Question

Using R statistical software

(a) Generate n = 100 observations from following time series model xt =2cos(2πt/4)+ωt, where ωt is i.i.d N(0,1). (b) Apply the moving average to xt and get time series yt, such that yt = (xt + xt−1 + xt−2 + xt−3)/4. [hint: Use filter(x,rep(1/4,4)),sides=1] (c) Plot xt as a line and superimpose yt as a dashed line. (d) Describe the relationship between xt and yt.

Answer 1

The R code is given as follows

The graph is given as follows

The relationship between y(t) and x(t) is that y(t) is a smoother version of x(t) since some noise or randomness of the data was removed by the moving average method. This can also be very well observed in the above graph.