Package 'cointReg'

Title:	Parameter Estimation and Inference in a Cointegrating Regression
Description:	Cointegration methods are widely used in empirical macroeconomics and empirical finance. It is well known that in a cointegrating regression the ordinary least squares (OLS) estimator of the parameters is super-consistent, i.e. converges at rate equal to the sample size T. When the regressors are endogenous, the limiting distribution of the OLS estimator is contaminated by so-called second order bias terms, see e.g. Phillips and Hansen (1990) <DOI:10.2307/2297545>. The presence of these bias terms renders inference difficult. Consequently, several modifications to OLS that lead to zero mean Gaussian mixture limiting distributions have been proposed, which in turn make standard asymptotic inference feasible. These methods include the fully modified OLS (FM-OLS) approach of Phillips and Hansen (1990) <DOI:10.2307/2297545>, the dynamic OLS (D-OLS) approach of Phillips and Loretan (1991) <DOI:10.2307/2298004>, Saikkonen (1991) <DOI:10.1017/S0266466600004217> and Stock and Watson (1993) <DOI:10.2307/2951763> and the new estimation approach called integrated modified OLS (IM-OLS) of Vogelsang and Wagner (2014) <DOI:10.1016/j.jeconom.2013.10.015>. The latter is based on an augmented partial sum (integration) transformation of the regression model. IM-OLS is similar in spirit to the FM- and D-OLS approaches, with the key difference that it does not require estimation of long run variance matrices and avoids the need to choose tuning parameters (kernels, bandwidths, lags). However, inference does require that a long run variance be scaled out. This package provides functions for the parameter estimation and inference with all three modified OLS approaches. That includes the automatic bandwidth selection approaches of Andrews (1991) <DOI:10.2307/2938229> and of Newey and West (1994) <DOI:10.2307/2297912> as well as the calculation of the long run variance.
Authors:	Philipp Aschersleben [aut, cre], Martin Wagner [aut] (Author of underlying MATLAB code.)
Maintainer:	Philipp Aschersleben <[email protected]>
License:	GPL-3
Version:	0.2.0.9000
Built:	2024-11-07 03:26:18 UTC
Source:	https://github.com/aschersleben/cointreg

Help Index

The cointReg package
Check list D.options.
Variable check for single objects.
Multiple variable checks for certain values.
Estimation and Inference for cointegrating regressions
Dynamic OLS
Fully Modified OLS
Integrated Modified OLS
Automatic Bandwidth Selection
Leads and Lags
Long-Run Variance
Weights for Long-Run Variance
Get D OLS model.
Leads-and-Lags Matrix
Plot Method for Cointegration Models (Modified OLS).
Print Method for Cointegration Models (Modified OLS).

The cointReg package

Description

Parameter Estimation and Inference in a Cointegrating Regression

Details

See the vignette:
vignette("cointReg")

See the DESCRIPTION:
help(package = cointReg)

See the README:
https://github.com/aschersleben/cointReg/blob/master/README.md

Open the package documentation page:
package?cointReg

Further information and bug reporting:
https://github.com/aschersleben/cointReg

Functions

cointReg(method = c("FM", "D", "IM"), ...)
General function to estimate parameters of the given model. Three methods are possible; they can be choosen directly by using one of the following functions:
- cointRegFM: Fully Modified OLS
- cointRegD: Dynamic OLS
- cointRegIM: Integrated Modified OLS
print
Print clear results.
plot
Plot the residuals of a cointReg model.
Helper functions:
- Checking inputs and arguments:
  checkObject, checkVars
- Calculation of bandwidth and long run variance:
  getBandwidth, getBandwidthAnd, getBandwidthNW
  getLongRunVar, getLongRunWeights
- Additional D-OLS functions:
  getLeadLag, makeLeadLagMatrix, getModD, checkDoptions

Check list D.options.

Description

Checking the list D.options, that is an argument of cointRegD.

Usage

checkDoptions(n.lag = NULL, n.lead = NULL, kmax = c("k4", "k12"),
  info.crit = c("AIC", "BIC"))
checkDoptions(n.lag = NULL, n.lead = NULL, kmax = c("k4", "k12"),
  info.crit = c("AIC", "BIC"))

Arguments

`n.lag`, `n.lead`	[`NULL` \| `numeric(1)`] Have to be "integerish" and > 0.
`kmax`	[`NULL` \| `character(1)`] One of `"k4"` or `"k12"`.
`info.crit`	[`NULL` \| `character(1)`] One of `"AIC"` or `"BIC"`.

Value

[list]. List with the checked and (if necessary) converted arguments.

If one of n.lag and n.lead is NULL, only kmax and info.crit will be not NULL.

Examples

checkDoptions(n.lag = 3, n.lead = 4)
checkDoptions(info.crit = "BIC")
checkDoptions()

# It's not sufficient to include only one of "n.lag" and "n.lead":
checkDoptions(n.lag = 2)

checkDoptions(n.lag = 3, n.lead = 4)
checkDoptions(info.crit = "BIC")
checkDoptions()

# It's not sufficient to include only one of "n.lag" and "n.lead":
checkDoptions(n.lag = 2)

Variable check for single objects.

Description

Checking the variable and convert it for internal use, if necessary. (Also used by the cointmonitoR package.)

