Simulate an AR(1) process with uniform innovations

Question

I need to plot an AR(1) graph for the process

y[k] = 0.75 * y[k-1] + e[k] for y0 = 1. 

Assume that e[k] is uniformly distributed on the interval [-0.5, 0.5] .

I am trying to use arima.sim :

library(tseries)
y.0 <- arima.sim(model=list(ar=.75), n=100)
plot(y.0)

It does not seem correct. Also, what parameters do I change if y[0] = 10 ?

Answer 1

We want to use R base function arima.sim for this task, and no extra libraries are required.

By default, arima.sim generates ARIMA with innovations ~ N(0,1) . If we want to change this, we need to control the rand.gen or innov argument. For example, you want innovations from uniform distributions U[-0.5, 0.5] , we can do either of the following:

arima.sim(model=list(ar=.75), n=100, rand.gen = runif, min = -0.5, max = 0.5)

arima.sim(model=list(ar=.75), n = 100, innov = runif(100, -0.5, 0.5))

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Example

set.seed(0)
y <- arima.sim(model=list(ar=.75), n = 100, innov = runif(100, -0.5, 0.5))
ts.plot(y)

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In case we want to have explicit control on y[0] , we can just shift the above time series such that it starts from y[0] . Suppose y0 is our desired starting value, we can do

y <- y - y[1] + y0

For example, starting from y0 = 1 :

y <- y - y[1] + 1
ts.plot(y)