In the talk we consider rather simple autoregression
process
$$
X_{t,s}=aX_{t-1,s}+ bX_{t,s-1}+\e_{t,s},
$$
where $\e_{t,s}, (t,s)\in Z^2$ are i.i.d. random variables with $E\e_{1,1}=0, E\e_{1,1}^2=1.$
Two limit theorems for self-normalized sums $\sum_{(t,s)\in D_n}X_{t,s},$ where $D_n$ is some sequence of increasing subsets of $Z^2,$ will be presented.
The talk is based on paper [1].
References
1. Paulauskas, V., Zove, R., A note on selfnormalization
for a simple spatial autoregressive model , to appear in Lithuanian Math. J., (2007).
|
2