Usage

checkObject(obj, obj.name, ..., out = "return", .env)
checkObject(obj, obj.name, ..., out = "return", .env)

Arguments

`obj`	[`any`] Variable or value to check and convert.
`obj.name`	[`character(1)`] Name of the object to check. If `missing`, the name of `obj` has to be one of the possible names (see details).
`...`	[`any`] An alternative to the use of the `obj` and `obj.name` arguments is to directly give the name and the variable to be checked via `name = variable` arguments (see examples). In the case of more than one `...` argument, `checkVars` will be called internally.
`out`	[`character`] Whether to `"return"` or to `"assign"` the checked (and converted) object. Also possible: `c("return", "assign")`.
`.env`	[`environment`] Environment to which to assign the converted `obj` (usually the same on that contains `obj`, if it's a variable). Required, if argument `out` contains `"assign"`.

Details

Possible values of obj.name to check:

"y", "x.stat":: Of type numeric, matrix or data.frame. Only the first row/column will be used.
Converted to object: column matrix
"y.fm", "x.coint", "deter":: Of type numeric, matrix or data.frame.
Converted to object: column matrix
"m":: Of type numeric(1), has to be greater than 0.
"model":: One of c("FM", "D", "IM").
"signif.level":: Of type numeric(1), has to be in the interval [0.01, 0.1].
"trend", "return.stats", "return.input", "demeaning", "t.test":: Converted to object: logical(1).
"kernel":: One of c("ba", "bo", "da", "pa", "qs", "th", "tr").
"bandwidth":: One of c("and", "nw").
"selector":: One or both c(1, 2).

Value

The checked and converted argument is assigned to the given environment (.env) and/or returned (depending on the argument out).

Examples

x = matrix(1:20, nrow = 2)
x2 = checkObject(x, "x.coint")
x2

env = environment()
y = 1:10
checkObject(y, out = "assign", .env = env)
y

# example for the use of the ... argument:
det = rbind(1, 1:10)
x3 = sin(10:20)
det2 = checkObject(deter = det)
det2
(checkObject(deter = det, x.stat = x3))

x = matrix(1:20, nrow = 2)
x2 = checkObject(x, "x.coint")
x2

env = environment()
y = 1:10
checkObject(y, out = "assign", .env = env)
y

# example for the use of the ... argument:
det = rbind(1, 1:10)
x3 = sin(10:20)
det2 = checkObject(deter = det)
det2
(checkObject(deter = det, x.stat = x3))

Multiple variable checks for certain values.

Description

Check the arguments and convert them for internal use, if necessary.

Usage

checkVars(..., out = "assign", .env)
checkVars(..., out = "assign", .env)

Arguments

`...`	[`any`] Variables to check, see details.
`out`	[`character`] Whether to `"return"` or to `"assign"` the checked (and converted) object. Also possible: `c("return", "assign")`.
`.env`	[`environment`] Environment to which to assign the converted `obj` (usually the same on that contains `obj`, if it's a variable). Required, if argument `out` contains `"assign"`.

Details

See checkObject for details.

Value

The checked and converted arguments are assigned to the given environment (.env) or invisibly returned as a list.

Examples

env = environment()
x.data = data.frame(a = 1:10, b = 20:11)
y.data = 1:10
checkVars(x.coint = x.data, y = y.data, .env = env)
x.coint
y

test = checkVars(x.coint = x.data, y = y.data, out = "return")
str(test)

# If the variables already have the "right" (= argument's) name,
# there's no need to do something like
# checkVars(kernel = kernel, bandwidth = bandwidth) -
# just call checkVars without specifing the arguments:
kernel = "q"
bandwidth = "a"
(checkVars(kernel, bandwidth, out = "return"))

env = environment()
x.data = data.frame(a = 1:10, b = 20:11)
y.data = 1:10
checkVars(x.coint = x.data, y = y.data, .env = env)
x.coint
y

test = checkVars(x.coint = x.data, y = y.data, out = "return")
str(test)

# If the variables already have the "right" (= argument's) name,
# there's no need to do something like
# checkVars(kernel = kernel, bandwidth = bandwidth) -
# just call checkVars without specifing the arguments:
kernel = "q"
bandwidth = "a"
(checkVars(kernel, bandwidth, out = "return"))

Estimation and Inference for cointegrating regressions

Description

Computes either the Phillips and Hansen (1990) Fully Modified OLS estimator, or the Saikkonen (1990) Dynamic OLS estimator, or the Vogelsang and Wagner (2014) Integrated Modified OLS estimator.

Usage

cointReg(method = c("FM", "D", "IM"), x, y, ...)
cointReg(method = c("FM", "D", "IM"), x, y, ...)

Arguments

`method`	[`character(1)`] Select the method for the estimation of your cointegration model: `"FM"`: FM-OLS (default), see details at cointRegFM `"D"`: D-OLS, see details at cointRegD `"IM"`: IM-OLS, see details at cointRegIM
`x`	[`numeric` \| `matrix` \| `data.frame`] RHS variables on which to apply the model estimation.
`y`	[`numeric` \| `matrix` \| `data.frame`] LHS variable(s) on which to apply the model estimation. Usually one-dimensional, but a `matrix` or `data.frame` with more than one column is also possible (only for FM-OLS).
`...`	[`any`] Arguments passed to the corresponding `cointReg` function, like: `x`, `y`, `deter`: data to include in the model `kernel`, `bandwidth`: parameters for calculating the long-run variance `n.lead`, `n.lag`, `kmax`, `info.crit`: D-OLS specific arguments. `selector`, `t.test`: IM-OLS specific arguments. `check`: Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.

