Package 'Largevars'

Cointegration test for settings of large N and T

Description

Runs the Bykhovskaya-Gorin test for cointegration. Paper can be found at: https://doi.org/10.48550/arXiv.2202.07150

Usage

largevar(
  data = NULL,
  k = 1,
  r = 1,
  fin_sample_corr = FALSE,
  plot_output = TRUE,
  significance_level = 0.05
)

Arguments

data	A numeric matrix where the columns contain individual time series that will be examined for the presence of cointegrating relationships.
k	The number of lags that we wish to employ in the vector autoregression. The default value is k = 1.
r	The number of largest eigenvalues used in the test. The default value is r = 1.
fin_sample_corr	A boolean variable indicating whether we wish to employ finite sample correction on our test statistic. The default value is fin_sample_corr = FALSE.
plot_output	A boolean variable indicating whether we wish to generate a plot of the empirical distribution of eigenvalues. The default value plot_output = TRUE.
significance_level	Specify the significance level at which the decision about H0 should be made. The default value is significance_level = 0.05.

Value

A list that contains the test statistic, a table with theoretical quantiles presented for r=1 to r=10, and the decision about H0 at the significance level specified by the user.

Examples

largevar(
  data = matrix(rnorm(60, mean = 0.05, sd = 0.01), 20, 3),
  k = 1,
  r = 1,
  fin_sample_corr = FALSE,
  plot_output = FALSE,
  significance_level = 0.05
)

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Quantiles for the limiting distribution of the test

Description

A data frame containing the simulated quantiles for the test statistic used in the largevar function. More details about how these simulations were conducted can be found in Section 4 of the vignette.

Format

A data frame with 99 rows and 11 variables:

Source

Calculated through own simulations (see details in Section 4 of vignette).

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Creates the quantile table output for largevar function

Description

Outputs the quantile tables from the package's corresponding vignette.

Usage

quantile_tables(r = 1)

Arguments

r	Which partial sum the quantile table should be returned for. (Only r<=10 is available.) Default is r=1.

Value

A numeric matrix.

Examples

quantile_tables(r=3)

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Stock price data for example in vignette

Description

A data frame containing weekly S&P100 prices over ten years: 01.01.2010 - 01.01.2020, The S&P100 includes 101 leading U.S. stocks of which 92 were collected here.

Format

A data frame with 522 rows and 93 variables:

Source

Refer to the data source used in: A. Bykhovskaya and V. Gorin. Cointegration in large vars. Annals of Statistics, 2022.

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Empirical p-value for cointegration test

Description

Runs a simulation on the H0 for the Bykhovskaya-Gorin test for cointegration and returns an empirical p-value. Paper can be found at: https://doi.org/10.48550/arXiv.2202.07150

Usage

sim_function(
  N = NULL,
  tau = NULL,
  stat_value = NULL,
  k = 1,
  r = 1,
  fin_sample_corr = FALSE,
  sim_num = 1000
)

Arguments

N	The number of time series used in simulations.
tau	The length of the time series used in simulations.
stat_value	The test statistic value for which the p-value is calculated.
k	The number of lags that we wish to employ in the vector autoregression. The default value is k = 1.
r	The number of largest eigenvalues used in the test. The default value is r = 1.
fin_sample_corr	A boolean variable indicating whether we wish to employ finite sample correction on our test statistics. The default value is fin_sample_corr = FALSE.
sim_num	The number of simulations that the function conducts for H0. The default value is sim_num = 1000.

Value

A list that contains the simulation values, the empirical percentage (realizations larger than the test statistic provided by the user) and a histogram.

Examples

sim_function(N=90, tau=501, stat_value=-0.27,k=1,r=1,sim_num=50)

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