Type:	Package
Title:	Make Symmetric and Asymmetric ARDL Estimations
Version:	0.1.1
Maintainer:	Huseyin Karamelikli <hakperest@gmail.com>
Description:	Implements estimation procedures for Autoregressive Distributed Lag (ARDL) and Nonlinear ARDL (NARDL) models, which allow researchers to investigate both short- and long-run relationships in time series data under mixed orders of integration. The package supports simultaneous modeling of symmetric and asymmetric regressors, flexible treatment of short-run and long-run asymmetries, and automated equation handling. It includes several cointegration testing approaches such as the Pesaran-Shin-Smith F and t bounds tests, the Banerjee error correction test, and the restricted ECM test, together with diagnostic tools including Wald tests for asymmetry, ARCH tests, and stability procedures (CUSUM and CUSUMQ). Methodological foundations are provided in Pesaran, Shin, and Smith (2001) <doi:10.1016/S0304-4076(01)00049-5> and Shin, Yu, and Greenwood-Nimmo (2014, ISBN:9780123855079).
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
Imports:	stats, msm, lmtest, nlWaldTest, car, utils
RoxygenNote:	7.3.3
Suggests:	knitr, rmarkdown, officer, flextable, equatags, magrittr, rlang, ggplot2, tidyr, dplyr, testthat (≥ 3.0.0)
NeedsCompilation:	no
VignetteBuilder:	knitr
Packaged:	2025-10-06 12:27:43 UTC; huseyin
Author:	Huseyin Karamelikli [aut, cre], Huseyin Utku Demir [aut]
Depends:	R (≥ 3.5.0)
Config/testthat/edition:	3
Repository:	CRAN
Date/Publication:	2025-10-09 12:10:11 UTC

ARCH Test

Description

Autoregressive conditional heteroskedasticity ARCH(q)

{\hat{\epsilon}}_t^2 = \alpha_0 + \sum_{i=1}^{q} \alpha_i {\hat{\epsilon}}_{t-i}^2

Usage

archtest(resid, q = 1)

Arguments

Value

A list of class "kardl" containing the following components:

• type: Type of the test

• statistic: The F-statistic of the test

• parameter: The degrees of freedom of the test

• p.value: The p-value of the test

• Fval: The F-value of the test

References

Engle, Robert F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica. 50 (4): 987–1007.

See Also

bgtest bptest resettest

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
archtest(kardl_model$finalModel$model$residuals,2)


# Summary of ARCH test
summary(archtest(kardl_model$finalModel$model$residuals))

Wald tests for asymmetries

Description

The asymmetry test is a statistical procedure used to assess the presence of asymmetry in the relationship between variables in a model. It is particularly useful in econometric analysis, where it helps to identify whether the effects of changes in one variable on another are symmetric or asymmetric. The test involves estimating a model that includes both positive and negative components of the variables and then performing a Wald test to determine if the coefficients of these components are significantly different from each other. If the test indicates significant differences, it suggests that the relationship is asymmetric, meaning that the impact of increases and decreases in the variables differs.

The non-linear model with one asymmetric variables is specified as follows:

\Delta{y_{t}} = \psi + \eta_{0}y_{t - 1} + \eta^{+}_{1} x^{+}_{t - 1}+ \eta^{-}_{1} x^{-}_{t - 1} + \sum_{j = 1}^{p}{\gamma_{j}\Delta y_{t - j}} + \sum_{j = 0}^{q}{\beta^{+}_{j}\Delta x^{+}_{t - j}} + \sum_{j = 0}^{m}{\beta^{-}_{j}\Delta x^{-}_{t - j}} + e_{t}

This function performs the asymmetry test both for long-run and short-run variables in a kardl model. It uses the nlWaldtest function from the nlWaldTest package for long-run variables and the linearHypothesis function from the car package for short-run variables. The hypotheses for the long-run variables are:

H_{0}: -\frac{\eta^{+}_{1}}{\eta_{0}} = -\frac{\eta^{-}_{1}}{\eta_{0}}

H_{1}: -\frac{\eta^{+}_{1}}{\eta_{0}} \neq -\frac{\eta^{-}_{1}}{\eta_{0}}

The hypotheses for the short-run variables are:

H_{0}: \sum_{j = 0}^{q}{\beta^{+}_{j}} = \sum_{j = 0}^{m}{\beta^{-}_{j}}

H_{1}: \sum_{j = 0}^{q}{\beta^{+}_{j}} \neq \sum_{j = 0}^{m}{\beta^{-}_{j}}

Usage

asymmetrytest(model)

Arguments

Details

This function performs a Wald test to assess the validity of linearity or symmetry in both the short-run and long-run.

This function evaluates whether the inclusion of a particular variable in the model follows a linear relationship or exhibits a non-linear pattern. By analyzing the behavior of the variable, the function helps to identify if the relationship between the variable and the outcome of interest adheres to a straight-line assumption or if it deviates, indicating a non-linear interaction. This distinction is important in model specification, as it ensures that the variable is appropriately represented, which can enhance the model's accuracy and predictive performance.

Value

A list with class "kardl" containing the following components:

• Lhypotheses: A list containing the null and alternative hypotheses for the long-run variables.

• Lwald: A data frame containing the Wald test results for the long-run variables, including F-statistic, p-value, degrees of freedom, and residual degrees of freedom.

• Shypotheses: A list containing the null and alternative hypotheses for the short-run variables.

• Swald: A data frame containing the Wald test results for the short-run variables, including F-statistic, p-value, degrees of freedom, residual degrees of freedom, and sum of squares.

• type: The type of the test, which is "asymmetrytest".

References

Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. Festschrift in honor of Peter Schmidt: Econometric methods and applications, 281-314.

See Also

kardl, pssf, psst, banerjee, recmt, narayan

Examples

 kardl_model<-kardl(imf_example_data,
                    CPI~ER+PPI+asym(ER+PPI)+deterministic(covid)+trend,
                    mode=c(1,2,3,0,1))
 ast<- asymmetrytest(kardl_model)
 ast
 ast$Lhypotheses

 # Using magrittr package
 library(magrittr)
 imf_example_data %>% kardl(CPI~ER+PPI+asym(ER+PPI)+deterministic(covid)+trend,
                    mode=c(1,2,3,0,1)) %>% asymmetrytest()

 # Detailed results of the test:

 summary(ast)
 #Or, utilizing magrittr package
 imf_example_data %>% kardl(CPI~ER+PPI+asym(ER+PPI)+deterministic(covid)+trend,
                    mode=c(1,2,3,0,1)) %>% asymmetrytest() %>% summary()

Banerjee cointegration test

Description

The Banerjee t test is designated for small data length. It is not recommended to be utilized for data with more than 100 observations.