Value

[cointReg] object.

References

Phillips, P.C.B. and B. Hansen (1990): "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, 57, 99–125, DOI:10.2307/2297545.
Phillips, P.C.B. and M. Loretan (1991): "Estimating Long Run Economic Equilibria," Review of Economic Studies, 58, 407–436, DOI:10.2307/2298004.
Saikkonen, P. (1991): "Asymptotically Efficient Estimation of Cointegrating Regressions," Econometric Theory, 7, 1–21, DOI:10.1017/S0266466600004217.
Stock, J.H. and M.W. Watson (1993): "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, 61, 783–820, DOI:10.2307/2951763.
Vogelsang, T.J. and M. Wagner (2014): "Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions," Journal of Econometrics, 148, 741–760, DOI:10.1016/j.jeconom.2013.10.015.

Examples

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
cointReg("FM", x = x, y = y, deter = deter, kernel = "ba",
         bandwidth = "and")

# Compare the results of all three models:
res = sapply(c("FM", "D", "IM"), cointReg, x = x, y = y, deter = deter)
do.call(cbind, lapply(res, "[[", "theta"))

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
cointReg("FM", x = x, y = y, deter = deter, kernel = "ba",
         bandwidth = "and")

# Compare the results of all three models:
res = sapply(c("FM", "D", "IM"), cointReg, x = x, y = y, deter = deter)
do.call(cbind, lapply(res, "[[", "theta"))

Dynamic OLS

Description

Computes the Saikkonen (1990) Dynamic OLS estimator.

Usage

cointRegD(x, y, deter, kernel = c("ba", "pa", "qs", "tr"),
  bandwidth = c("and", "nw"), n.lead = NULL, n.lag = NULL,
  kmax = c("k4", "k12"), info.crit = c("AIC", "BIC"), demeaning = FALSE,
  check = TRUE, ...)
cointRegD(x, y, deter, kernel = c("ba", "pa", "qs", "tr"),
  bandwidth = c("and", "nw"), n.lead = NULL, n.lag = NULL,
  kmax = c("k4", "k12"), info.crit = c("AIC", "BIC"), demeaning = FALSE,
  check = TRUE, ...)

Arguments

`x`	[`numeric` \| `matrix` \| `data.frame`] RHS variables on which to apply the D-OLS estimation (see Details).
`y`	[`numeric` \| `matrix` \| `data.frame`] LHS variable(s) on which to apply the D-OLS estimation (see Details). Has to be one-dimensional. If `matrix`, it may have only one row or column, if `data.frame` just one column.
`deter`	[`numeric` \| `matrix` \| `data.frame` \| `NULL`] Deterministic variable to include in the equation (see Details). If it's `NULL` or missing, no deterministic variable is included in the model.
`kernel`	[`character(1)`] The kernel function to use for calculating the long-run variance. Default is Bartlett kernel (`"ba"`), see Details for alternatives.
`bandwidth`	[`character(1)` \| `integer(1)`] The bandwidth to use for calculating the long-run variance. Default is Andrews (1991) (`"and"`), an alternative is Newey West (1994) (`"nw"`).
`n.lead`, `n.lag`	[`numeric(1)` \| `NULL`] Numbers of Leads and Lags (see Details). Default is `NULL`.
`kmax`	[`character(1)`] Maximal value for lags and leads if generated automatically (see Details). Default is `"k4"`.
`info.crit`	[`character(1)`] Information criterion to use for the automatical calculation of lags and leads. Default is `"AIC"`.
`demeaning`	[`logical`] Demeaning of residuals in `getLongRunVar`. Default is `FALSE`.
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.
`...`	Arguments passed to `getBandwidthNW`.

Details

The equation for which the FM-OLS estimator is calculated:

$y = \delta \cdot D + \beta \cdot x + u$

with $D$ as the deterministics matrix. Then $\theta = (\delta', \beta')'$ is the full parameter vector.

Information about the D-OLS specific arguments:

n.lag, n.lead: A positive number to set the number of lags and leads. If at least one of them is equal to NULL (default), the function getLeadLag will be used to calculate them automatically (see Choi and Kurozumi (2012) for details). In that case, the following two arguments are needed.
kmax: Maximal value for lags and leads, when they are calculated automatically. If "k4", then the maximum is equal to floor(4 * (x.T/100)^(1/4)), else it's floor(12 * (x.T/100)^(1/4)) with x.T is equal to the data's length. One of "k4" or "k12". Default is "k4".
info.crit: Information criterion to use for the automatical calculation of lags and leads. One of "AIC" or "BIC". Default is "AIC".

