We design primal and dual bounding methods for multistage adjustable robust optimization (MSARO) problems by adapting two families of decision rules rooted in stochastic programming literature. This framework approximates the primal and dual formulations of an MSARO problem with two-stage models. We develop several appropriate solution methods for the obtained approximations. Our framework is general-purpose and does not require strong assumptions such as a temporal independent stochastic progress, and can consider integer adjustable decision variables. Computational experiments on newsvendor, location-transportation, and capital budgeting problems show that our bounds yield considerably smaller optimality gaps compared to the existing methods.