README

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Largevars

The Largevars R package conducts a cointegration test for high-dimensional vector autoregressions of order \(k\) based on the large \(N,T\) asymptotics of Bykhovskaya and Gorin (2021, doi:10.48550/arXiv.2006.14179), Bykhovskaya and Gorin (2022, doi:10.48550/arXiv.2202.07150). The implemented test is a modification of the Johansen likelihood ratio test. In the absence of cointegration the test converges to the partial sum of the Airy\(_1\) point process. This package contains simulated quantiles of the first ten partial sums of the Airy\(_1\) point process that are precise up to the first \(3\) digits.

Installation

library(devtools)
install_github("eszter-kiss/Largevars")
#> Skipping install of 'Largevars' from a github remote, the SHA1 (a2e411ef) has not changed since last install.
#>   Use `force = TRUE` to force installation
library(Largevars)

Example

The following example is a replication of the S&P100 example from Bykhovskaya and Gorin (2022), Bykhovskaya and Gorin (2024).

We use logarithms of weekly adjusted closing prices of assets in the S&P100 over ten years (01.01.2010-01.01.2020), which gives us \(\tau=522\) observations across time. The S&P100 includes 101 stocks, with Google having two classes of stocks. We use 92 of those stocks, those for which data were available for our chosen time period. Only one of Google’s two listed stocks is kept in the sample. Therefore, \(N = 92\), \(T = 521\) and \(T/N \approx 5.66\). The data that we use are accessible from the data folder in the package.

library(Largevars)

## load data
library(readr)
s_p100_price <- read_csv("data/s_p100_price_adj.csv",show_col_types = FALSE)

## Transform data according to researcher needs
dataSP <- log(s_p100_price[,seq(2,dim(s_p100_price)[2])])

## Turn data frame into numeric matrix to match function requirements
dataSP <- as.matrix(dataSP)

## Use the package documentation by calling help
?largevar
#> ℹ Rendering development documentation for "largevar"

## Use largevar function
### Save the function output (list)
result <- largevar(data=dataSP,k=1,r=1,fin_sample_corr = FALSE,
      plot_output=TRUE,significance_level=0.05)


### Display the result
result
#> Output for the largevars function 
#> =================================== 
#> Cointegration test for high-dimensional VAR(k)                  T= 521 , N= 92 
#> 
#> 10% Critical value  5% Critical value  1% Critical value         Test stat. 
#>               0.45               0.98               2.02              -0.28 
#> 
#> If the test statistic is larger than the quantile, reject H0 at the chosen level. 
#> ============================================================================ 
#> Test statistic: -0.2777314 
#> The p-value is 0.23 
#> Decision about H0:  0

If we want to individually access certain values from the output list, we can do it in the usual way, by referencing the elements of the list:

result$statistic
#> [1] -0.2777314
result$significance_test$p_value
#> [1] 0.23
result$significance_test$boolean_decision
#> [1] 0
result$significance_test$significance_table
#>      10% Critical value 5% Critical value 1% Critical value  Test stat.
#> r=1                0.45              0.98              2.02  -0.2777314
#> r=2               -1.87             -1.09              0.42  -1.4995879
#> r=3               -5.90             -4.90             -2.99  -5.4154889
#> r=4              -11.35            -10.15             -7.87 -10.5527603
#> r=5              -18.07            -16.69            -14.07 -16.7460847
#> r=6              -25.95            -24.40            -21.45 -23.2178976
#> r=7              -34.90            -33.19            -29.95 -31.1080001
#> r=8              -44.88            -43.01            -39.47 -39.3197363
#> r=9              -55.82            -53.80            -49.99 -49.8419822
#> r=10             -67.70            -65.53            -61.45 -60.4894485

If we want to see an empirical p-value, we can use the function below. By default, it will print a message to console to remind the user that precise computations of the statistics need a large number of simulation iterations. You can suppress this message the usual way, by using the suppressMessages() wrapper.

# result2 <- sim_function(N=92,tau=522,stat_value=-0.2777,k=1,r=1,
#              fin_sample_corr = FALSE,sim_num=30)
# result2

# # To provide the function while suppressing messages:
result3 <- suppressMessages(sim_function(N=92,tau=522,stat_value=-0.2777,k=1,r=1,
               fin_sample_corr = FALSE,sim_num=30))

result3
#> Output for the sim_function function 
#> =================================== 
#> The empirical p-value is  0.1

Authors

Cite our package

citation("Largevars")
#> To cite Largevars in publications use:
#> 
#>   Bykhovskaya A, Gorin V, Kiss E (2024). "Largevars: An R Package for Testing Large VARs for the Presence of Cointegration."
#>   _TBD_.
#> 
#> A BibTeX entry for LaTeX users is
#> 
#>   @Article{largevarspaper,
#>     title = {Largevars: An R Package for Testing Large VARs for the Presence of Cointegration},
#>     author = {Anna Bykhovskaya and Vadim Gorin and Eszter Kiss},
#>     journal = {TBD},
#>     year = {2024},
#>   }

License

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.