Value

[cointReg]. List with components:

beta [numeric]: coefficients of the regressors
delta [numeric]: coefficients of the deterministics
theta [numeric]: combined coefficients of beta and delta
sd.theta [numeric]: standard errors for theta
t.theta [numeric]: t-values for theta
p.theta [numeric]: p-values for theta
theta.all [numeric]: combined coefficients of beta, delta and the auxiliary leads-and-lags regressors
residuals [numeric]: D-OLS residuals (length depends on leads and lags)
omega.u.v [numeric]: conditional long-run variance based on OLS residuals
varmat [matrix]: variance-covariance matrix
Omega [list]: the whole long-run variance matrix and parts of it
bandwidth [list]: number and name of the calculated bandwidth
kernel [character]: abbr. name of kernel type
lead.lag [list]: leads-and-lags parameters

References

Phillips, P.C.B. and M. Loretan (1991): "Estimating Long Run Economic Equilibria," Review of Economic Studies, 58, 407–436, DOI:10.2307/2298004.
Saikkonen, P. (1991): "Asymptotically Efficient Estimation of Cointegrating Regressions," Econometric Theory, 7, 1–21, DOI:10.1017/S0266466600004217.
Stock, J.H. and M.W. Watson (1993): "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, 61, 783–820, DOI:10.2307/2951763.

Examples

set.seed(1909)
x1 <- cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 <- cumsum(rnorm(100, sd = 0.1)) + 1
x3 <- cumsum(rnorm(100, sd = 0.2)) + 2
x <- cbind(x1, x2, x3)
y <- x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter <- cbind(level = 1, trend = 1:100)
test <- cointRegD(x, y, deter, n.lead = 2, n.lag = 2,
                    kernel = "ba", bandwidth = "and")
print(test)
test2 <- cointRegD(x, y, deter, kmax = "k4", info.crit = "BIC",
                     kernel = "ba", bandwidth = "and")
print(test2)

set.seed(1909)
x1 <- cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 <- cumsum(rnorm(100, sd = 0.1)) + 1
x3 <- cumsum(rnorm(100, sd = 0.2)) + 2
x <- cbind(x1, x2, x3)
y <- x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter <- cbind(level = 1, trend = 1:100)
test <- cointRegD(x, y, deter, n.lead = 2, n.lag = 2,
                    kernel = "ba", bandwidth = "and")
print(test)
test2 <- cointRegD(x, y, deter, kmax = "k4", info.crit = "BIC",
                     kernel = "ba", bandwidth = "and")
print(test2)

Fully Modified OLS

Description

Computes the Phillips and Hansen (1990) Fully Modified OLS estimator.

Usage

cointRegFM(x, y, deter, kernel = c("ba", "pa", "qs", "tr"),
  bandwidth = c("and", "nw"), demeaning = FALSE, check = TRUE, ...)
cointRegFM(x, y, deter, kernel = c("ba", "pa", "qs", "tr"),
  bandwidth = c("and", "nw"), demeaning = FALSE, check = TRUE, ...)

Arguments

`x`	[`numeric` \| `matrix` \| `data.frame`] RHS variables on which to apply the FM-OLS estimation (see Details).
`y`	[`numeric` \| `matrix` \| `data.frame`] LHS variable(s) on which to apply the FM-OLS estimation (see Details). Usually one-dimensional, but a `matrix` or `data.frame` with more than one column is also possible.
`deter`	[`numeric` \| `matrix` \| `data.frame` \| `NULL`] Deterministic variable to include in the equation (see Details). If it's `NULL` or missing, no deterministic variable is included in the model.
`kernel`	[`character(1)`] The kernel function to use for calculating the long-run variance. Default is Bartlett kernel (`"ba"`), see Details for alternatives.
`bandwidth`	[`character(1)` \| `integer(1)`] The bandwidth to use for calculating the long-run variance. Default is Andrews (1991) (`"and"`), an alternative is Newey West (1994) (`"nw"`).
`demeaning`	[`logical`] Demeaning of residuals in `getLongRunVar`. Default is `FALSE`.
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.
`...`	Arguments passed to `getBandwidthNW`.

Details

The equation for which the FM-OLS estimator is calculated:

$y = \delta \cdot D + \beta \cdot x + u$

with $D$ as the deterministics matrix. Then $\theta = (\delta', \beta')'$ is the full parameter vector.

The calculation of t-values and the variance-covariance matrix is only possible, if y is one-dimensional.

Value

[cointReg]. List with components:

delta [numeric | matrix]: coefficients of the deterministics
beta [numeric | matrix]: coefficients of the regressors
theta [numeric | matrix]: combined coefficients of beta and delta
sd.theta [numeric]: standard errors for theta
t.theta [numeric]: t-values for theta
p.theta [numeric]: p-values for theta
residuals [numeric]: FM-OLS residuals (first value is always missing)
omega.u.v [numeric]: conditional long-run variance based on OLS residuals.
varmat [matrix]: variance-covariance matrix
Omega [list]: the whole long-run variance matrix and parts of it
beta.OLS [numeric | matrix]: OLS coefficients as vector / matrix
delta.OLS [numeric | matrix]: OLS coefficients as vector / matrix
u.OLS [numeric]: OLS residuals
bandwidth [list]: number and name of bandwidth
kernel [character]: abbr. name of kernel type

References

Phillips, P.C.B. and B. Hansen (1990): "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, 57, 99–125, DOI:10.2307/2297545.

Examples

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
test = cointRegFM(x, y, deter, kernel = "ba", bandwidth = "and")
print(test)

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
test = cointRegFM(x, y, deter, kernel = "ba", bandwidth = "and")
print(test)

Integrated Modified OLS

Description

Computes the Vogelsang and Wagner (2014) Integrated Modified OLS estimator.

