Package 'bootCT'

Bootstrap ARDL

Description

This is the main function of the package. It performs the bootstrap version of the ARDL bound test for cointegration.

Usage

boot_ardl(
  data,
  yvar = NULL,
  xvar = NULL,
  fix.ardl = NULL,
  info.ardl = "AIC",
  fix.vecm = NULL,
  info.vecm = "AIC",
  maxlag = 5,
  a.ardl = 0.05,
  a.vecm = 0.05,
  nboot = 2000,
  case = 3,
  a.boot.H0 = c(0.05, 0.025, 0.01),
  print = T
)

Arguments

data	Input dataset. Must contain a dependent and a set of independent variables.
yvar	Name of the dependent variable, enclosed in quotation marks. If NULL, the first variable will be used.
xvar	Vector of names of the independent variables, each enclosed in quotation marks. If NULL, all variables except the first will be used.
fix.ardl	Fixed lagged differences for the short term part of the ARDL equation.
info.ardl	Selection criterion for the auto_ardl function. Options are "AIC", "AICc", BIC, "R2", "adjR2", if fix.ardl is null. Defaults to AIC.
fix.vecm	Fixed lagged differences for the short term part of the VECM equation.
info.vecm	Selection criterion for the VARselect function. Options are "AIC", "HQ", "SC", "FPE", if fix.vecm is null. Defaults to AIC.
maxlag	Max number of lags for the auto_ardl and VARselect procedures, if fix.ardl or fix.vecm are null, respectively.
a.ardl	Threshold significance for the short-term ARDL coefficients significance.
a.vecm	Threshold significance for the short-term VECM coefficients significance.
nboot	Number of bootstrap replications.
case	Model case, pertaining to the treatment of intercept and trend. Must be integer from 1 to 5. Defaults to 3.
a.boot.H0	Probability/ies by which the critical quantiles of the bootstrap distribution(s) must be calculated.
print	Show the progress bar.

Value

List of several elements including

• data: the data used to perform estimation and testing

• ARDL: the estimated ARDL conditional model

• VECM: the estimated VECM unconditional model

• jo.testX: Johansen cointegration test on the independent variables

• pssbounds: the PSS bound test output

• smgbounds: the SMG bound test critical values

• fov.stat: the test statistics on the conditional Fov tests

• t.stat: the test statistics on the conditional t test

• find.stat: the test statistics on the conditional Find tests

• quantfov: the bootstrap conditional F Overall test critical value(s)

• quantt: the bootstrap conditional t-test critical value(s)

• quantfind: the bootstrap conditional F Independent test critical value(s)

• fakecoint: indication of the situation in which $a_{y.x}\neq 0$ but $a_{y.x}^{UC}=0$, signaling absence of cointegration.

Examples

## Not run: 
#LOAD DATA
data("ger_macro")
# DATA PREPARATION
LNDATA = apply(ger_macro[,-1], 2, log)
col_ln = paste0("LN", colnames(ger_macro)[-1])
LNDATA = as.data.frame(LNDATA)
colnames(LNDATA) = col_ln
LNDATA$DATE = ger_macro$DATE
#ARDL BOOT 
BCT_res = boot_ardl(data = LNDATA,
                   yvar = "LNCONS",
                   xvar = c("LNINCOME","LNINVEST"),
                   maxlag = 5,
                   a.ardl = 0.1,
                   a.vecm = 0.1,
                   nboot = 2000,
                   case = 3,
                   a.boot.H0 = c(0.05),
                   print = T)
summary(boot_res)

## End(Not run)

---

Investment, Income and Consumption dataset.

Description

The data set contains quarterly, seasonally adjusted time series for West German fixed investment, disposable income, and consumption expenditures in billions of DM from 1960Q1 to 1982Q4. It was produced from file E1 of the data sets associated with Lutkepohl (2007). Originally obtained from Deutsche Bundesbank.

Usage

ger_macro

Format

A data frame with 92 rows and 4 variables:

DATE

Quarter

INVEST

Fixed investment (DM Billions)

INCOME

Disposable income (DM Billions)

CONS

Consumption expenditures (DM Billions)

Source

http://www.jmulti.de/download/datasets/e1.dat

---

Export, Foreign Investment and GDP dataset.

Description

The data set contains yearly, time series for Italian log GDP, log foreign direct investment, and log exports, from 1970 to 2020. Obtained from the World Bank Database.

Usage

ita_macro

Format

A data frame with 51 rows and 4 variables:

YEAR

From 1970 to 2020

LEXP

log Exports (Adjusted for DGP deflator)

LFI

log Foreign Direct Investment (Adjusted for DGP deflator)

LGDP

log GDP

Source

World Bank Database

---

Create matrix of lagged variables

Description

This function lags a set of variables in a matrix, each with a separate index. It is also possible to retain only the last lag order.

Usage

lag_mts(X, k, last.only = F)

Arguments

X	numeric matrix whose columns are subject to lagging
k	vector of lag orders
last.only	If TRUE only the k-th order lag will be computed, otherwise all lags from 1 to k

Value

a matrix whose columns are the original variables and the k-th order lagged variables. Column name suffix ".lx".

