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| Write an R function "GenAR" which simulates autoregression model with Gaussian white noise. You need to achieve the following: • The input of the function must include: length of simulated time series (sample size), variance of Gaussian white noise, the coefficient vector (ao,a1,…..,ap) and the initial value vector (r-p+1,T-p+2;… .. , 2o). • The output is a vector (preferably a ts object) containing the simulated time series. You may directly make use of "filter" function in R.

| Write an R function "GenAR" which simulates autoregression model with Gaussian white noise. You need to achieve the following: • The input of the function must include: length of simulated time series (sample size), variance of Gaussian white noise, the coefficient vector (ao,a1,…..,ap) and the initial value vector (r-p+1,T-p+2;… .. , 2o). • The output is a vector (preferably a ts object) containing the simulated time series. You may directly make use of "filter" function in R.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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|Write an R function "GenAR" which simulates autoregression model with Gaussian white noise. You need to achieve the following: • The input of the function must include: length of simulated time series (sample size), variance of Gaussian white noise, the coefficient vector (ao, a1,. ., ap) and the initial value vector (x_p+1,X–p+2,• . . , xo). • The output is a vector (preferably a ts object) containing the simulated time series. You may directly make use of "filter" function in R. Use the function to simulate the following model t = 1, 2, 3,..., 1000 Xt – 2xt-1 + Xt_2 = Wt, where wz is Gaussian white noise with variance equal to 2, and initial values are set as x_1 =1, xo = 0. Discuss briefly what you observe. Does the time series curve look smoother or rougher compared to the random walk time series you saw in lecture? |Difference (with lag 1) the simulated time series and plot the resulting time series. What do you observe this time?
Transcribed Image Text:|Write an R function "GenAR" which simulates autoregression model with Gaussian white noise. You need to achieve the following: • The input of the function must include: length of simulated time series (sample size), variance of Gaussian white noise, the coefficient vector (ao, a1,. ., ap) and the initial value vector (x_p+1,X–p+2,• . . , xo). • The output is a vector (preferably a ts object) containing the simulated time series. You may directly make use of "filter" function in R. Use the function to simulate the following model t = 1, 2, 3,..., 1000 Xt – 2xt-1 + Xt_2 = Wt, where wz is Gaussian white noise with variance equal to 2, and initial values are set as x_1 =1, xo = 0. Discuss briefly what you observe. Does the time series curve look smoother or rougher compared to the random walk time series you saw in lecture? |Difference (with lag 1) the simulated time series and plot the resulting time series. What do you observe this time?
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