Consider the second order differential equation correspondingto a damped harmonic oscillator.d2xdt2+ ?1dxdt + ?2x = fDiscretize this equation, using a time step of ?, and do thefollowing:(a) Express it as an AR(2) processxt = ?1xt?? + ?2xt?2? + wtbeing sure to clearly link the ??s to the ??s. Let ? = 1 andprovide R code that simulates a realization with ?2w = 1,and ?1 = 1.5 and ?2 = ?0.75.(b) Now, express the AR(2) process as an multivariate AR(1)model. Provide R code and simulate the identical realizationsto part (a). (Note: you will need to set the randomnumber seed to be the same).

Time Series Analysis STAT 4390/5390 OCEAN 4210/5210 Assignment 3: Due Mon 3 Feb, 2014 2 1. Consider the AR(1) model xt = 1 xt1 +wt where wt N ID(0, w ). Show that for ||