Usage

banerjee(model, signif_level = "auto")

Arguments

Details

This function conducts the Banerjee cointegration test, which is specifically designed for datasets with a limited number of observations. The test assesses whether a long-term equilibrium relationship exists between variables by examining the residuals from a regression model. The Banerjee t-test is most effective for small sample sizes and is not recommended for datasets containing more than 100 observations, as its accuracy may decrease with larger data lengths. This test is useful for analyzing cointegration in small datasets, providing insights into the stability of relationships among variables over time.

Value

A list containing the results of the Banerjee cointegration test, including:

• type: The type of test performed, which is "cointegration".

• case: The case number used in the test (1, 2, 3, 4, or 5).

• statistic: The t-statistic value calculated from the test.

• k: The number of long-run variables in the model.

• Cont: The conclusion of the test, indicating whether cointegration is present, inconclusive, or absent.

• BoundNum: A numeric representation of the conclusion, where 1 indicates cointegration, 0 indicates inconclusive, and -1 indicates no cointegration.

• siglvl: The significance level used in the test, either "auto" or one of the specified numeric levels.

• criticalValues: A vector of critical values for the test, corresponding to the significance levels.

• parameter: The names of the long-run variables in the model.

• FH0: The null hypothesis of the test, which includes the long-run variables set to zero.

• Fmodel: The linear hypothesis model used in the test.

• warnings: Any warnings generated during the test, such as sample size concerns.

• method: The method used for the test, which is "Narayan".

References

Anindya Banerjee, Juan Dolado, Ricardo Mestre (1998) Error-correction Mechanism Tests for Cointegration in a Single-equation Framework, Journal of Time Series Analysis, Volume 19, Issue 3

See Also

pssf psst recmt narayan

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
A<- banerjee(kardl_model)
cat(paste0("The ECM parameter = ",A$coef,", k=",A$k," and the t statistics=",A$statistic,"."))
cat(paste0("\nWe found '",A$Cont, "' at ",A$siglvl,"."))


# Using magrittr
library(magrittr)
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                    mode=c(1,2,3,0)) %>% banerjee()

# critical Values are
A$criticalValues

# Getting details of the test.
 mySummary<-summary(A)
 mySummary

# The null hypothesis :
mySummary$H0

 # Using magrittr
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                    mode=c(1,2,3,0)) %>% banerjee() %>% summary()

IMF Example Data

Description

This is an example data set used for testing purposes.

Usage

imf_example_data

Format

A data frame with 470 rows and 4 variables:

ER

Numeric. Exchange rate of Turkey.

CPI

Numeric. CPI of Turkey.

PPI

Numeric. PPI of Turkey.

covid

Integer.Covid19 dummy variable.

Details

These data obtained from imf.data package. The sample data is not updated and obtained by following codes.:

install.packages("imf.data")
library("imf.data")
IFS <- load_datasets("IFS")

• PCPI_IX Prices, Consumer Price Index, All items, Index
  

• AIP_IX Economic Activity, Industrial Production, Index
  

• ENDE_XDC_USD_RATE Exchange Rates, Domestic Currency per U.S. Dollar, End of Period, Rate

trdata<-IFS$get_series(freq = "M", ref_area = "TR", indicator = c("PCPI_IX","AIP_IX","ENDE_XDC_USD_RATE"),start_period = "1985-01",end_period = "2024-02")
PeriodRow<-trdata[,1]
trdata[,1]<-NULL
colnames(trdata)<-c("ER","CPI","PPI")
trdata<-log(as.data.frame(lapply(trdata, function(x) as.numeric(x))))
rownames(trdata)<-PeriodRow

Inserting covid dummy variable

trdata<-cbind(trdata,covid=0)
trdata[420:470,4]<-1

See Also

load_datasets

Examples

data(imf_example_data)
head(imf_example_data)

Estimation of ARDL and NARDL

Description

This function estimates an Autoregressive Distributed Lag (ARDL) or Nonlinear ARDL (NARDL) model based on the provided data and model formula. It allows for flexible specification of variables, including deterministic terms, asymmetric variables, and trend components. The function also supports automatic lag selection using various information criteria.

Usage

kardl(
  data = NULL,
  model = NULL,
  maxlag = NULL,
  mode = NULL,
  criterion = NULL,
  differentAsymLag = NULL,
  batch = NULL,
  ...
)

Arguments

Details

Note: All arguments of this function can be set using kardl_set function.

Value

A list containing the final model, input parameters, and estimation results.

• inputs: The input parameters used for the model.

• finalModel: A list containing the final model formula, model object, number of parameters (k), sample size (n), start and end indices, and time span.

• start_time: The time when the model estimation started.

• end_time: The time when the model estimation ended.

• properLag: The optimal lag values for the short-run variables.

• TimeSpan: The total time span of the model.

• OptLag: A data frame containing the optimal lags and their corresponding criterion values.

• LagCriteria: A matrix containing the lag combinations and their corresponding criterion values.

• type: A string indicating the type of model, which is "kardlmodel".

See Also

recmt, kardl_set, kardl_get, kardl_reset, modelCriterion

Examples

# Sample article: THE DYNAMICS OF EXCHANGE RATE PASS-THROUGH TO DOMESTIC PRICES IN TURKEY
 library(dplyr)

  kardl_set(model=CPI~ER+PPI+asym(ER)+deterministic(covid)+trend ,
           data=imf_example_data,
           maxlag=2
           ) # setting the default values of the kardl function


 kardl_model_grid<-kardl( mode = "grid")
 kardl_model_grid
 kardl_model<- imf_example_data %>% kardl(mode = "grid_custom")
 kardl_model
 kardl_model2<-kardl(mode = c( 2    ,  1    ,  1   ,   3 ))

 # Getting the results
 kardl_model2

 # Getting the summary of the results
 summary(kardl_model)

 # OR
 imf_example_data %>% kardl(model=CPI~PPI+asym(ER)) %>% summary()

 # using . in the formula means that all variables in the data will be used

 kardl(model=CPI~.+deterministic(covid),mode = "grid")

