In an adaptive optics (AO) system, finite time delays contribute a relatively large amount to the overall wavefront error. The temporal error, due to the time delays, adds to the speckle halo which is visible in the science plane of a high contrast imaging (HCI) instrument. The halo limits the inner working angle, preventing HCI from probing regions where we expect Earth-like planets. Our research focuses on understanding the non-stationary behavior of atmospheric turbulence and its effects on the temporal error and the contrast. The wind vector greatly influences the turbulence-induced wavefront phase error. In the framework of the von Karman power spectral density (PSD) of wavefront phase, the wind speed changes the cut-off frequency as well as the gain of the spectrum. We aim to understand the behavior of the wind vector on sub-second timescales using data from the Thirty Meter Telescope site testing campaign at Mauna Kea. The nocturnal measurements we study are from 287 nights throughout the years of 2006-2008, taken at a height of 7 m with a maximum sampling rate of 60 Hz. We first compare the observational PSD to the Kaimal PSD. We then present an expression for the observational PSD, a fit to a more general PSD similar to the Kaimal PSD, to describe the wind speed located at Area E (northern plateau) on Mauna Kea. Using the fitted PSD, we construct a fractionally integrated ARMA model that can be used to create an artificial wind speed time series to be fed into phase screen simulations to generate realistic wind-varying phase screens. We examine how the contrast, achieved by the AO system, varies with the wind fluctuations.