Write a function in R to generate a series of length T, i.e. from the model x_i = x_i-1 + w_i. You can enter the parameter directly and we only have on fixed parameter . Also, the index i should start from 2.

This will be similar to:

randomwalk=function(sigsq,T){ x=rep(0,T) w=rnorm(T,sd=sqrt(sigsq)) for ( i in 2:T){ x[i]=x[i-1]+w[i] } x }

AND

masim=function(thetas, sigsq, T){ q=length(thetas) noise=rnorm(T+q, sd=sqrt(sigsq)) x=c(noise[1:q],rep(0,T)) #put the initial noise terms in and set the rest to zero for (i in (q+1):(T+q)){ #this loop generates the MA series x[i]=thetas %*% noise[i-(1:q)] +noise[i] } x=x[(q+1):(T+q)] #throw away those initial starting points x }