Click on the R icon
If no R icon, go to Start and then All Programs to find R
To quit R:
> q()
What does it ask you? What does this mean?
For R HELP, for example to get help about the function rnorm ,
> help(rnorm)
You can also go to Help on the R toolbar and select R Help.
Generate a sample of n=100, N(0,1) random variables.
> help(rnorm)
> rnorm(100)
What happened?
Now, let's try:
> temp <- rnorm(100)
What is in the object temp?
What is the length of the oject temp?
Make a informative plot of temp?
Q: How can you make a time series plot of the data? (The model is: Zt = at)
Let's now use the R function set.seed() to allow us to reproduce our results! Repeat the above command: (temp <- rnorm(100) after
> set.seed(1)
Compare what is in the object temp with a neighbor. It should be exactly the same!
The model: Zt = φ1Zt-1 + at
R function: arima.sim
We need to use help to find out about this function.
> help(arima.sim)
What arguments does this function take?
What is a list?
Simulate and plot the time series for φ1 = 0.5
> y.50 <- arima.sim(model=list(ar=.5), n=100)
> plot(y.50)
Plot the ACF.
> acf(y.50)
> temp <- acf(y.50, plot=F)
What's in temp? What do you get when you type the following?
> temp$acf
Let's now use the R function set.seed() to allow us to reproduce our results! Repeat the above commands after
> set.seed(1)
> y.50 <- arima.sim(model=list(ar=.5), n=100)
Now, for the PACF,
> acf(y.50,type="partial")
You can look at plot of Z_t versus Z_t-1 for the AR(1) series
> plot(lag(y.50,1), y.50, xlab=expression(Z[t-1]), ylab=expression(Z[t]))
Simulate and plot the time series for φ1 = 0, φ1 = 0.5, φ1 = -0.5, and φ1 = 0.9.
Let's look at sample code in ar1.ex1.r
Now plot the ACF and PACF of the time series. How would you describe the characteristics?
Let's look at sample code in ar1.ex2.r
Let's look at the sample code in random_walk_ex.r
Q: What happens when you change (larger and smaller) the standard deviation of ythe noise?
The model: Zt = φ1Zt-1 + φ2Zt-2 + at
Simulate and plot the ACF of the time series for φ1 = -0.5, φ2 = 0.3
> y <- arima.sim(model=list(ar=c(-0.5,0.3)), n=100)
> acf(y)
> pacf(y)
Activity 1: Compare your sample ACF and PACF to Table 3.3 and Figure 3.8 Plots.Activity 2: Look at the theoretical ACF and PACF plots in Figure 3.7 and locate the plot that the parameter values satisfy.
Activity 3: Calculate the theoretical ACF and PACF for k=0,1,2, and 3.
Hint: For the ACF use (3.1.19), (3.1.20), and (3.31); For the PACF use (3.1.23a), (3.1.23b), and (3.1.23c).
Compare the theoretical values to the sample values.
Repeat ALL of the above by using n=1000 (or more)!
Due to Popular Demand, Let's go to R Markdown instead!
in: STAT 575 Lab 1 and using the Dr. Dribble Example 2.
Here is a R Markdown Tutorial!
The model: Zt = at -
θ1at-1 (Book)
The model: Zt = at + b1at-1 (R)
Note: θ1 is the MA coefficient (Book)
Simulate and plot the ACF and PACF of the time series for θ1 = 0.5
> y <- arima.sim(model=list(ma=0.5), n=100)
OR y1 <- arima.sim(model=list(ma=-0.5), n=100)?
> acf(y)
> acf(y, type="partial")
Notice that ma=0.5 produces an ACF that looks like a θ1 < 0 on p. 49.
We will just have to keep straight the difference in notation between your book and R!
So, to simulate the above model consistent with your book, we should use
> y <- arima.sim(model=list(ma=-0.5), n=100)
> acf(y)
> acf(y, type="partial")
> help(arima) Gives details!
Here are some knitr resources
Send me more and I will gladly add to this!
Here is a HW template that I have made for you (Thanks Nick!): STAT673HW0.Rnw
From the STAT 672 Lab1 for Example 2 (Dr. Dribble) and Example 3
Let's make a template for STAT 673 Lab1 from Example 2: the Random Walk (or something up there!).
Try going through the following Intro. Lessons. The # sign is a comment, so you can copy and paste.
Here are some Introductory Lessons in R
Here are some nice Tutorials
Let's look at sample code in ar1sim.r