Block size in subsampling and bootstrap for time series
I have a dependent variable, a time series of 80 periods (discrete decisions). I am doing maximum likelihood estimation with 10 parameters. Now I want to get the standard error or confidence interval of the estimates of these 10 parameters. One feature of my likelihood function is that the decisions is determined by all the history of $x$ , and the weight of past $x$ decreases geometrically: $x_t+\rho x_{t-1}+\rho^2 x_{t-2}$ ... where $\rho$ is one of the parameters needed to be estimated. So I am thinking that moving block bootstrapping perhaps is not suitable to sustain the data structure, and I should use subsampling. But subsampling of a given block size leaves me a very few subsamples. For example, if I choose a block size of 40, I get only 41 subsamples. Should I concern about it? Is it sufficient? Can I use multiple block sizes to construct a confidence interval? Is there any other alternatives that I could use to get standard error or confidence interval?