Object of class ‘varest’; generated by
VAR(), or an object of class ‘vec2var’;
generated by vec2var().
lags.pt
An integer specifying the lags to be used for the
Portmanteau statistic.
lags.bg
An integer specifying the lags to be used for the
Breusch-Godfrey statistic.
type
Character, the type of test. The default is an asymptotic
Portmanteau test.
Details
The Portmanteau statistic for testing the absence of up to the order h
serially correlated disturbances in a stable VAR(p) is defined as:
Q_h = T ∑_{j = 1}^h
tr(hat{C}_j'hat{C}_0^{-1}hat{C}_jhat{C}_0^{-1}) quad ,
where hat{C}_i = frac{1}{T}∑_{t = i + 1}^T old{hat{u}}_t
old{hat{u}}_{t - i}'. The test statistic is approximately
distributed as χ^2(K^2(h - p)). This test statistic is
choosen by setting type = "PT.asymptotic". For smaller sample sizes
and/or values of h that are not sufficiently large, a corrected
test statistic is computed as:
The null hypothesis is: H_0: B_1 = … = B_h = 0 and
correspondingly the alternative hypothesis is of the form H_1:
exists ; B_i \ne 0 for i = 1, 2, …, h. The test statistic
is defined as:
where \tilde{Σ}_R and \tilde{Σ}_e assign the
residual covariance matrix of the restricted and unrestricted
model, respectively. The test statistic LM_h is distributed as
χ^2(hK^2). This test statistic is calculated if type =
"BG" is used.
Edgerton and Shukur (1999) proposed a small sample correction, which
is defined as:
with R_r^2 = 1 - |\tilde{Σ}_e | / |\tilde{Σ}_R|,
r = ((K^2m^2 - 4)/(K^2 + m^2 - 5))^{1/2}, q = 1/2 K m - 1
and N = T - K - m - 1/2(K - m + 1), whereby n is the
number of regressors in the original system and m = Kh. The
modified test statistic is distributed as F(hK^2, int(Nr -
q)). This modified statistic will be returned, if type =
"ES" is provided in the call to serial().
Value
A list with class attribute ‘varcheck’ holding the
following elements:
resid
A matrix with the residuals of the VAR.
pt.mul
A list with objects of class attribute ‘htest’
containing the multivariate Portmanteau-statistic (asymptotic and
adjusted.
LMh
An object with class attribute ‘htest’
containing the Breusch-Godfrey LM-statistic.
LMFh
An object with class attribute ‘htest’
containing the Edgerton-Shukur F-statistic.
Note
This function was named serial in earlier versions of package
vars; it is now deprecated. See vars-deprecated too.
Author(s)
Bernhard Pfaff
References
Breusch, T . S. (1978), Testing for autocorrelation in dynamic linear
models, Australian Economic Papers, 17: 334-355.
Edgerton, D. and Shukur, G. (1999), Testing autocorrelation in a
system perspective, Econometric Reviews, 18: 43-386.
Godfrey, L. G. (1978), Testing for higher order serial correlation in
regression equations when the regressors include lagged dependent
variables, Econometrica, 46: 1303-1313.
Hamilton, J. (1994), Time Series Analysis, Princeton
University Press, Princeton.
Lütkepohl, H. (2006), New Introduction to Multiple Time Series
Analysis, Springer, New York.
See Also
VAR, vec2var, plot
Examples
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
serial.test(var.2c, lags.pt = 16, type = "PT.adjusted")