Integrated Modified OLS
Computes the Vogelsang and Wagner (2014) Integrated Modified OLS estimator.
cointRegIM(x, y, deter, selector = 1, t.test = TRUE, kernel = c("ba",
"pa", "qs", "tr"), bandwidth = c("and", "nw"), check = TRUE, ...)x |
[ |
y |
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deter |
[ |
selector |
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t.test |
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kernel |
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bandwidth |
[ |
check |
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... |
Arguments passed to |
The equation for which the IM-OLS estimator is calculated (type 1):
S[y] = δ * S[D] + β * S[x] + γ * 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 θ = (δ', β', γ')' is the full parameter vector.
The equation for which the IM-OLS estimator is calculated (type 2):
S[y] = δ * S[D] + β * S[x] + γ * x + λ * 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 θ = (δ', β', γ', λ')' is the full parameter vector.
[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
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.
Other cointReg: cointRegD,
cointRegFM, cointReg,
plot.cointReg, print.cointReg
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.