Type:	Package
Title:	Make Symmetric and Asymmetric ARDL Estimations
Version:	1.1.0
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, and the restricted ECM test. 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, ggplot2, utils
RoxygenNote:	7.3.3
Suggests:	knitr, rmarkdown, officer, flextable, equatags, magrittr, rlang, tidyr, dplyr, testthat (≥ 3.0.0)
NeedsCompilation:	no
VignetteBuilder:	knitr
Packaged:	2026-03-09 10:29:54 UTC; huseyin
Author:	Huseyin Karamelikli [aut, cre], Huseyin Utku Demir [aut]
Depends:	R (≥ 3.5.0)
Config/testthat/edition:	3
Repository:	CRAN
Date/Publication:	2026-03-09 11:00:02 UTC

Produce Bootstrap Confidence Intervals for Dynamic Multipliers

Description

This function computes bootstrap confidence intervals (CI) for dynamic multipliers of a specified variable in a model estimated using the kardl package. The bootstrap method generates resampled datasets to estimate the variability of the dynamic multipliers, providing upper and lower bounds for the confidence interval.

Usage

bootstrap(kmodel, horizon = 80, replications = 100, level = 95, minProb = 0)

Arguments

Details

The mpsi component of the output contains the dynamic multiplier estimates along with their upper and lower confidence intervals. These values are provided for each variable and at each time horizon.

Value

A list containing the following elements:

• mpsi: A data frame containing the dynamic multiplier estimates along with their upper and lower confidence intervals for each variable and time horizon.

• level: The confidence level used for the intervals (e.g 95).

• horizon: The horizon over which the multipliers were computed (e.g., 40).

• vars: A list of variable information extracted from the model, including dependent variable, independent variables, asymmetric variables, and deterministic terms.

• replications: The number of bootstrap replications performed.

• type: A character string indicating the type of analysis, in this case "bootstrap".

See Also

mplier for calculating dynamic multipliers

Examples

library(dplyr)

  # Example usage of the bootstrap function


 # Fit a model using kardl
 kardl_model <- kardl(imf_example_data,
                      CPI ~ ER + PPI + asy(ER) +
                       det(covid) + trend,
                      mode = c(1, 2, 3, 0))

 # Perform bootstrap with specific variables for plotting
 boot <-
   bootstrap(kardl_model,   replications=5)
 # The boot object will include all plots for the specified variables
 # Displaying the boot object provides an overview of its components
 names(boot)


 # Inspect the first few rows of the dynamic multiplier estimates
  head(boot$mpsi)


  summary(boot)

 # Retrieve plots generated during the bootstrap process
 # Accessing all plots
  plot(boot)

 # Accessing the plot for a specific variable by its name
  plot(boot, variable = "PPI")
 plot(boot, variable = "ER")



 # Using dplyr
 library(dplyr)

   imf_example_data %>% kardl( CPI ~ PPI + asym(ER) +trend, maxlag=2) %>%
   bootstrap(replications=5) %>% plot(variable = "ER")

Perform the Error Correction Model (ECM) test to assess cointegration in the model

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

ecm(
  data = NULL,
  formula = NULL,
  case = 3,
  maxlag = NULL,
  mode = NULL,
  criterion = NULL,
  differentAsymLag = NULL,
  batch = NULL,
  ...
)

Arguments

Value

A list containing the results of the restricted ECM test, including:

• ecm: The estimated ECM model objects including:

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

  • EcmResLagged: The lagged error correction term used in the ECM model.

  • ecmL: The estimated long-run model object.

  • shortrunEQ: The estimated short-run model equation object.

  • longrunEQ: The estimated long-run model equation object.

• argsInfo: A list of input arguments used for the estimation. It includes the data, formula, maxlag, mode, criterion, differentAsymLag, and batch settings.

• extractedInfo: A list containing extracted information from the input data and formula, such as variable names, deterministic terms, asymmetric variables, and the prepared dataset for estimation.

• timeInfo: A list containing timing information for the estimation process, including start time, end time, and total duration.

• lagInfo: A list containing lag selection information, including the optimal lag configuration and criteria values for different lag combinations.

• estInfo: A list containing estimation details, such as the type of model, estimation method, model formula, number of parameters (k), number of observations (n), start and end points of the fitted values, and total time span.