Usage

cointRegIM(x, y, deter, selector = 1, t.test = TRUE, kernel = c("ba",
  "pa", "qs", "tr"), bandwidth = c("and", "nw"), check = TRUE, ...)
cointRegIM(x, y, deter, selector = 1, t.test = TRUE, kernel = c("ba",
  "pa", "qs", "tr"), bandwidth = c("and", "nw"), check = TRUE, ...)

Arguments

`x`	[`numeric` \| `matrix` \| `data.frame`] RHS variables on which to apply the IM-OLS estimation (see Details).
`y`	[`numeric` \| `matrix` \| `data.frame`] LHS variable(s) on which to apply the IM-OLS estimation (see Details). Has to be one-dimensional. If `matrix`, it may have only one row or column, if `data.frame` just one column.
`deter`	[`numeric` \| `matrix` \| `data.frame` \| `NULL`] Deterministic variable to include in the equation (see Details). If it's `NULL` or missing, no deterministic variable is included in the model.
`selector`	[`numeric`] Choose the regression type: `1`, `2`, or `c(1, 2)` (see Details). Default is `1`.
`t.test`	[`logical`] Wheather to calculate t-values for the coefficients of the first regression. Default is `TRUE`. Attention: Needs more calculation time, because an additional FM-OLS model has to be fitted to get the long-run variance.
`kernel`	[`character(1)`] The kernel function to use for calculating the long-run variance. Default is Bartlett kernel (`"ba"`), see Details for alternatives.
`bandwidth`	[`character(1)` \| `integer(1)`] The bandwidth to use for calculating the long-run variance. Default is Andrews (1991) (`"and"`), an alternative is Newey West (1994) (`"nw"`).
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.
`...`	Arguments passed to `getBandwidthNW`.

Details

The equation for which the IM-OLS estimator is calculated (type 1):

$S_y = \delta \cdot S_{D} + \beta \cdot S_{x} + \gamma \cdot x + u$

where $S_y$ , $S_x$ and $S_D$ are the cumulated sums of $y$ , $x$ and $D$ (with $D$ as the deterministics matrix). Then $\theta = (\delta', \beta', \gamma')'$ is the full parameter vector.

The equation for which the IM-OLS estimator is calculated (type 2):

$S_y = \delta \cdot S_D + \beta \cdot S_x + \gamma \cdot x + \lambda \cdot Z + u$

where $S_y$ , $S_x$ and $S_D$ are the cumulated sums of $y$ , $x$ and $D$ (with $D$ as the deterministics matrix) and $Z$ as defined in equation (19) in Vogelsang and Wagner (2015). Then $\theta = (\delta', \beta', \gamma', \lambda')'$ is the full parameter vector.

Value

[cointReg]. List with components:

delta [numeric]: coefficients of the deterministics (cumulative sum $S_{deter}$ )
beta [numeric]: coefficients of the regressors (cumulative sum $S_{x}$ )
gamma [numeric]: coefficients of the regressors (original regressors $x$ )
theta [numeric]: combined coefficients of beta, delta
sd.theta [numeric]: standard errors for the theta coefficients
t.theta [numeric]: t-values for the theta coefficients
p.theta [numeric]: p-values for the theta coefficients
theta.all [numeric]: combined coefficients of beta, delta, gamma
residuals [numeric]: IM-OLS residuals. Attention: These are the first differences of $S_u$ – the original residuals are stored in u.plus.
u.plus [numeric]: IM-OLS residuals, not differenced. See residuals above.
omega.u.v [numeric]: conditional long-run variance based on OLS residuals, via cointRegFM (in case of argument t.test is TRUE) or NULL
varmat [matrix]: variance-covariance matrix
Omega [matrix]: NULL (no long-run variance matrix for this regression type)
bandwidth [list]: number and name of bandwidth if t.test = TRUE
kernel [character]: abbr. name of kernel type if t.test = TRUE
delta2 [numeric]: coefficients of the deterministics (cumulative sum $S_{deter}$ ) for regression type 2
beta2 [numeric]: coefficients of the regressors (cumulative sum $S_{x}$ ) for regression type 2
gamma2 [numeric]: coefficients of the regressors (original regressors $x$ ) for regression type 2
lambda2 [numeric]: coefficients of the Z regressors for regression type 2
theta2 [numeric]: combined coefficients of beta2, delta2, gamma2 and lambda2 for regression type 2
u.plus2 [numeric]: IM-OLS residuals for regression type 2

References

Vogelsang, T.J. and M. Wagner (2014): "Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions," Journal of Econometrics, 148, 741–760, DOI:10.1016/j.jeconom.2013.10.015.

Examples

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
test = cointRegIM(x, y, deter, selector = c(1, 2), t.test = TRUE,
                    kernel = "ba", bandwidth = "and")
print(test)

set.seed(1909)
x1 = cumsum(rnorm(100, mean = 0.05, sd = 0.1))
x2 = cumsum(rnorm(100, sd = 0.1)) + 1
x3 = cumsum(rnorm(100, sd = 0.2)) + 2
x = cbind(x1, x2, x3)
y = x1 + x2 + x3 + rnorm(100, sd = 0.2) + 1
deter = cbind(level = 1, trend = 1:100)
test = cointRegIM(x, y, deter, selector = c(1, 2), t.test = TRUE,
                    kernel = "ba", bandwidth = "and")
print(test)

Automatic Bandwidth Selection

Description

Automatic bandwidth selection of Andrews (1991) and of Newey and West (1994).