 # Setting max lag instead of default value [4]
 kardl(imf_example_data,
       CPI~ER+PPI+asymL(ER),
       maxlag = 3, mode = "grid_custom")

 # Using another criterion for finding the best lag#'
 kardl_set(criterion = "HQ") # setting the criterion to HQ
 kardl( mode = "grid_custom")

 # using default values of lags
 kardl( mode=c(1,2,3,0))

 # summary( myNewStarSigns)
 # For using different lag values for negative and positive decompositions of non-linear variables
 # setting the same lags for positive and negative decompositions.
 kardl_set(differentAsymLag = FALSE)

 diffAsymLags<-kardl(model=CPI~asym(ER),maxlag=2, mode = "grid_custom")
 diffAsymLags$properLag


 # setting the different lags for positive and negative decompositions
 kardl_set(differentAsymLag = TRUE)
 sameAsymLags<-kardl(model=CPI~asym(ER),maxlag=2, mode = "grid_custom")
 sameAsymLags$properLag

 # Setting the preffixes and suffixes for non-linear variables
 kardl_set(AsymPrefix = c("asyP_","asyN_"), AsymSuffix = c("_PP","_NN"))
 kardl()

 # For having the lags plot
 library(ggplot2)

 #  kardl_model_grid[["LagCriteria"]] is a matrix, convert it to a data frame
 LagCriteria <- as.data.frame(kardl_model_grid[["LagCriteria"]])
 # Rename columns for easier access and convert relevant columns to numeric
 colnames(LagCriteria) <- c("lag", "AIC", "BIC", "AICc", "HQ")

 LagCriteria <- LagCriteria %>%  mutate(across(c(AIC, BIC, HQ), as.numeric))

 # Pivot the data to a long format excluding AICc
 library(tidyr)

 LagCriteria_long <- LagCriteria %>%
 select(-AICc) %>%
 pivot_longer(cols = c(AIC, BIC, HQ), names_to = "Criteria", values_to = "Value")
 # Find the minimum value for each criterion
 min_values <- LagCriteria_long %>%  group_by(Criteria) %>%
 slice_min(order_by = Value) %>%  ungroup()

 # Create the ggplot with lines, highlight minimum values, and add labels
 ggplot(LagCriteria_long, aes(x = lag, y = Value, color = Criteria, group = Criteria)) +
  geom_line() +
   geom_point(data = min_values, aes(x = lag, y = Value), color = "red", size = 3, shape = 8) +
     geom_text(data = min_values, aes(x = lag, y = Value, label = lag),
      vjust = 1.5, color = "black", size = 3.5) +
      labs(title = "Lag Criteria Comparison ", x = "Lag Configuration",  y = "Criteria Value") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Function to get settings

Description

This function retrieves options from the kardl package settings.

Usage

kardl_get(...)

Arguments

Value

If no arguments are provided, returns all options as a list. If one option is requested, returns its value directly. If multiple options are requested, returns a list of those options.

See Also

kardl_set, kardl_reset

Examples

# Get specific options
kardl_get("criterion", "differentAsymLag")

# Get all options
# Note: In interactive use, avoid calling this directly to prevent cluttering the console.
a<-kardl_get()
a$AsymSuffix

Calculating the long-run parameters

Description

All long-run estimated parameters are standardized by dividing them by the negative of the long-run parameter of the dependent variable.

Usage

kardl_longrun(model)

Arguments

Details

This function is used to calculate the long-run parameters of a model produced by the kardl function.

It calculates the long-run multipliers and their standard errors, and returns a list containing the kardl_longrun coefficients, standard errors, and a data frame with the results.

Value

a list of class kardl with the following elements:

• type: the type of the model, in this case "kardl_longrun"

• coef: the estimated coefficients of the long-run parameters

• delta_se: the standard errors of the long-run parameters

• results: a data frame with the estimated coefficients, standard errors, t-values, p-values, and significance stars

• starsDesc: a description of the significance stars used in the results

See Also

kardl, pssf, psst

Examples

kardl_model<-kardl(imf_example_data,
                  CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                  mode=c(1,2,3,0))
kardl_longrun(kardl_model)

# Using magrittr
library(magrittr)

imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                  mode=c(1,2,3,0)) %>% kardl_longrun()

Function to reset kardl package settings

Description

This function resets all options in the kardl package to their default values.

Usage

kardl_reset(. = FALSE)

Arguments

Value

Returns the default options as a list.

See Also

kardl_set, kardl_get

Examples

# Set some options
kardl_set(criterion = "BIC", differentAsymLag = TRUE)
# Reset to default values
kardl_get("criterion")  # Check current settings
kardl_reset()
kardl_get("criterion")  # Check settings after reset

library(magrittr)
 MyFormula<-CPI~ER+PPI+asym(ER)+deterministic(covid)+trend
imf_example_data %>%
  kardl_set(LongCoef= "K1{lag}w1{varName}",differentAsymLag= FALSE ) %>%  kardl(MyFormula ) %>%
    kardl_reset()
kardl_get()

imf_example_data %>%
  kardl_reset() %>%
    kardl_set(LongCoef= "K2{lag}w2{varName}",differentAsymLag=FALSE ) %>%  kardl(MyFormula)

kardl_get(c("LongCoef","differentAsymLag","ShortCoef","batch"))

Function to get or set settings

Description

This function allows you to get or set various options related to the kardl package.

Usage

kardl_set(. = FALSE, ...)

Arguments

Value

If no arguments are provided, returns all options as a list. If named arguments are provided, sets those options and returns the updated list.

See Also

kardl_get, kardl_reset

Examples

# Set options
kardl_set(criterion = "BIC", differentAsymLag = TRUE)
# Get specific options
kardl_get("criterion", "differentAsymLag")
# Get all options.

# Note: In interactive use, avoid calling this directly to prevent cluttering the console.


kardl_get()


# Utilizing the magrittr pipe
library(magrittr)
# Set options and then get them

MyFormula<-CPI~ER+PPI+asym(ER)+deterministic(covid)+trend
kardl_set(ShortCoef = "L___{lag}.d.{varName}")
imf_example_data %>%   kardl(MyFormula)

kardl_reset()
kardl_get()

imf_example_data %>%  kardl_set(LongCoef= "LK{lag}_{varName}",ShortCoef = "D{lag}.d.{varName}") %>%
kardl(MyFormula)
kardl_get(c("LongCoef","ShortCoef"))

Merge two lists, accenting the first list.