• model: The fitted linear model object of class lm representing the estimated ARDL or NARDL model.

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 ecm narayan

Examples

suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(tidyr))
suppressPackageStartupMessages(library(ggplot2))


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

 ecm_model_grid<- ecm(mode = "grid")
 ecm_model_grid

 # Checking the cointegration test results using pesaran t test
 psst(ecm_model_grid)
 # Getting the details of psst result
 summary(psst(ecm_model_grid))

 # using the grid_custom mode for faster execution without console output
 ecm_model<- imf_example_data %>% ecm(mode = "grid_custom")
 ecm_model

 # Estimating the model with user-defined lag values
 ecm_model2<-ecm(mode = c( 2    ,  1    ,  1   ,   3 ))
 # Getting the results
 ecm_model2
 # Getting the summary of the results
 summary(ecm_model2)
 # OR using pipe operator
 imf_example_data %>% ecm(CPI~PPI+asym(ER) +trend,case=4) %>% summary()

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



 # 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<-ecm( mode = "grid_custom")
 diffAsymLags$lagInfo$OptLag

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


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

 # For having the lags plot

 #  ecm_model_grid[["LagCriteria"]] is a matrix, convert it to a data frame
 LagCriteria <- as.data.frame(ecm_model_grid$lagInfo$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

 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))

IMF Example Data

Description

This is an example data set used for testing purposes. It contains monthly data on exchange rates, consumer price index, producer price index, and a dummy variable for the COVID-19 pandemic for Turkey from January 1985 to February 2024.

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)

Estimate an ARDL or NARDL model with automatic lag selection

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,
  formula = 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

An object of class kardl_lm containing the estimated ARDL or NARDL model. The object includes the following components:

• argsInfo: A list of input arguments used for the estimation. It includes the data, formula, maxlag, mode, criterion, differentAsymLag, and batch settings.

• extractedInfo: A list containing extracted information from the input data and formula, such as variable names, deterministic terms, asymmetric variables, and the prepared dataset for estimation.

• timeInfo: A list containing timing information for the estimation process, including start time, end time, and total duration.

• lagInfo: A list containing lag selection information, including the optimal lag configuration and criteria values for different lag combinations.

• estInfo: A list containing estimation details, such as the type of model, estimation method, model formula, number of parameters (k), number of observations (n), start and end points of the fitted values, and total time span.

• model: The fitted linear model object of class lm representing the estimated ARDL or NARDL model.

See Also

ecm, kardl_set, kardl_get, kardl_reset, modelCriterion

Examples

suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(tidyr))
suppressPackageStartupMessages(library(ggplot2))

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

kardl_set(formula =CPI~ER+PPI+Asymmetr(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(formula=CPI~PPI+Asymmetric(ER)) %>% summary()

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

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

# Setting max lag instead of default value [4]
kardl(imf_example_data,
      CPI~ER+PPI+Lasymmetric(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))

# For using different lag values for negative and positive decompositions of non-linear variables
# setting the same lags for positive and negative decompositions.

same<-kardl(formula=CPI~Asymmetric(ER),maxlag=2, mode = "grid_custom",differentAsymLag = FALSE)
dif<-kardl(formula=CPI~Sasymmetric(ER),maxlag=2, mode = "grid_custom",differentAsymLag = TRUE)

same$lagInfo$OptLag
dif$lagInfo$OptLag

# 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

#  kardl_model_grid[["LagCriteria"]] is a matrix, convert it to a data frame
LagCriteria <- as.data.frame(kardl_model_grid$lagInfo$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

 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
 ggplot2::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 KARDL Package Options

Description

This function retrieves the current settings of the kardl package. Users can specify option names to get their values or call the function without arguments to retrieve all current settings.

Usage

kardl_get(...)

Arguments

Value

If no arguments are provided, returns all options as a list. If specific option names are provided, returns their values.

See Also

kardl_set, kardl_reset

Examples

# Get all options
kardl_get()
# Get specific options
kardl_get("maxlag", "mode")

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

a<-kardl_get()
a$AsymSuffix

Calculate long-run multipliers from a KARDL model

Description

This function calculates the long-run parameters of a KARDL model estimated using the kardl function. The long-run parameters are calculated by dividing the negative of the coefficients of the independent variables by the coefficient of the dependent variable. If an intercept is included in the model, it is also standardized by dividing it by the negative of the long-run parameter of the dependent variable.