Usage

getBandwidth(u, bandwidth = c("and", "nw"), kernel, ..., check = TRUE)

getBandwidthAnd(u, kernel = c("ba", "pa", "qs", "th", "tr"), check = TRUE)

getBandwidthNW(u, kernel = c("ba", "pa", "qs"), inter = FALSE,
  u.weights = NULL, check = TRUE)
getBandwidth(u, bandwidth = c("and", "nw"), kernel, ..., check = TRUE)

getBandwidthAnd(u, kernel = c("ba", "pa", "qs", "th", "tr"), check = TRUE)

getBandwidthNW(u, kernel = c("ba", "pa", "qs"), inter = FALSE,
  u.weights = NULL, check = TRUE)

Arguments

`u`	[`numeric`] Data on which to apply the bandwidth selction.
`bandwidth`	[`character(1)`] The bandwidth selection method to use. Default is Andrews (1991) (`"and"`), an alternative is Newey West (1994) (`"nw"`).
`kernel`	[`character(1)`] The kernel function to use for selecting the bandwidth. Default is Bartlett kernel (`"ba"`), see Details for alternatives.
`...`	Arguments passed to `getBandwidthNW`.
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.
`inter`	[`logical`] The first column will be ignored, if `TRUE` (intercept). Default is `FALSE`.
`u.weights`	[`numeric`] How to weight the columns of `u`. If `NULL` (default), uses identical weights for all columns.

Details

For Andrews (1991), the AR(1) individual version is implemented.

The kernel that is used for calculating the long-run variance can be one of the following:

"ba": Bartlett kernel
"pa": Parzen kernel
"qs": Quadratic Spectral kernel
"th": Tukey-Hanning kernel (only if bandwidth = "and")
"tr": Truncated kernel (only if bandwidth = "and")

Value

[numeric(1)]. Bandwidth

Functions

getBandwidthAnd: Automatic bandwidth selection of Andrews (1991).
getBandwidthNW: Automatic bandwidth selection of Newey and West (1994).

References

Andrews, D.W.K. (1991): "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, 59, 817–854, DOI:10.2307/2938229.
Newey, W.K. and K.D. West (1994): "Automatic Lag Selection in Covariance Matrix Estimation", Review of Economic Studies, 61, 631–653, DOI:10.2307/2297912.

Examples

set.seed(1909)
x <- rnorm(100)
getBandwidth(x, kernel = "ba")
getBandwidth(x, bandwidth = "nw", kernel = "ba")

x2 <- arima.sim(model = list(ar = c(0.7, 0.2)), innov = x, n = 100)
getBandwidth(x2, kernel = "qs")
getBandwidth(x2, bandwidth = "nw", kernel = "qs")

set.seed(1909)
x <- rnorm(100)
getBandwidth(x, kernel = "ba")
getBandwidth(x, bandwidth = "nw", kernel = "ba")

x2 <- arima.sim(model = list(ar = c(0.7, 0.2)), innov = x, n = 100)
getBandwidth(x2, kernel = "qs")
getBandwidth(x2, bandwidth = "nw", kernel = "qs")

Leads and Lags

Description

Generates "optimal" numbers of leads and lags for the Dynamic OLS estimator.

Usage

getLeadLag(x, y, deter, max.lag, max.lead, ic = c("AIC", "BIC"),
  symmet = FALSE, check = FALSE)
getLeadLag(x, y, deter, max.lag, max.lead, ic = c("AIC", "BIC"),
  symmet = FALSE, check = FALSE)

Arguments

`x`	[`numeric` \| `matrix` \| `data.frame`] RHS variables on which to apply the D-OLS estimation (see Details).
`y`	[`numeric` \| `matrix` \| `data.frame`] LHS variable(s) on which to apply the D-OLS estimation (see Details). Has to be one-dimensional. If `matrix`, it may have only one row or column, if `data.frame` just one column.
`deter`	[`numeric` \| `matrix` \| `data.frame` \| `NULL`] Deterministic variable to include in the equation (see Details). If it's `NULL` or missing, no deterministic variable is included in the model.
`max.lead`, `max.lag`	[`numeric(1)`] Maximal numbers of leads and lags, have to be non-negative integer values.
`ic`	[`character(1)`] Information criterion (one of `"AIC"` or `"BIC"`).
`symmet`	[`logical(1)`] If `TRUE`, only looks for equal leads and lags.
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.

Value

[numeric(2)]. "Optimal" numbers of leads and lags.