Description

The first list of values takes precedence. When both lists have items with the same names, the values from the first list will be applied. In merging the two lists, priority is given to the left list, so if there are overlapping items, the corresponding value from the left list will be used in the merged result.

Usage

lmerge(first, second, ...)

Arguments

Value

list

See Also

append

Examples

a<-list("a"="first a","b"="second a","c"=list("w"=12,"k"=c(1,3,6)))
b<-list("a"="first b","b"="second b","d"=14,"e"=45)
theResult<- lmerge(a,b)
unlist(theResult)

# for right merge
lmerge(b,a)

# Unisted return
theResult<- lmerge(a,b,c("v1"=11,22,3,"v5"=5))
theResult

m2<-list("m1"="kk2","m1.2.3"=list("m1.1.1"=333,"m.1.4"=918,"m.1.5"=982,"m.1.6"=981,"m.1.7"=928))
m3<-list("m1"="kk23","m2.3"=2233,"m1.2.4"=list("m1.1.1"=333444,"m.1.5"=982,"m.1.6"=91,"m.1.7"=928))
a<-c(32,34,542,"k"=35)
b<-c(65,"k"=34)

h1<-lmerge(a, m2)
unlist( h1)
h2<-lmerge(a,b,m2,m3,list("m1.1"=4))
unlist(h2)

Model Selection Criterion

Description

Computes a model selection criterion (AIC, BIC, AICc, or HQ) or applies a user-defined function to evaluate a statistical model.

Usage

modelCriterion(cr, model, ...)

Arguments

Details

This function returns model selection criteria used to compare the quality of different models. All criteria are defined such that lower values indicate better models (i.e., the goal is minimization).

If you wish to compare models using a maximization approach (e.g., log-likelihood), you can multiply the result by -1.

Note: The predefined string options (e.g., "AIC") are not the same as the built-in R functions AIC() or BIC(). In particular, the values returned by this function are adjusted by dividing by the sample size n (i.e., normalized AIC/BIC), which makes it more comparable across datasets of different sizes.

The function returns:

• "AIC": \frac{2k - 2\ell}{n} Akaike Information Criterion divided by n.

• "BIC": \frac{\log(n) \cdot k - 2\ell}{n} Bayesian Information Criterion divided by n.

• "AICc": \frac{2k(k+1)}{n - k - 1} + \frac{2k - 2\ell}{n} Corrected Akaike Information Criterion divided by n.

• "HQ": \frac{2 \log(\log(n)) \cdot k - 2\ell}{n} Hannan–Quinn Criterion divided by n.

where:

• k is the number of parameters,

• n is the sample size,

• \ell is the log-likelihood of the model.

If cr is a function, it is called with the fitted model and any additional arguments passed through ....

Value

A numeric value representing the selected criterion, normalized by the sample size if one of the predefined options is used.

See Also

kardl

Examples

model <- list(model = lm(mpg ~ wt + hp, data = mtcars), k = 3, n = nrow(mtcars))
modelCriterion(AIC, model)
#
modelCriterion("AIC", model)
modelCriterion("BIC", model)

# Using a custom criterion function
my_cr_fun <- function(mod, ...) { AIC(mod) / length(mod$model[[1]]) }
modelCriterion(my_cr_fun, model)

NARAYAN test

Description

This function performs the Narayan test, which is designed to assess cointegration using critical values specifically tailored for small sample sizes. Unlike traditional cointegration tests that may rely on asymptotic distributions, the Narayan test adjusts for the limitations of small samples, providing more accurate results in such contexts. This makes the test particularly useful for studies with fewer observations, as it accounts for sample size constraints when determining the presence of a long-term equilibrium relationship between variables.

Usage

narayan(model, case = 3, signif_level = "auto")

Arguments

Value

A list with class "kardl" containing the following components:

• type: The type of the test, which is "cointegration".

• case: The case of the test, which is a numeric value (1, 2, 3, 4, or 5).

• statistic: The calculated F-statistic for the test.

• k: The number of long-run variables in the model.

• Cont: The conclusion of the test, indicating whether cointegration is found, inconclusive, or not found.

• BoundNum: A numeric value indicating the result of the test: 1 for cointegration, 0 for inconclusive, and -1 for no cointegration.

• siglvl: The significance level used in the test, which can be "auto", "0.10", "0.1", "0.05", "0.025", or "0.01".

• criticalValues: A numeric vector containing the critical values for the test based on the specified case and significance level.

• parameter: A character vector containing the names of the long-run parameters in the model.

• FH0: The null hypothesis of the test, which is a character string describing the hypothesis being tested.

• Fmodel: The detailed F test results, including the F-statistic, p-value, degrees of freedom, and residual degrees of freedom.

• warnings: A character vector containing any warnings generated during the test, such as issues with the model specification or data length.

• method: The method used for the test.

Hypothesis testing

The null hypothesis (H0) of the F Bound test is that there is no cointegration among the variables in the model. In other words, it tests whether the long-term relationship between the variables is statistically significant. If the calculated F-statistic exceeds the upper critical value, we reject the null hypothesis and conclude that there is cointegration. Conversely, if the F-statistic falls below the lower critical value, we fail to reject the null hypothesis, indicating no evidence of cointegration. If the F-statistic lies between the two critical values, the result is inconclusive.

\Delta {y}_t = \psi + \varphi t + \eta _0 {y}_{t-1} + \sum_{i=1}^{k} { \eta _i {x}_{i,t-1} } + \sum_{j=1}^{p} { \gamma_{j} \Delta {y}_{t-j} }+ \sum_{i=1}^{k} {\sum_{j=0}^{q_i} { \beta_{ij} \Delta {x}_{i,t-j} } }+ e_t

Cases 1, 3, 5:

\mathbf{H_{0}:} \eta_0 = \eta_1 = \dots = \eta_k = 0

\mathbf{H_{1}:} \eta_{0} \neq \eta_{1} \neq \dots \neq \eta_{k} \neq 0

Case 2:

\mathbf{H_{0}:} \eta_0 = \eta_1 = \dots = \eta_k = \psi = 0

\mathbf{H_{1}:} \eta_{0} \neq \eta_{1} \neq \dots \neq \eta_{k} \neq \psi \neq 0

Case 4:

\mathbf{H_{0}:} \eta_0 = \eta_1 = \dots = \eta_k = \varphi = 0

\mathbf{H_{1}:} \eta_{0} \neq \eta_{1} \neq \dots \neq \eta_{k} \neq \varphi \neq 0

References

Narayan, P. K. (2005). The saving and investment nexus for China: evidence from cointegration tests. Applied economics, 37(17), 1979-1990.

