Our aim is to test the autoregression parameter . We study stable (|| < 1) and unstable (|| =1) cases. We study strong consistency of the maximum likelihood estimator of , and local asymptotic normality (LAN) of the sequence of the related statistical experiments. The main gain of the second result is that we obtain at once asymptotically optimal tests. 1. Introduction Our aim is to consider some statistical questions arising in a HJM type interest rate model. Such models were proposed by Gáll, Pap and Zuijlen [3]. We will study a no-arbitrage discrete time forward interest rate curve model {f () k,ℓ : k,ℓ ≥ 0} given for each parameter ∈ R by f () k,ℓ − f () k−1,ℓ+1 − (f () k,ℓ−1 − f () k−1,ℓ )= η k,ℓ + G ℓ (), k,ℓ ≥ 1, f () k,0 − f () k−1,1 = η k,0 + G 0 (), k ≥ 1, where {η k,ℓ : k ≥ 1,ℓ ≥ 0} are independent standard normal random variables on a probability space (Ω, F , P), G ℓ () := 1 2 ∑ 2ℓ j=0 j for ∈ R, and the initial values {f () 0,ℓ : ℓ ≥ 0} are given real numbers. Here f () k,ℓ means the forward interest rate at time k ≥ 0 with time to maturity date ℓ ≥ 0, i.e., it is supposed to hold for the time period [k + ℓ,k + ℓ + 1). The process {f () k,ℓ : k,ℓ ≥ 0} is a spatial autoregressive process. It is called stable, unstable, or explosive, if || < 1, || =1, or || > 1, respectively. The main goal of this paper is to test the autoregression parameter based on a sample f () := (f () k,ℓ ) 1≤k≤K, 0≤ℓ≤L . Of course, the difficulty is that the sample consists of nonindependent random variables. Moreover, no explicit formula is available for the maximum likelihood estimators of . 15th European Young Statisticians Meeting 15thEYSM September 10-14, 2007 Castro Urdiales (Spain)