Examples

set.seed(1909)
y <- matrix(cumsum(rnorm(100)), ncol = 1)
x <- matrix(rep(y, 4) + rnorm(400, mean = 3, sd = 2), ncol = 4)
deter <- cbind(1, 1:100)
cointReg:::getLeadLag(x = x, y = y, deter = deter, max.lag = 5,
                      max.lead = 5, ic = "AIC", symmet = FALSE)
set.seed(1909)
y <- matrix(cumsum(rnorm(100)), ncol = 1)
x <- matrix(rep(y, 4) + rnorm(400, mean = 3, sd = 2), ncol = 4)
deter <- cbind(1, 1:100)
cointReg:::getLeadLag(x = x, y = y, deter = deter, max.lag = 5,
                      max.lead = 5, ic = "AIC", symmet = FALSE)

Long-Run Variance

Description

This function computes the long-run variance Omega, the one sided long-run variance Delta (starting with lag 0) and the variance Sigma from an input matrix of residuals.

Usage

getLongRunVar(u, bandwidth = c("and", "nw"), kernel = c("ba", "bo", "da",
  "pa", "qs", "tr"), demeaning = FALSE, check = TRUE, ...)
getLongRunVar(u, bandwidth = c("and", "nw"), kernel = c("ba", "bo", "da",
  "pa", "qs", "tr"), demeaning = FALSE, check = TRUE, ...)

Arguments

`u`	[`numeric` \| `matrix`] Data on which to apply the calculation of the long-run variance.
`bandwidth`	[`numeric(1)`] The bandwidth to use for calculating the long-run variance as a positive intergerish value.
`kernel`	[`character(1)`] The kernel function to use for selecting the bandwidth. Default is Bartlett kernel (`"ba"`), see Details for alternatives.
`demeaning`	[`logical`] Demeaning of the data before the calculation (default is `FALSE`).
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.
`...`	Arguments passed to `getBandwidthNW`.

Details

The bandwidth can be one of the following:

"ba": Bartlett kernel
"bo": Bohmann kernel
"da": Daniell kernel
"pa": Parzen kernel
"qs": Quadratic Spectral kernel
"tr": Truncated kernel

Value

[list] with components:

Omega [matrix]: Long-run variance matrix
Delta [matrix]: One-sided long-run variance matrix
Sigma [matrix]: Variance matrix

Examples

set.seed(1909)
x <- rnorm(100)
band <- getBandwidthAnd(x, kernel = "ba")
getLongRunVar(x, kernel = "ba", bandwidth = band)
# shorter:
getLongRunVar(x, kernel = "ba", bandwidth = "and")

x2 <- arima.sim(model = list(ar = c(0.7, 0.2)), innov = x, n = 100)
x2 <- cbind(a = x2, b = x2 + rnorm(100))
getLongRunVar(x2, kernel = "ba", bandwidth = "nw")

set.seed(1909)
x <- rnorm(100)
band <- getBandwidthAnd(x, kernel = "ba")
getLongRunVar(x, kernel = "ba", bandwidth = band)
# shorter:
getLongRunVar(x, kernel = "ba", bandwidth = "and")

x2 <- arima.sim(model = list(ar = c(0.7, 0.2)), innov = x, n = 100)
x2 <- cbind(a = x2, b = x2 + rnorm(100))
getLongRunVar(x2, kernel = "ba", bandwidth = "nw")

Weights for Long-Run Variance

Description

Compute the weights corresponding to some kernel funtions.

Usage

getLongRunWeights(n, bandwidth, kernel)
getLongRunWeights(n, bandwidth, kernel)

Arguments

`n`	[`numeric(1)`] Length of weights' vector.
`bandwidth`	[`numeric(1)`] The bandwidth (as number).
`kernel`	[`character(1)`] The kernel function (see `getLongRunVar` for possible values).

Value

[list] with components:

w [numeric]: Vector of weights
upper [numeric(1)]: Index to largest non-zero entry in w

Examples

lrw.ba = cointReg:::getLongRunWeights(100, kernel = "ba", bandwidth = 25)
plot(lrw.ba$w)

lrw.ba = cointReg:::getLongRunWeights(100, kernel = "ba", bandwidth = 25)
plot(lrw.ba$w)

Get D OLS model.

Description

Generates an lm model for the Dynamic OLS estimator.

Usage

getModD(x, y, deter, n.lag, n.lead, check = FALSE)
getModD(x, y, deter, n.lag, n.lead, check = FALSE)

Arguments

`x`	[`matrix`] RHS variables of the D OLS estimation.
`y`	[`matrix`] LHS variable(s) of the D OLS estimation.
`deter`	[`matrix`] Matrix of deterministic variables to include in the D OLS model.
`n.lag`, `n.lead`	[`numeric(1)`] Number of lags and leads, have to be non-negative integer values.
`check`	[`logical`] Wheather to check (and if necessary convert) the arguments. See `checkVars` for further information.

Value

[lm]. An lm object, containing an additional list element (aux) with D-OLS specific objects:

Z [matrix]: jointed matrix of deterministics and x
x.delta [matrix]: differences of x
dx.all [matrix]: leads-and-lags matrix
all.trunc [matrix]: truncated version of jointed matrix of Z and dx.all
y.trunc [matrix]: truncated version of y

Examples

set.seed(1909)
y <- matrix(cumsum(rnorm(100)), ncol = 1)
x <- matrix(rep(y, 4) + rnorm(400, mean = 3, sd = 2), ncol = 4)
deter <- cbind(1, 1:100)
cointReg:::getModD(x = x, y = y, deter = deter, n.lag = 2, n.lead = 3)
set.seed(1909)
y <- matrix(cumsum(rnorm(100)), ncol = 1)
x <- matrix(rep(y, 4) + rnorm(400, mean = 3, sd = 2), ncol = 4)
deter <- cbind(1, 1:100)
cointReg:::getModD(x = x, y = y, deter = deter, n.lag = 2, n.lead = 3)

Leads-and-Lags Matrix

Description

Generates leads-and-lags matrix for the Dynamic OLS estimator.