Usage

kardl_longrun(model)

Arguments

Details

The function also calculates the standard errors of the long-run multipliers using the delta method, which accounts for the covariance between the coefficients. The fitted values and residuals of the long-run model are calculated based on the original data and the long-run multipliers.

The function returns an object of class kardl_long_run, which contains the long-run multipliers, their standard errors, t-statistics, p-values, fitted values, residuals, and other relevant information for further analysis and diagnostics.

Note that the fitted values and residuals from the long-run model are not centered (i.e., they do not have a mean of zero) by design, which means that diagnostic plots and residual-based tests may not be valid for this model. The primary focus of this function is on the estimation of the long-run multipliers and their associated statistics.

LongRunMultiplier_i = -\frac{\beta_i}{\beta_{dep}}

. t-values and p-values are calculated using the standard errors obtained from the delta method, which accounts for the covariance between the coefficients.

Value

An object of class kardl_long_run, which is a list containing:

• coefficients: A named vector of long-run multipliers.

• residuals: A vector of residuals from the long-run model.

• effects: A vector of effects from the long-run model.

• rank: The rank of the long-run model.

• fitted.values: A vector of fitted values from the long-run model.

• assign: A vector indicating the assignment of coefficients to terms in the long-run model.

• qr: The QR decomposition of the design matrix of the long-run model.

• df.residual: The degrees of freedom of the residuals of the long-run model.

• xlevels: A list of factor levels used in the long-run model.

• call: The matched call used to create the long-run model.

• terms: The terms object of the long-run model.

• model: The data frame used in the long-run model.

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))
long<-kardl_longrun(kardl_model)

# Calculate the long-run multipliers
long
# Details of the long-run multipliers
summary(long)


# Using magrittr
library(magrittr)

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

Function to Reset KARDL Package Options to Default Values

Description

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

Usage

kardl_reset(. = FALSE)

Arguments

Value

If resetting options, returns the provided value (if any) or invisibly returns the current settings as a list.

If resetting options, returns the provided value (if any) or invisibly returns the current settings as a list.

See Also

kardl_set, kardl_get

Examples

# Set some options
kardl_set(criterion = "BIC", differentAsymLag = TRUE)

# Reset to default options
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 Set KARDL Package Options

Description

This function allows users to set options for the kardl package. Users can specify named arguments to set options or call the function without arguments to retrieve all current settings.

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.

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(maxlag = 5, mode = "grid")
# Get all options
kardl_get()
# Get specific options
kardl_get("maxlag", "mode")

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


kardl_get()


# Example with magrittr pipe
library(magrittr)
# Set custom coefficient naming conventions

MyFormula<-CPI~ER+PPI+asym(ER)+deterministic(covid)+trend
kardl_set(ShortCoef = "L___{lag}.d.{varName}", formula = MyFormula, data = imf_example_data)
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, giving precedence to the first list for overlapping names

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

A merged list with unique names, prioritizing values from the first list in case of name conflicts.

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(estModel, cr, ...)

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

# Example usage of modelCriterion function with a linear model
mylm<- lm(mpg ~ wt + hp, data = mtcars)
modelCriterion(mylm, AIC )
modelCriterion(mylm, "BIC" )
mm<-AIC(mylm)
 class(mm) == class(modelCriterion(mylm, "AIC"))

 # Example usage of modelCriterion function with a kardl model
 kardl_model <- kardl(imf_example_data,
                      CPI ~ ER + PPI + asym(ER) + deterministic(covid) + trend,
                      mode = c(1, 2, 3, 0))
 modelCriterion(kardl_model, "AIC")
 modelCriterion(kardl_model, AIC)
 AIC(kardl_model)
 modelCriterion(kardl_model, "BIC")

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

Calculating multipliers of estimated model

Description

By running m<-mplier(kardl_model), the object m$mpsi contains the final multiplier values, m$omega holds the omega values, and m$lambda returns the Lambda values of the model.

