infer
Infer vector error-correction (VEC) model innovations
Description
uses additional
options specified by one or more name-value arguments. For example, E
= infer(Mdl
,Y
,Name,Value
)'Y0',Y0,'X',X
specifies
Y0
as presample responses and X
as
exogenous predictor data for the regression component.
Examples
Input Arguments
Output Arguments
Algorithms
infer
infers innovations by evaluating the VEC modelMdl
with respect to the innovations using the supplied dataY
,Y0
, andX
. The inferred innovations areinfer
uses this process to determine the time origin t0 of models that include linear time trends.If you do not specify
Y0
, then t0 = 0.Otherwise,
infer
sets t0 tosize(Y0,1)
–Mdl.P
. Therefore, the times in the trend component are t = t0 + 1, t0 + 2,..., t0 +numobs
, wherenumobs
is the effective sample size (size(Y,1)
afterinfer
removes missing values). This convention is consistent with the default behavior of model estimation in whichestimate
removes the firstMdl.P
responses, reducing the effective sample size. Althoughinfer
explicitly uses the firstMdl.P
presample responses inY0
to initialize the model, the total number of observations inY0
andY
(excluding missing values) determines t0.
References
[1] Hamilton, James D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[2] Johansen, S. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press, 1995.
[3] Juselius, K. The Cointegrated VAR Model. Oxford: Oxford University Press, 2006.
[4] Lütkepohl, H. New Introduction to Multiple Time Series Analysis. Berlin: Springer, 2005.