cointRegIM {cointReg} | R Documentation |
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, ...)
Arguments
x |
[ |
y |
[ |
deter |
[ |
selector |
[ |
t.test |
[ |
kernel |
[ |
bandwidth |
[ |
check |
[ |
... |
Arguments passed to |
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 inu.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 argumentt.test
isTRUE
) orNULL
varmat
[matrix
]-
variance-covariance matrix
Omega
[matrix
]-
NULL
(no long-run variance matrix for this regression type) bandwidth
[list
]-
number
andname
of bandwidth ift.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
andlambda2
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.
See Also
Other cointReg: cointRegD
,
cointRegFM
, cointReg
,
plot.cointReg
, print.cointReg
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)