See Also

pssf psst banerjee recmt

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
A<-narayan(kardl_model)
A
cat(paste0("The F statistics=",A$statistic," where k=",A$k,"."))
cat(paste0("\nWe found '",A$Cont, "' at ",A$siglvl,"."))
cat(paste0("\nThe proboblity is = ",sprintf("%.10f",A$Fmodel[["Pr(>F)"]][2])))

# Utilising magrittr:

library(magrittr)
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0)) %>% narayan()


# Getting details of the test.
mySummary<-summary(A)
mySummary

# Utilising magrittr:
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0)) %>% narayan()  %>% summary()


# Critical Values are
A$criticalValues
# The null hypothesis :
A

# getting H0
mySummary$H0

# Detailed F test
A$Fmodel

Extract Variables from a Formula

Description

The parseFormula() unction extracts and lists variables from specific parts of a formula, especially those within parentheses of specified function types. This enables users to isolate and analyze segments of a model formula, such as variables within custom functions, with an option to ignore case sensitivity in pattern matching.

Usage

parseFormula(formula_, matchPattern = "asym", ignore.case = FALSE)

Arguments

Value

A list containing:

• Parsed variables: Variables that are located within the specified matchPattern part of the formula.

• Remaining model: The rest of the formula, excluding the parsed variables.

See Also

replaceValues, formula

Examples

# Identify variables within specific functions, such as 'asymS'
parsed<-parseFormula(y ~ x +det(s + d) + asymS(d + s),"asymS()")
parsed

 # Parse formulas containing various collection types like () or []
formula_ <- y ~ x +det(s -gg- d) + asymS(d2 -rr+ s)-mm[y1+y2+y3]+asym[k1+k2+k3]+trend-huseyin

# Extract variables in the 'asymS' function
parseFormula(formula_,"asymS")

# Use multiple functions to extract variables. If a specified function, such as "uuu",
# is not found, nothing is returned for it
a<-parseFormula(formula_,c("mm","det","uuu"))

 # To obtain variables not enclosed within any function, specify them directly
 parseFormula(formula_,c("trend","huseyin"))

# By default, 'parseFormula()' is case-sensitive.
# For case-insensitive matching, set 'ignore.case = TRUE'

parseFormula(formula_,"asyms", TRUE)

PSS F Bound test

Description

This function performs the Pesaran et al. F Bound test

Usage

pssf(model, case = 3, signif_level = "auto")

Arguments

Details

This function performs the Pesaran, Shin, and Smith (PSS) F Bound test to assess the presence of a long-term relationship (cointegration) between variables in the context of an autoregressive distributed lag (ARDL) model. The PSS F Bound test examines the joint significance of lagged levels of the variables in the model. It provides critical values for both the upper and lower bounds, which help determine whether the variables are cointegrated. If the calculated F-statistic falls outside these bounds, it indicates the existence of a long-term equilibrium relationship. This test is particularly useful when the underlying data includes a mix of stationary and non-stationary variables.

Value

A list with class "kardl" containing the following components:

• type: The type of the test, which is "cointegration".

• case: The case of the test, which is a numeric value (1, 2, 3, 4, or 5).

• statistic: The calculated F-statistic for the test.

• k: The number of long-run variables in the model.

• Cont: The conclusion of the test, indicating whether cointegration is found, inconclusive, or not found.

• BoundNum: A numeric value indicating the result of the test: 1 for cointegration, 0 for inconclusive, and -1 for no cointegration.

• siglvl: The significance level used in the test, which can be "auto", "0.10", "0.1", "0.05", "0.025", or "0.01".

• criticalValues: A numeric vector containing the critical values for the test based on the specified case and significance level.

• parameter: A character vector containing the names of the long-run parameters in the model.

• FH0: The null hypothesis of the test, which is a character string describing the hypothesis being tested.

• Fmodel: The detailed F test results, including the F-statistic, p-value, degrees of freedom, and residual degrees of freedom.

• warnings: A character vector containing any warnings generated during the test, such as issues with the model specification or data length.

• method: The method used for the test.

Hypothesis testing

The null hypothesis (H0) of the F Bound test is that there is no cointegration among the variables in the model. In other words, it tests whether the long-term relationship between the variables is statistically significant. If the calculated F-statistic exceeds the upper critical value, we reject the null hypothesis and conclude that there is cointegration. Conversely, if the F-statistic falls below the lower critical value, we fail to reject the null hypothesis, indicating no evidence of cointegration. If the F-statistic lies between the two critical values, the result is inconclusive.

\Delta {y}_t = \psi + \varphi t + \eta _0 {y}_{t-1} + \sum_{i=1}^{k} { \eta _i {x}_{i,t-1} } + \sum_{j=1}^{p} { \gamma_{j} \Delta {y}_{t-j} }+ \sum_{i=1}^{k} {\sum_{j=0}^{q_i} { \beta_{ij} \Delta {x}_{i,t-j} } }+ e_t

Cases 1, 3, 5:

\mathbf{H_{0}:} \eta_0 = \eta_1 = \dots = \eta_k = 0

\mathbf{H_{1}:} \eta_{0} \neq \eta_{1} \neq \dots \neq \eta_{k} \neq 0

Case 2:

\mathbf{H_{0}:} \eta_0 = \eta_1 = \dots = \eta_k = \psi = 0

\mathbf{H_{1}:} \eta_{0} \neq \eta_{1} \neq \dots \neq \eta_{k} \neq \psi \neq 0

Case 4:

\mathbf{H_{0}:} \eta_0 = \eta_1 = \dots = \eta_k = \varphi = 0

\mathbf{H_{1}:} \eta_{0} \neq \eta_{1} \neq \dots \neq \eta_{k} \neq \varphi \neq 0

References

Pesaran, M. H., Shin, Y. and Smith, R. (2001), “Bounds Testing Approaches to the Analysis of Level Relationship”, Journal of Applied Econometrics, 16(3), 289-326.

