Most Effective Sampling Scheme for Prediction of Stationary Stochastic Processes

<div>Locations of observations <svg height="11.5564pt" id="M14" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 18.9642 11.5564" width="18.9642pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.673,0)"><path d="M540 9V501H48V9H540Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.304,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> and missing value <span class="nowrap"><svg height="11.6086pt" id="M15" style="vertical-align:-2.26806pt" version="1.1" viewbox="-0.0498162 -9.34054 19.9076 11.6086" width="19.9076pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M799 12L418 655H408L27 12L34 0H792L799 12ZM711 50H115L413 553L711 50Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.276,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg>.</span> Upper figure shows three schemes for interpolation while lower figure shows interpolation and extrapolation.</div>

Complexity

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Figure 1

Figure 1: Most Effective Sampling Scheme for Prediction of Stationary Stochastic Processes 