Examples

data(ger_macro)

lag_mts(X = ger_macro, k = 3, last.only = FALSE)

---

Generate data from a VECM/ARDL equation

Description

Generate data from a VECM/ARDL equation

Usage

sim_vecm_ardl(
  nobs,
  case = 1,
  sigma.in,
  gamma.in,
  axx.in,
  ayx.uc.in,
  ayy.in,
  mu.in = NULL,
  eta.in = NULL,
  azero.in = NULL,
  aone.in = NULL,
  burn.in = nobs * 0.5,
  seed.in = NULL
)

Arguments

nobs	number of observations.
case	case related to intercept and trend
sigma.in	error covariance matrix $\boldsymbol\Sigma$
gamma.in	list of VECM short-run parameter matrices $\boldsymbol\Gamma_j$
axx.in	long-run relationships between the independent variables $\mathbf A_{xx}$
ayx.uc.in	long-run unconditional relationship between dependent and independent variables, $\mathbf a_{yx}$. The second component ayxC, derived from conditioning, is calculated as $\mathbf a_{yx}^{(C)}= - \boldsymbol\omega'\mathbf A_{xx}$
ayy.in	long-run relationship for the dependent variable $a_{yy}$
mu.in	VAR intercept vector $\boldsymbol\mu$ (CASE II)
eta.in	VAR trend vector $\boldsymbol\eta$ (CASE IV)
azero.in	VECM intercept $\boldsymbol{\alpha}_{0}$ (CASE III-IV-V)
aone.in	VECM trend $\boldsymbol{\alpha}_{1}$ (CASE V)
burn.in	burn-in number of observations
seed.in	optional seed number for random error generation.

Value

A list that includes

• dims: a vector with the dataset dimension

• case: the case given as input

• data: the generated data

• diffdata: the data first difference

• ut: the generated random error matrix.

• sigma: the error covariance matrix $\boldsymbol\Sigma$.

• omega: the $\boldsymbol\omega$ vector of parameters generated via conditioning

• at: the conditional long-run parameter matrix $\widetilde{\mathbf A}$

• ayy: the coefficient weighting the EC term, $a_{yy}$

• ayx.uc: the unconditional subvector of the ARDL equation $\mathbf a_{yx}$

• ayx2: the conditioning effect $\omega'A_{xx}$

• ayx.c: the conditional subvector of the ARDL equation $\widetilde{a}_{y.x}=a_{yx}-\omega'A_{xx}$

• gammalist: the list of unconditional $\boldsymbol\Gamma_j$ parameter matrices

• psilist: the list of conditional $\boldsymbol\gamma_{y.x,j}$ parameter matrices

• vmu: the VAR intercept $\boldsymbol\mu$

• veta: the VAR trend $\boldsymbol\eta$

• azero: the unconditional VECM intercept $\boldsymbol\alpha_0$

• aone: the unconditional VECM trend $\boldsymbol\alpha_1$

• azero.c: the conditional VECM intercept $\boldsymbol\alpha_0^c$

• aone.c: the conditional VECM trend $\boldsymbol\alpha_1^c$

• interc.ardl: the conditional ARDL intercept $\alpha_{0.y}$ (case > 2)

• trend.ardl: the conditional ARDL trend $\alpha_{1.y}$ (case = 5)

• theta0: the $\theta_0$ coefficient in the EC term (case = 2)

• theta1: the $\theta_1$ coefficient in the EC term (case = 4)

• interc.ec: the conditional ARDL intercept derived from the EC tem $\alpha^{EC}_{0.y}$ (case = 2)

• trend.ec: the conditional ARDL trend derived from the EC tem $\alpha^{EC}_{1.y}$ (case = 4)

Examples

#PARAMETERS

#Sigma
corrm = matrix(0, ncol = 3, nrow = 3)
corrm[2,1] = 0.25
corrm[3,1] = 0.4
corrm[3,2] = -0.25
corrs = (corrm + t(corrm)) + diag(3)
sds = diag(c(1.3, 1.2, 1))
sigma = (sds %*% corrs %*% t(sds))

#Gamma
gammax = list()
gammax[[1]] = matrix(c(0.6, 0, 0.2, 0.1, -0.3, 0, 0, -0.3, 0.2), nrow = 3, ncol = 3, byrow = TRUE)
gammax[[2]] = matrix(c(0.2, 0, 0.1, 0.05, -0.15, 0, 0, 0, 0.1), nrow = 3, ncol = 3, byrow = TRUE)

#DATA GENERATION
data_sim = sim_vecm_ardl(nobs = 200,
                         case = 3,
                         sigma.in = sigma,
                         gamma.in = gammax,
                         axx.in = matrix(c(0.3, 0.5, 0.4, 0.3), nrow = 2, ncol = 2),
                         ayx.uc.in = c(0.5,0.6),
                         ayy.in = 0.7,
                         mu.in = rep(0, 3),
                         eta.in = rep(0, 3),
                         azero.in = rep(0.4, 3),
                         aone.in = rep(0, 3),
                         burn.in = 50,
                         seed.in = 10)

---

Critical values of the F-test on the independent variables in the conditional ARDL model.

Description

This internal data contains critical values of the Find test of Sam et al (2018), for several sample sizes and lag orders. Applicable only for cases I, III, and V. Critical values at significance levels 1%, 2.5%, 5% and 10%.

Usage

smk_crit

Format

A data frame with 144 rows and 17 variables

case

case related to intercept and trend specification. Only I, III or V

prob

significance levels. 0.01, 0.025, 0.05 or 0.10

num

sample size, 30 to 80 and beyond for asymptotic critical values

I0_x

right threshold for accepting the null of zero coefficients in the Find test. x: 1 to 7

I1_x

left threshold for rejecting the null of zero coefficients in the Find test. x: 1 to

---

Summary method

Description

This function summarizes the ARDL bootstrap test and all the other asymptotic procedures all together.

Usage

## S3 method for class 'bootCT'
summary(object, ...)

Arguments

object	an object of class "bootCT"
...	additional arguments, e.g. out: subset of output to print. Options (can be multiple) are: "all", "ARDL", "VECM", "cointVECM", "cointARDL". Defaults to "all".

Value

the function returns a list of summary statistics, already present in the function boot_ardl, and displays them in an appropriate manner. Depending on the out argument, ARDL/VECM estimation outputs and/or ARDL/VECM cointegration tests can be displayed.

---