Usage

makeLeadLagMatrix(x, n.lag, n.lead)
makeLeadLagMatrix(x, n.lag, n.lead)

Arguments

`x`	[`matrix`] Matrix for which to generate the leads-and-lags matrix.
`n.lag`, `n.lead`	[`numeric(1)`] Number of lags and leads, have to be non-negative integer values. If greater than `nrow(x)`, produces 0-rows.

Value

[matrix]. Leads-and-lags matrix.

Examples

x <- matrix(1:20, 2, byrow = TRUE)
cointReg:::makeLeadLagMatrix(x = x, n.lag = 2, n.lead = 3)
x <- matrix(1:20, 2, byrow = TRUE)
cointReg:::makeLeadLagMatrix(x = x, n.lag = 2, n.lead = 3)

Plot Method for Cointegration Models (Modified OLS).

Description

Plotting objects of class "cointReg". Currently, only the residuals will be plotted.

Usage

## S3 method for class 'cointReg'
plot(x, type, main, xlab, ylab, axes = TRUE, ...)
## S3 method for class 'cointReg'
plot(x, type, main, xlab, ylab, axes = TRUE, ...)

Arguments

`x`	[`cointReg`] Object of class `"cointReg"`, i.e. the result of `cointRegFM`, `cointRegD`, or `cointRegIM`.
`type`	[`character`] Plot type (from `plot`). Default is `"l"`.
`main`, `xlab`, `ylab`	[`character`] Title and axis titles (from `plot`). Default values will be generated from the contents of `x`.
`axes`	[`logical`] Whether to add axes (from `plot`) to the plot.
`...`	[`any`] Further arguments passed to `plot`.

Examples

set.seed(42)
x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
y = x$x1 - x$x2 + 10 + eps1
deter = cbind(level = rep(1, 200))
test = cointRegFM(x = x, y = y, deter = deter)
plot(test)

set.seed(42)
x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
y = x$x1 - x$x2 + 10 + eps1
deter = cbind(level = rep(1, 200))
test = cointRegFM(x = x, y = y, deter = deter)
plot(test)

Print Method for Cointegration Models (Modified OLS).

Description

Printing objects of class "cointReg".

Usage

## S3 method for class 'cointReg'
print(x, ..., digits = getOption("digits"),
  all.coeffs = FALSE)
## S3 method for class 'cointReg'
print(x, ..., digits = getOption("digits"),
  all.coeffs = FALSE)

Arguments

`x`	[`cointReg`] Object of class `"cointReg"`, i.e. the result of `cointRegFM`, `cointRegD` or `cointRegIM`.
`...`	ignored
`digits`	[`numeric`] Number of significant digits to be used.
`all.coeffs`	[`logical`] Whether to show all coefficients (i. e. the "real" regressors AND the auxiliary regressors). Default is `FALSE`.

Value

[matrix]
A matrix including the coefficients along with standard errors, t and p values.

Examples

set.seed(42)
x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
y = x$x1 - x$x2 + 10 + eps1
deter = cbind(level = rep(1, 200))

test.fm = cointRegFM(x = x, y = y, deter = deter)
print(test.fm)

test.d = cointRegD(x = x, y = y, deter = deter)
print(test.d)

test.im2 = cointRegIM(x = x, y = y, deter = deter)
print(test.im2)

## Not run: 
# The coefficients matrix can be transferred e.g. to LaTeX via xtable:
if (!require("xtable")) {install.packages("xtable"); library("xtable")}
xtab = xtable(print(test.fm))
print.xtable(xtab)

## End(Not run)

set.seed(42)
x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
y = x$x1 - x$x2 + 10 + eps1
deter = cbind(level = rep(1, 200))

test.fm = cointRegFM(x = x, y = y, deter = deter)
print(test.fm)

test.d = cointRegD(x = x, y = y, deter = deter)
print(test.d)

test.im2 = cointRegIM(x = x, y = y, deter = deter)
print(test.im2)

## Not run: 
# The coefficients matrix can be transferred e.g. to LaTeX via xtable:
if (!require("xtable")) {install.packages("xtable"); library("xtable")}
xtab = xtable(print(test.fm))
print.xtable(xtab)

## End(Not run)

Package 'cointReg'

Help Index

The cointReg package

Description

Details

Functions

Check list D.options.

Description

Usage

Arguments

Value

See Also

Examples

Variable check for single objects.

Description

Usage

Arguments

Details

Value

See Also

Examples

Multiple variable checks for certain values.

Description

Usage

Arguments

Details

Value

See Also

Examples

Estimation and Inference for cointegrating regressions

Description

Usage

Arguments

Value

References

See Also

Examples

Dynamic OLS

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Fully Modified OLS

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Integrated Modified OLS

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Automatic Bandwidth Selection

Description

Usage

Arguments

Details

Value

Functions

References

See Also

Examples

Leads and Lags

Description

Usage

Arguments

Value

See Also