See Also

psst banerjee recmt narayan

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
A<-pssf(kardl_model)
A
cat(paste0("The F statistics=",A$statistic," where k=",A$k,"."))
cat(paste0("\nWe found '",A$Cont, "' at ",A$siglvl,". "))
cat(paste0("\nThe proboblity is = ",sprintf("%.10f",A$Fmodel[["Pr(>F)"]][2])))

# Using magrittr :

library(magrittr)
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0)) %>% pssf()

# Getting details of the test.
mySummary<-summary(A)
mySummary

# Using magrittr:
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0)) %>% pssf() %>% summary()

# Critical Values are
A$criticalValues
# The null hypothesis :
A

# getting H0
mySummary$H0

# Detailed F test
A$Fmodel

PSS t Bound test

Description

This function performs the Pesaran t Bound test

Usage

psst(model, case = 3, signif_level = "auto")

Arguments

Details

This function performs the Pesaran, Shin, and Smith (PSS) t Bound test, which is used to detect the existence of a long-term relationship (cointegration) between variables in an autoregressive distributed lag (ARDL) model. The t Bound test specifically focuses on the significance of the coefficient of the lagged dependent variable, helping to assess whether the variable reverts to its long-term equilibrium after short-term deviations. The test provides critical values for both upper and lower bounds. If the t-statistic falls within the appropriate range, it confirms the presence of cointegration. This test is particularly useful when working with datasets containing both stationary and non-stationary variables.

Value

A list containing the results of the PSS t Bound test, including:

• type: The type of test performed, which is "cointegration".

• case: The case number used in the test (1, 2, 3, 4, or 5).

• statistic: The t-statistic value calculated from the test.

• k: The number of long-run variables in the model.

• Cont: The conclusion of the test, indicating whether cointegration is present, inconclusive, or absent.

• BoundNum: A numeric representation of the conclusion, where 1 indicates cointegration, 0 indicates inconclusive, and -1 indicates no cointegration.

• siglvl: The significance level used in the test, either "auto" or one of the specified numeric levels.

• criticalValues: A vector of critical values for the test, corresponding to the significance levels.

• parameter: The names of the long-run variables in the model.

• FH0: The null hypothesis of the test, which includes the long-run variables set to zero.

• Fmodel: The linear hypothesis model used in the test.

• warnings: Any warnings generated during the test, such as sample size concerns.

• method: The method used for the test, which is "Narayan".

Hypothesis testing

The PSS t Bound test evaluates the null hypothesis that the long-run coefficients of the model are equal to zero against the alternative hypothesis that at least one of them is non-zero. The test is conducted under different cases, depending on the model specification.

\Delta {y}_t = \psi + \varphi t + \eta _0 {y}_{t-1} + \sum_{i=1}^{k} { \eta _i {x}_{i,t-1} } + \sum_{j=1}^{p} { \gamma_{j} \Delta {y}_{t-j} }+ \sum_{i=1}^{k} {\sum_{j=0}^{q_i} { \beta_{ij} \Delta {x}_{i,t-j} } }+ e_t

\mathbf{H_{0}:} \eta_0 = 0

\mathbf{H_{1}:} \eta_{0} \neq 0

References

Pesaran, M. H., Shin, Y. and Smith, R. (2001), “Bounds Testing Approaches to the Analysis of Level Relationship”, Journal of Applied Econometrics, 16(3), 289-326.

See Also

pssf banerjee recmt narayan

Examples

kardl_model<-kardl(imf_example_data,
                    CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                    mode=c(1,2,3,0))
A<- psst(kardl_model)
cat(paste0("The t statistics=",A$statistic," where k=",A$k,"."))
 cat(paste0("\nWe found '",A$Cont, "' at ",A$siglvl,"."))


# Using magrittr

library(magrittr)
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                    mode=c(1,2,3,0)) %>% psst()

# critical Values are
A$criticalValues

# Getting details of the test.
mySummary<-summary(A)
mySummary

# The null hypothesis :
mySummary$H0

imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                    mode=c(1,2,3,0)) %>% psst() %>% summary()

Restricted ECM test

Description

This function is used to perform the Error Correction Model (ECM) test, which is designed to determine whether there is cointegration in the model. Cointegration indicates a long-term equilibrium relationship between variables, despite short-term deviations. The ECM test helps identify if such a long-term relationship exists by examining the short-run dynamics and adjusting for deviations from equilibrium. If the test confirms cointegration, it suggests that the variables move together over time, maintaining a stable long-term relationship. This is critical for ensuring that the model properly captures both short-term fluctuations and long-term equilibrium behavior.

Usage

recmt(
  data = NULL,
  model = NULL,
  case = 3,
  signif_level = "auto",
  maxlag = NULL,
  mode = NULL,
  criterion = NULL,
  differentAsymLag = NULL,
  batch = NULL,
  ...
)

Arguments

Value

A list containing the results of the PSS t Bound test and recm, including:

• type: The type of test performed, which is "cointegration".

• case: The case number used in the test (1, 2, 3, 4, or 5).

• statistic: The t-statistic value calculated from the test.

• k: The number of long-run variables in the model.

• Cont: The conclusion of the test, indicating whether cointegration is present, inconclusive, or absent.

• BoundNum: A numeric representation of the conclusion, where 1 indicates cointegration, 0 indicates inconclusive, and -1 indicates no cointegration.

• siglvl: The significance level used in the test, either "auto" or one of the specified numeric levels.

• criticalValues: A vector of critical values for the test, corresponding to the significance levels.

• parameter: The names of the long-run variables in the model.

• coef: The estimated coefficient of the error correction term.

• FH0: The null hypothesis of the test, which includes the long-run adjustment coefficient set to zero.

• longrunEQ: The long-run equation used in the test.

• shortrunEQ: The short-run equation used in the test.

• ecmL: The linear model fitted to the long-run equation.

• ecmS: The short-run model fitted to the error correction term.

• ecmResiduals: The residuals from the long-run model.

• EcmResLagged: The lagged residuals from the long-run model.

• finalModel: The final model used in the test, which includes the error correction model.

• OptLag: The optimal lag length determined for the model.

• warnings: Any warnings generated during the test, such as sample size concerns.

• method: The method used for the test, which is "recmt".

