  Sketching is a stochastic dimension reduction method that preserves geometric
structures of data and has applications in high-dimensional regression, low
rank approximation and graph sparsification. In this work, we show that
sketching can be used to compress simulation data and still accurately estimate
time autocorrelation and power spectral density. For a given compression ratio,
the accuracy is much higher than using previously known methods. In addition to
providing theoretical guarantees, we apply sketching to a molecular dynamics
simulation of methanol and find that the estimate of spectral density is 90%
accurate using only 10% of the data.