Usage

mplier(kmodel, horizon = 80, minProb = 0)

Arguments

Details

The mplier function computes dynamic multipliers based on the coefficients and lag structure of a model estimated using the kardl package. The function extracts necessary information from the model, such as coefficients, lag structure, and variable names, to compute the dynamic multipliers. It calculates the short-run coefficients, Lambda values, and omega values based on the model's parameters and lag structure. The output includes a matrix of dynamic multipliers (mpsi), which can be used for further analysis or visualization. The dynamic multipliers provide insight into how changes in the independent variables affect the dependent variable over time, allowing for a deeper understanding of the relationships captured by the model. The function also allows users to set a minimum p-value threshold for including coefficients in the calculation, providing flexibility in focusing on statistically significant effects. The function is designed to work specifically with models estimated using the kardl package, and it ensures that the input model is of the correct class before proceeding with the calculations. The resulting multipliers can be used for various applications, including forecasting, policy analysis, and understanding the dynamic relationships between variables in time series data.

{{\psi_{h}^{+} = {\sum_{i = 0}^{h}\frac{\partial y_{t + i}}{\partial x_{t}^{+}}}} ; {\psi_{h}^{-} = {\sum_{i = 0}^{h}\frac{\partial y_{t + i}}{\partial x_{t}^{-}}}}}

The above equation represents the cumulative dynamic multipliers for positive and negative changes in an independent variable (x) on the dependent variable (y) over a specified horizon (h). The multipliers are calculated as the sum of the partial derivatives of the dependent variable with respect to the positive and negative changes in the independent variable across the time horizon. These multipliers provide insight into how changes in the independent variable affect the dependent variable over time, allowing for a deeper understanding of the relationships captured by the model.

Value

A list containing the following elements:

• mpsi: A matrix of dynamic multipliers for each variable across the specified horizon. The first column typically represents the time horizon (e.g., 0 to 40), while the subsequent columns contain the multiplier values for each variable.

• omega: A vector of omega values calculated based on the model's parameters and lag structure. These values are used in the calculation of the dynamic multipliers and provide insight into the persistence of effects over time.

• lambda: A matrix of Lambda values that represent the short run coefficients and their transformations based on the model's parameters. These values are essential for understanding the immediate effects of changes in the independent variables on the dependent variable.

• horizon: The horizon over which the multipliers were computed, as specified in the function's input. This value indicates the time frame for which the dynamic multipliers are relevant and can be used for interpretation and analysis of the results.

• model: The original model object that was passed to the function. This allows users to reference the model used for the calculations and can be useful for further analysis or validation of the results.

See Also

bootstrap

Examples

# This example demonstrates how to use the mplier function to calculate dynamic multipliers
# from a model estimated using the kardl package. The example includes fitting a model with
# the kardl function, calculating the multipliers, and visualizing the results using both
# base R plotting and ggplot2.

 kardl_model<-kardl(imf_example_data, CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
 mode=c(1,2,3,0))
 m<-mplier(kardl_model,40)
 head(m$mpsi)
 head(m$omega)
 head(m$lambda)

 # Displaying the summary of the multipliers object
 summary(m)

 # Visualize the dynamic multipliers

plot(m)

 # For plotting specific variables, you can specify them in the plot function. For example,
 # to plot the multipliers for the variable "ER":

 plot(m, variable = "ER")

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(kmodel, case = 3, signif_level = "auto")

Arguments

Value

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

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

• method: A character string indicating the method used for the test, which is Bounds F-Test".

• data.name: A character string giving the name of the data used in the test.

• k: The number of independent variables in the model.

• notes: A character vector containing any notes or warnings related to the test results, such as sample size considerations or adjustments made to the case based on model characteristics.

• sig: The significance level used for the test, either specified by the user or determined automatically.

• alternative: The alternative hypothesis being tested.

• case: The case used for the test, either specified by the user or determined automatically based on the model's characteristics.

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 ecm

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
my_test<-narayan(kardl_model)
# Getting the results of the test.
my_test
# Getting details of the test.
my_summary<-summary(my_test)
my_summary

# Getting the critical values of the test.
my_summary$crit_vals




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

Parse a formula to detect specific variable patterns

Description

The parseFormula() function analyzes a given formula to identify and extract variables that match specified patterns. It is particularly useful for isolating variables enclosed within certain functions or constructs in the formula, such as asym(), det(), or any user-defined patterns.

Usage

parse_formula_vars(formula)

Arguments

Value

A list containing:

• response: The response variable(s) extracted from the formula.

• intercept: A logical value indicating whether the formula includes an intercept (default is TRUE).

• dot: A logical value indicating whether the formula includes a dot (.) representing all other variables (default is FALSE).