Hypothesis testing

The restricted ECM test, also known as the PSS t Bound test, is a statistical test used to assess the presence of cointegration in a model. Cointegration refers to a long-term equilibrium relationship between two or more time series variables. The PSS t Bound test is based on the work of Pesaran, Shin, and Smith (2001) and is particularly useful for models with small sample sizes.

The null and alternative hypotheses for the restricted ECM test are as follows:

\mathbf{H_{0}:} \theta = 0

\mathbf{H_{1}:} \theta \neq 0

The null hypothesis (H_{0}) states that there is no cointegration in the model, meaning that the long-run relationship between the variables is not significant. The alternative hypothesis (H_{1}) suggests that there is cointegration, indicating a significant long-term relationship between the variables.

The test statistic is calculated as the t-statistic of the coefficient of the error correction term (\theta) in the ECM model. If the absolute value of the t-statistic exceeds the critical value from the PSS t Bound table, we reject the null hypothesis in favor of the alternative hypothesis, indicating that cointegration is present.

The cases for the restricted ECM Bound test are defined as follows:

• case 1: No constant, no trend.

  This case is used when the model does not include a constant term or a trend term. It is suitable for models where the variables are stationary and do not exhibit any long-term trends.

  The model is specified as follows:

  \begin{aligned} \Delta y_t = \sum_{j=1}^{p} \gamma_j \Delta y_{t-j} + \sum_{i=1}^{k} \sum_{j=0}^{q_i} \beta_{ij} \Delta x_{i,t-j} + \theta (y_{t-1} - \sum_{i=1}^{k} \alpha_i x_{i,t-1} ) + e_t \end{aligned}

• case 2: Restricted constant, no trend.

  This case is used when the model includes a constant term but no trend term. It is suitable for models where the variables exhibit a long-term relationship but do not have a trend component. The model is specified as follows:

  \begin{aligned} \Delta y_t &= \sum_{j=1}^{p} \gamma_j \Delta y_{t-j} + \sum_{i=1}^{k} \sum_{j=0}^{q_i} \beta_{ij} \Delta x_{i,t-j} + \theta (y_{t-1} - \alpha_0 - \sum_{i=1}^{k} \alpha_i x_{i,t-1} ) + e_t \end{aligned}

• case 3: Unrestricted constant, no trend.

  This case is used when the model includes an unrestricted constant term but no trend term. It is suitable for models where the variables exhibit a long-term relationship with a constant but do not have a trend component.

  The model is specified as follows:

  \begin{aligned} \Delta y_t &= \sum_{j=1}^{p} \gamma_j \Delta y_{t-j} + \sum_{i=1}^{k} \sum_{j=0}^{q_i} \beta_{ij} \Delta x_{i,t-j} + \theta (y_{t-1} - \alpha_0 - \sum_{i=1}^{k} \alpha_i x_{i,t-1} ) + e_t \end{aligned}

• case 4: Unrestricted Constant, restricted trend.

  This case is used when the model includes an unrestricted constant term and a restricted trend term. It is suitable for models where the variables exhibit a long-term relationship with a constant and a trend component.

  The model is specified as follows:

  \begin{aligned} \Delta y_t &= \phi + \sum_{j=1}^{p} \gamma_j \Delta y_{t-j} + \sum_{i=1}^{k} \sum_{j=0}^{q_i} \beta_{ij} \Delta x_{i,t-j} + \theta (y_{t-1} - \pi (t-1) - \sum_{i=1}^{k} \alpha_i x_{i,t-1} ) + e_t \end{aligned}

• case 5: Unrestricted constant, unrestricted trend.

The Error Correction Model (ECM) is specified as follows:

\begin{aligned} \Delta y_t &= \phi + \varphi t + \sum_{j=1}^{p} \gamma_j \Delta y_{t-j} + \sum_{i=1}^{k} \sum_{j=0}^{q_i} \beta_{ij} \Delta x_{i,t-j} + \theta (y_{t-1} - \sum_{i=1}^{k} \alpha_i x_{i,t-1} ) + e_t \end{aligned}

See Also

kardl pssf psst recmt narayan

Examples

 # Sample article: THE DYNAMICS OF EXCHANGE RATE PASS-THROUGH TO DOMESTIC PRICES IN TURKEY
 library(magrittr)
 kardl_set(model=CPI~ER+PPI+asym(ER)+deterministic(covid)+trend ,
           data=imf_example_data ,
           maxlag=3)

 recmt_model_grid<-recmt(mode = "grid")
 recmt_model_grid
 recmt_model<- imf_example_data %>% recmt(mode = "grid_custom")
 recmt_model
 recmt_model2<-recmt(mode = c( 2    ,  1    ,  1   ,   3 ))
 # Getting the results
 recmt_model2
 # Getting the summary of the results
 summary(recmt_model2)
 # OR
 imf_example_data %>% recmt(CPI~PPI+asym(ER) +trend,case=4) %>% summary()

 # For increasing the performance of finding the most fitted lag vector
 recmt(mode = "grid_custom")
 # Setting max lag instead of default value [4]
 recmt(maxlag = 2, mode = "grid_custom")
 # Using another criterion for finding the best lag
 recmt(criterion = "HQ", mode = "grid_custom")



 # summary( myNewStarSigns)
 # For using different lag values for negative and positive decompositions of non-linear variables

 # setting the same lags for positive and negative decompositions.
 kardl_set(differentAsymLag = FALSE)

 diffAsymLags<-recmt( mode = "grid_custom")
 diffAsymLags$OptLag

 # setting the different lags for positive and negative decompositions
 sameAsymLags<-recmt(differentAsymLag = TRUE , mode = "grid_custom" )
 sameAsymLags$OptLag


 # Setting the preffixes and suffixes for non-linear variables
 kardl_reset()
 kardl_set(AsymPrefix = c("asyP_","asyN_"), AsymSuffix = c("_PP","_NN"))
 customizedNames<-recmt(imf_example_data, CPI~ER+PPI+asym(ER) )
 customizedNames$ecmS$finalModel$model

 # For having the lags plot
 library(ggplot2)
 library(dplyr)

 #  recmt_model_grid[["LagCriteria"]] is a matrix, convert it to a data frame
 LagCriteria <- as.data.frame(recmt_model_grid$ecmS$LagCriteria)
 # Rename columns for easier access and convert relevant columns to numeric
 colnames(LagCriteria) <- c("lag", "AIC", "BIC", "AICc", "HQ")
 LagCriteria <- LagCriteria %>%  mutate(across(c(AIC, BIC, HQ), as.numeric))

