Overview

The combcoint package implements the combined non-cointegration test developed by Bayer and Hanck (2013) doi:10.1111/j.1467-9892.2012.00814.x. This statistical approach improves the reliability of cointegration detection by aggregating p-values from multiple individual cointegration tests into a single joint test statistic. Specifically, it combines the outcomes of the Engle-Granger, Johansen, Boswijk and Banerjee tests using a Fisher-type combination method. The approach enhances the power and robustness of cointegration testing, particularly in situations where individual tests yield mixed or inconclusive results.

Methodology

The combined test aggregates p-values from the following individual cointegration tests: Engle-Granger Johansen Boswijk Banerjee

The combined test statistic is calculated using Fisher’s combination formula:

\[C = -2 \sum_{i=1}^{k} \ln(p_i)\] where \(p_i\) are the \(p\)-values from the individual tests. Under the null hypothesis of no cointegration, C follows a chi-squared distribution with 2\(\cdot\)k degrees of freedom.

Installation

You can install the package from CRAN:

install.packages("combcoint")

Or from GitHub

remotes::install_github("Janine-Langerbein/combcoint")

Dataset

The package includes an example dataset taken from Luetkepohl (2007) http://www.jmulti.de/download/datasets/e1.dat, often used for cointegration testing exercises.

The dataset is automatically available when the package is loaded. You can load it as follows:

data("lutkepohl_e1")

Applied Example

We demonstrate the application of both the classical Engle-Granger cointegration test and the combined Bayer-Hanck cointegration test using the dataset lutkepohl_e1 included in the package.

We first apply the Engle-Granger test:

englegranger(linvestment ~ lincome + lconsumption, data = lutkepohl_e1)
#> $test.stat
#> [1] -2.45286
#> 
#> $lags
#> [1] 1
#> 
#> $trend
#> [1] "const"
#> 
#> $test
#> [1] "Engle-Granger"
#> 
#> $formula
#> linvestment ~ lincome + lconsumption

Next, we apply the combined cointegration test on the same dataset:

bayerhanck(linvestment ~ lincome + lconsumption, data = lutkepohl_e1)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
#> ----------------------------------------------------------
#> Bayer Hanck Test for Non-Cointegration
#> ----------------------------------------------------------
#> Test statistic: 12.4303
#> p-Value: 0.1858

By default, the function uses the lags = 1. Optionally, the user can specify the lag length manually, e.g., with 4 lags:

bayerhanck(linvestment ~ lincome + lconsumption, data = lutkepohl_e1, lags = 4)
#> ----------------------------------------------------------
#> Bayer Hanck Test for Non-Cointegration
#> ----------------------------------------------------------
#> Test statistic: 9.1603
#> p-Value: 0.3111