In aschersleben/cointReg: Parameter Estimation and Inference in a Cointegrating Regression

```{R, include = FALSE} knitr::opts_chunk$set(fig.path = "figures/vignette-", fig.width = 5, message = FALSE)

## Install cointReg

```{R, eval = FALSE}
install.packages("cointReg")

If you like to use the development version, you can install the package directly from GitHub: ```{R, eval = FALSE} devtools::install_github("aschersleben/cointReg", build_vignettes = TRUE)

Load the package:
```{R}
library("cointReg")

Basic examples

Simple test model with one regression variable

Generate a regression variable x and a dependant variable y. The fastest and easiest way to plot both time series is matplot(...).

set.seed(42)
x <- cumsum(rnorm(200, mean = 0, sd = 0.1)) + 10
y <- x + rnorm(200, sd = 0.4) + 2
matplot(1:200, cbind(y, x), type = "l", main = "Cointegration Model")

Now you can estimate the model parameters with the FM-OLS method and include an intercept in the model via the deter variable:

deter <- rep(1, 200)
test <- cointRegFM(x = x, y = y, deter = deter)

Print the results:

print(test)

You can see that both the intercept and the regression variable are significant.

Finally, you can plot the residuals:

plot(test, main = "Residuals of the Cointegration Model")

Another test model with three regression variables and a linear trend

set.seed(1909)
x1 <- cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 <- cumsum(rnorm(100, sd = 0.1)) + 1
x3 <- cumsum(rnorm(100, sd = 0.2)) + 2
x <- cbind(x1, x2, x3)
y <- x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
matplot(1:100, cbind(y, x), type = "l", main = "Cointegration Model")

deter <- cbind(level = 1, trend = 1:100)
test <- cointRegFM(x, y, deter, kernel = "ba", bandwidth = "and")
print(test)

plot(test, main = "Residuals of the Cointegration Model")

Spurious regression example

This is why you should use modified OLS methods instead of a normal OLS model to estimate parameters of a cointegrating regression:

set.seed(26)
x <- cumsum(rnorm(200))
y <- cumsum(rnorm(200))
summary(lm(y ~ x))

The independant variable x seems to be significant at a very secure level.

And now have a look at the results of an FM-OLS regression:

cointRegFM(x = x, y = y, deter = rep(1, 200))

So the x variable doesn't have an influence on y -- which makes sense because they were generated independently.

aschersleben/cointReg documentation built on May 12, 2019, 4:33 a.m.