 # Pivot the data to a long format excluding AICc
 library(tidyr)

 LagCriteria_long <- LagCriteria %>%  select(-AICc) %>%
 pivot_longer(cols = c(AIC, BIC, HQ), names_to = "Criteria", values_to = "Value")
 # Find the minimum value for each criterion
 min_values <- LagCriteria_long %>%  group_by(Criteria) %>%
   slice_min(order_by = Value) %>%  ungroup()

 # Create the ggplot with lines, highlight minimum values, and add labels
 ggplot(LagCriteria_long, aes(x = lag, y = Value, color = Criteria, group = Criteria)) +
   geom_line() +
   geom_point(data = min_values, aes(x = lag, y = Value), color = "red", size = 3, shape = 8) +
   geom_text(data = min_values, aes(x = lag, y = Value, label = lag),
     vjust = 1.5, color = "black", size = 3.5) +
   labs(title = "Lag Criteria Comparison", x = "Lag Configuration",  y = "Criteria Value") +
   theme_minimal() +
   theme(axis.text.x = element_text(angle = 45, hjust = 1))

Replace Patterns with Evaluated Values

Description

The replaceValues() function allows you to replace placeholders in text with variable values or evaluated expressions. Placeholders are marked by {} brackets, and the function supports capturing both global and non-global variables, making it useful for templating and dynamic string generation in R.

Usage

replaceValues(original_text, x = FALSE, capture_warnings = TRUE)

Arguments

Value

A string with all placeholders replaced by evaluated values.

See Also

eval, parse, gregexpr, regmatches

Examples

 # Basic example with global variables
orjTXT <- "My F value is {thisF} and  its criterion is {CrF}"
thisF <- 2.33
CrF <- 32.43
replaceValues(orjTXT)
cat(replaceValues("The summary ls: {summary(lm(mpg ~ wt + hp, data = mtcars))}\n This is example"))

 # Nested function example for non-global variables
globalY <- 10
bb <- function(x){
  y <-  x+2;
 secondFunc <- function(x){
   replaceValues("The global value of Y+3 is {globalY+3}.  The non global value is {x}",x)
  }
  secondFunc(y)
}
bb(5)


 # Nested variables example. Something like $$ in PHP
FirstVar <- "First"
SecondVar <- "Second"
FirstSecondVar <- "_____________"
orjTXT <- "First var is {FirstVar}. The combinations of var names \"FirstSecondVar\" "
orjTXT <- paste0(orjTXT,"is= {{FirstVar}{SecondVar}Var}. Where SecondVar = {SecondVar} .")
replaceValues( orjTXT)

# Using mathematical expressions
MyVar = 3
replaceValues( "First var multiplying to 12 is {MyVar*12} and its power is {MyVar^12}.")

# Using templates from external files
# file_contents <- readLines(system.file("template", templateName, package = getPackageName()))
file_contents <- readLines(system.file("template", "printkardl.txt", package = "kardl"))
data(imf_example_data)
 MyFormula<-CPI~ER+PPI+asym(ER)+deterministic(covid)+trend
 kardl_model<-kardl(imf_example_data,MyFormula,mode="quick")
output<- replaceValues(file_contents,kardl_model)
cat(output)

Make Equations of used model in Latex or Office

Description

The writemath function generates all necessary equations for analysis, including those for ARDL, NARDL, short-run and long-run nonlinearities, and dynamic multipliers. It produces these equations in multiple formats: as text and as files compatible with MS Word, Markdown, LaTeX, and LibreOffice. This function provides a comprehensive set of formulas essential for econometric analysis, facilitating easy access to equations across various document formats for efficient reporting and presentation.

Usage

writemath(formula_, output = 1, verbose = FALSE)

Arguments

Value

print or save

See Also

kardl, kardl_longrun

Examples

# Note: The file creations in this examples were deactivated in the current examples
# because of CRAN policies.

# For saving all equations in a MS word document, \strong{docx}.
# The directory can be added alongside of the file name.
# For Windows OS directories could be written as \ not /.

# Here the tempdir() function is used to get a temporary directory path.
# Users can replace this with their desired directory path.


writemath(y~x+z+asym(v)+asymL(q+a),tempfile(fileext = ".docx"))


# For Markdown file the extenssion of the file should be assigned as \strong{md}.

writemath(y~x+z+asym(v+w)+asymL(q+a)+asymS(m),tempfile(fileext = ".md"))


# All equations are able to be saved in a PDF file.

writemath(y~x+z+asym(v+w)+asymL(q+a)+asymS(m),tempfile(fileext = ".pdf"))





# Following commad saves LibreOffice formulas in terminal.

# Copy and paste formulas there and after selecting related formula click on formula icon.

kardl_model<-kardl(imf_example_data,CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,mode=c(1,2,3,0))

# Following command writes all equations in a latex file in current directory.

# Note: The file creations in this examples were deactivated because of CRAN policies.


tmp <- tempfile(fileext = ".tex")
writemath(kardl_model,tmp)


# For printing the equations in Latex fomrat assignning of file name to 1 is required.
# A user's formula can be written directly in the function.
eq1 <- writemath(y~x+z+asym(v+w)+asymL(q+a)+asymS(m),1)

# To get all of the N/ARDL equations (in LaTeX format):
# Note: Here the output is limited to 1000 characters for better visibility.
print(eq1,1000)




# To saving outputs for different output type, in a list is available.
eq2 <- writemath(y~x+z+asym(v+w)+asymL(q+a)+asymS(m),1)
# To get the equations' subcomponents, here the long-run equation (in LaTeX format):
eq2$formulas$longRunEqFormula

# For printing the equations in Markdown fomrat assignning of file name to 2 is required.
eq3<- writemath(y~x+z+asym(v+w)+asymL(q+a)+asymS(m),2)
# To get the ECM equation (in Markdown format):
eq3$formulas$ECMEqFormula

# For printing the equations in OpenOffice fomrat assignning of file name to 3 is required.
eq4<-writemath(y~x+z+asym(v+w)+asymL(q+a)+asymS(m),3)
# To get the NARDL equation (in LibreOffice format):
eq4$formulas$NARDL_eq_Formula