Calibrated Horizon-Weighted Local Projection Designs for Markov Switchbacks

We study temporal assignment design for Markov switchback experiments when the reported object is a dynamic local-projection target. We develop a calibrated selector that chooses the feasible persistence minimizing the covariance, HAC, residual-bootstrap, or realized-schedule risk of the estimator and reporting object specified before the experiment. A balanced homoskedastic Markov benchmark yields a closed form because the lagged-assignment information matrix is AR(1)-Toeplitz with a tridiagonal inverse. The benchmark maps local-projection reporting weights into persistence recommendations within a prespecified first-order Markov class. Field recommendations replace the benchmark covariance with residualized, serially dependent, pilot-calibrated, or randomization-based risk. A semi-synthetic Low Carbon London evaluation uses observed half-hourly baseline dynamics and known injected responses to assess design risk. It evaluates the covariance calculations under realistic load autocovariance and identifies when calibrated covariance selection should replace the homoskedastic Markov formula. Near-boundary designs use randomization-first inference when many-spell normal approximations are unsupported.