In AUMath-AdvancedR2018/AR1: Tools for working with AR(1) processes.

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This is an introduction in how to use the AR1 package. The package contains a few functions that can fx simulate a AR(1) process.

Installing

A quick guide on how to install the package. Use the function install.package() to download it and then load it with;

library("AR1")

Examples of how to use the simulation function

We will here show an example, that should visualize how to use the function. Here we have a AR(1) process, $$Y_{n+1}=\varphi Y_n+\varepsilon_n$$ where the white noise, $\varepsilon_n$, is a process with zero mean and variance 1 and the parameter and t distribution with 1.5 degrees of freedom, and $\varphi = 0.8$. Futhermore we have that $Y_0=0$.

y <- simAR1(0, 300, 0.8, distfun = rnorm, 300)
plot(y, type = "l", main = "Normal distribution")
x <- simAR1(0, 300, 0, distfun = rt, 300, 1.5)
plot(y, type = "l", main = "t distribution")

Examples of the Law of Large Numbers function and the Central Limit Theorm function

The function LLN() will help determine if there is a Law of Large Numbers. The function also plots the mean. CLT() helps determine if $$\frac{\sum_{i=1}^n Y_i}{\sqrt{n}}$$ converges in distribution as $n\to\infty$ to a normal distribution. Here is an example of how to use the two functions:

x <- replicate(10, simAR1(0, 5000, 0.8, rnorm, 5000))
LLN(x)
w <- replicate(50000,simAR1(0, 1000, 0.8, rnorm, 1000))
CLT(w)

AUMath-AdvancedR2018/AR1 documentation built on May 24, 2019, 7:36 a.m.