Simulate Autoregressive Process

[Jared Greathouse]

I wanna simulate an AR process like this (see section 2).


I've tried this

clear


set obs 200


cls


set seed 1


egen id = seq(), f(1) t(20) b(10)

expand 10

bys id: g time = _n

xtset id time, g


// 20 units, 100 periods each


// R CODE: x1 <- 100 + arima.sim(model = list(ar = 0.999), n = 100)


bys id: g x = 100 +runiform()

bys id: g y = 1.2 * x + runiform()



cls

line y time if id ==4

But I don't know how to simulate an AR process in the x variable. How might I do this?

Note that I want this (as my code implies) to be a panel dataset, where multiple units have their own AR process. At present, the one I've created is noisier than I'd like, and I suspect knowing how to create an AR(1) term might be the key here.

[Jared Greathouse]

Presumably.... the answer lies, in part, here https://blog.stata.com/2016/06/21/un...ests-in-stata/

[Daniel Schaefer]

Hi Jared,

Would it help to see the R code for arima.sim()?

> arima.sim

function (model, n, rand.gen = rnorm, innov = rand.gen(n, ...),

    n.start = NA, start.innov = rand.gen(n.start, ...), ...)

{

    if (!is.list(model))

        stop("'model' must be list")

    if (n <= 0L)

        stop("'n' must be strictly positive")

    p <- length(model$ar)

    if (p) {

        minroots <- min(Mod(polyroot(c(1, -model$ar))))

        if (minroots <= 1)

            stop("'ar' part of model is not stationary")

    }

    q <- length(model$ma)

    if (is.na(n.start))

        n.start <- p + q + ifelse(p > 0, ceiling(6/log(minroots)),

            0)

    if (n.start < p + q)

        stop("burn-in 'n.start' must be as long as 'ar + ma'")

    d <- 0

    if (!is.null(ord <- model$order)) {

        if (length(ord) != 3L)

            stop("'model$order' must be of length 3")

        if (p != ord[1L])

            stop("inconsistent specification of 'ar' order")

        if (q != ord[3L])

            stop("inconsistent specification of 'ma' order")

        d <- ord[2L]

        if (d != round(d) || d < 0)

            stop("number of differences must be a positive integer")

    }

    if (!missing(start.innov) && length(start.innov) < n.start)

        stop(sprintf(ngettext(n.start, "'start.innov' is too short: need %d point",

            "'start.innov' is too short: need %d points"), n.start),

            domain = NA)

    x <- ts(c(start.innov[seq_len(n.start)], innov[1L:n]), start = 1 -

        n.start)

    if (length(model$ma)) {

        x <- filter(x, c(1, model$ma), sides = 1L)

        x[seq_along(model$ma)] <- 0

    }

    if (length(model$ar))

        x <- filter(x, model$ar, method = "recursive")

    if (n.start > 0)

        x <- x[-(seq_len(n.start))]

    if (d > 0)

        x <- diffinv(x, differences = d)

    as.ts(x)

}

<bytecode: 0x7fe3d564ae10>

<environment: namespace:stats>

[Jared Greathouse]

Perhaps! I'll dissect this later, then.