• outside: A vector of variables that are outside any specified patterns. It includes the variables that are not detected within the specified patterns in the formula.

• inside: A list where each element corresponds to a detected pattern (e.g., function name) and contains the variables found inside that pattern. For example, if the formula includes asym(x1 + x2), the inside list will have an element named "asym" containing the variables "x1" and "x2". This allows for easy identification of variables that are part of specific constructs in the formula.

See Also

formula and gregexpr

Examples

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

Pesaran et al. (2001) Bounds F-Test for KARDL Models

Description

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.

Usage

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

Arguments

Value

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

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

• method: A character string indicating the method used for the test, which is Bounds F-Test".

• data.name: A character string giving the name of the data used in the test.

• k: The number of independent variables in the model.

• notes: A character vector containing any notes or warnings related to the test results, such as sample size considerations or adjustments made to the case based on model characteristics.

• sig: The significance level used for the test, either specified by the user or determined automatically.

• alternative: The alternative hypothesis being tested.

• case: The case used for the test, either specified by the user or determined automatically based on the model's characteristics.

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 ecm narayan

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
my_pssF<-pssf(kardl_model)
# Getting the results of the test.
my_pssF
# Getting details of the test.
my_summary<-summary(my_pssF)
my_summary

# Getting the critical values of the test.
my_summary$crit_vals




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

PSS t Bound Test

Description

This function performs the Pesaran t Bound test

Usage

psst(kmodel, 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

The function returns an object of class "htest" containing the following components:

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

• method: A description of the test performed.

• data.name: The name of the data used in the test.

• k: The number of independent variables in the model.

• notes: Any notes or warnings related to the test results, such as sample size considerations or adjustments made to the case based on model characteristics.

• sig: The significance level used for the test, either specified by the user or determined automatically.

• alternative: The alternative hypothesis being tested.

• case: The case used for the test, either specified by the user or determined automatically based on the model's characteristics.

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 ecm narayan

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                   mode=c(1,2,3,0))
my_test<-psst(kardl_model)
# Getting the results of the test.
my_test
# Getting details of the test.
my_summary<-summary(my_test)
my_summary

# Getting the critical values of the test.
my_summary$crit_vals




# Using magrittr :

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

# Getting details of the test results using magrittr:
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER)+deterministic(covid)+trend,
                           mode=c(1,2,3,0)) %>% psst() %>% summary()

Symmetry Test for non-linear KARDL Models

Description

The symmetry test is a statistical procedure used to assess the presence of symmetry 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. This test returns results for both long-run and short-run variables in a KARDL model. Where applicable, it provides the Wald test statistics, p-values, degrees of freedom, sum of squares, and mean squares for each variable tested. If the null hypothesis of symmetry is rejected, it indicates that the effects of positive and negative changes in the variable are significantly different, suggesting an asymmetric relationship.

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 symmetry 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

symmetrytest(kmodel)

Arguments

Details

This function performs symmetry tests on non-linear KARDL models to assess whether the effects of positive and negative changes in independent variables are statistically different.

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:

• 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.

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

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

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, ecm, narayan

Examples

kardl_model<-kardl(imf_example_data,
                   CPI~Lasym(PPI+ER)+Sas(ER)+deterministic(covid)+trend)
ast<- symmetrytest(kardl_model)
ast
# Detailed results of the test:
summary(ast)
# The null hypothesis of the test is that the model is symmetric, while the alternative
# hypothesis is that the model is asymmetric. The test statistic and p-value are provided
# in the output. If the p-value is less than a chosen significance level (e.g., 0.05),
# we reject the null hypothesis and conclude that there is evidence of asymmetry in the model.

# To get symmetry test results in long-run, you can use the following code:
ast$Lwald

# To get symmetry test results in short-run, you can use the following code:
ast$Swald

# To get the null and alternative hypotheses of the test in long-run,
# you can use the following code:

ast$Lhypotheses

# To get the null and alternative hypotheses of the test in short-run,
# you can use the following code:

ast$Shypotheses

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

# To get the summary of the symmetry test results in one line, you can use the following code:
imf_example_data %>% kardl(CPI~ER+PPI+asym(ER+PPI)+deterministic(covid)+trend,
                           mode=c(1,0,1,1,0)) %>% symmetrytest() %>% summary()