# cointReg" In 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.

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cointReg documentation built on May 2, 2019, 3:45 a.m.