VAR: Estimation of a VAR(p)

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Estimation of a VAR by utilising OLS per equation.

Usage

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VAR(y, p = 1, type = c("const", "trend", "both", "none"),
season = NULL, exogen = NULL, lag.max = NULL,
ic = c("AIC", "HQ", "SC", "FPE"))
## S3 method for class 'varest'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

y

Data item containing the endogenous variables

p

Integer for the lag order (default is p=1).

type

Type of deterministic regressors to include.

season

Inlusion of centered seasonal dummy variables (integer value of frequency).

exogen

Inlusion of exogenous variables.

lag.max

Integer, determines the highest lag order for lag length selection according to the choosen ic.

ic

Character, selects the information criteria, if lag.max is not NULL.

x

Object with class attribute ‘varest’.

digits

the number of significant digits to use when printing.

...

further arguments passed to or from other methods.

Details

Estimates a VAR by OLS per equation. The model is of the following form:

\bold{y}_t = A_1 \bold{y}_{t-1} + … + A_p \bold{y}_{t-p} + CD_t + \bold{u}_t

where \bold{y}_t is a K \times 1 vector of endogenous variables and u_t assigns a spherical disturbance term of the same dimension. The coefficient matrices A_1, …, A_p are of dimension K \times K. In addition, either a constant and/or a trend can be included as deterministic regressors as well as centered seasonal dummy variables and/or exogenous variables (term CD_T, by setting the type argument to the corresponding value and/or setting season to the desired frequency (integer) and/or providing a matrix object for exogen, respectively. The default for type is const and for season and exogen the default is set to NULL.
If for lag.max an integer value is provided instead of NULL (the default), the lag length is determined by the selected information criteria in ic, the default is Akaike.

Value

A list with class attribute ‘varest’ holding the following elements:

varresult

list of ‘lm’ objects.

datamat

The data matrix of the endogenous and explanatory variables.

y

The data matrix of the endogenous variables

type

A character, specifying the deterministic regressors.

p

An integer specifying the lag order.

K

An integer specifying the dimension of the VAR.

obs

An integer specifying the number of used observations.

totobs

An integer specifying the total number of observations.

restrictions

Either NULL or a matrix object containing the zero restrictions of the VAR(p).

call

The call to VAR().

Author(s)

Bernhard Pfaff

References

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

summary, plot, coef, residuals, fitted, predict, irf, fevd, Phi, Psi, normality.test, arch.test, serial.test, VARselect, logLik

Examples

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data(Canada)
VAR(Canada, p = 2, type = "none")
VAR(Canada, p = 2, type = "const")
VAR(Canada, p = 2, type = "trend")
VAR(Canada, p = 2, type = "both")

Example output

Loading required package: MASS
Loading required package: strucchange
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Loading required package: sandwich
Loading required package: urca
Loading required package: lmtest

VAR Estimation Results:
======================= 

Estimated coefficients for equation e: 
====================================== 
Call:
e = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 

       e.l1     prod.l1       rw.l1        U.l1        e.l2     prod.l2 
 1.62046761  0.17973134 -0.04425592  0.11310425 -0.64815156 -0.11683270 
      rw.l2        U.l2 
 0.04475537 -0.06581206 


Estimated coefficients for equation prod: 
========================================= 
Call:
prod = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 

       e.l1     prod.l1       rw.l1        U.l1        e.l2     prod.l2 
-0.19389053  1.16559603  0.07426648 -0.66412399  0.20141693 -0.19089450 
      rw.l2        U.l2 
-0.06904805  0.77427171 


Estimated coefficients for equation rw: 
======================================= 
Call:
rw = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
-0.273036691 -0.078046604  0.900047886 -0.024808893  0.331264372 -0.008858991 
       rw.l2         U.l2 
 0.062587364 -0.175795886 


Estimated coefficients for equation U: 
====================================== 
Call:
U = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
-0.561791776 -0.091739246 -0.001960487  0.785638638  0.574926136  0.068715871 
       rw.l2         U.l2 
-0.002926763  0.145852929 



VAR Estimation Results:
======================= 

Estimated coefficients for equation e: 
====================================== 
Call:
e = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const 

         e.l1       prod.l1         rw.l1          U.l1          e.l2 
 1.637821e+00  1.672717e-01 -6.311863e-02  2.655848e-01 -4.971338e-01 
      prod.l2         rw.l2          U.l2         const 
-1.016501e-01  3.844492e-03  1.326893e-01 -1.369984e+02 


Estimated coefficients for equation prod: 
========================================= 
Call:
prod = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
  -0.1727658    1.1504282    0.0513039   -0.4785013    0.3852589   -0.1724119 
       rw.l2         U.l2        const 
  -0.1188510    1.0159180 -166.7755177 


Estimated coefficients for equation rw: 
======================================= 
Call:
rw = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const 

         e.l1       prod.l1         rw.l1          U.l1          e.l2 
 -0.268832871  -0.081065001   0.895478330   0.012130033   0.367848941 
      prod.l2         rw.l2          U.l2         const 
 -0.005180947   0.052676565  -0.127708256 -33.188338774 


Estimated coefficients for equation U: 
====================================== 
Call:
U = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
 -0.58076382  -0.07811707   0.01866214   0.61893150   0.40981822   0.05211668 
       rw.l2         U.l2        const 
  0.04180115  -0.07116885 149.78056487 



VAR Estimation Results:
======================= 

Estimated coefficients for equation e: 
====================================== 
Call:
e = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + trend 

       e.l1     prod.l1       rw.l1        U.l1        e.l2     prod.l2 
 1.63082118  0.16456040 -0.05764637  0.13231952 -0.64150027 -0.12338620 
      rw.l2        U.l2       trend 
 0.03934730 -0.04002238  0.01532917 


Estimated coefficients for equation prod: 
========================================= 
Call:
prod = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + trend 

       e.l1     prod.l1       rw.l1        U.l1        e.l2     prod.l2 
-0.14823958  1.09870431  0.01522531 -0.57940001  0.23074378 -0.21979021 
      rw.l2        U.l2       trend 
-0.09289334  0.88798355  0.06758938 


Estimated coefficients for equation rw: 
======================================= 
Call:
rw = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + trend 

       e.l1     prod.l1       rw.l1        U.l1        e.l2     prod.l2 
-0.23961487 -0.12701916  0.85682285  0.03721896  0.35273506 -0.03001403 
      rw.l2        U.l2       trend 
 0.04512982 -0.09254553  0.04948332 


Estimated coefficients for equation U: 
====================================== 
Call:
U = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + trend 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
-0.570210031 -0.079404090  0.008926991  0.770015126  0.569518122  0.074044380 
       rw.l2         U.l2        trend 
 0.001470425  0.124883916 -0.012463808 



VAR Estimation Results:
======================= 

Estimated coefficients for equation e: 
====================================== 
Call:
e = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const + trend 

         e.l1       prod.l1         rw.l1          U.l1          e.l2 
 1.635735e+00  1.716493e-01 -6.005622e-02  2.739686e-01 -4.842222e-01 
      prod.l2         rw.l2          U.l2         const         trend 
-9.766366e-02  1.689096e-03  1.433151e-01 -1.509574e+02 -5.706013e-03 


Estimated coefficients for equation prod: 
========================================= 
Call:
prod = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const + trend 

       e.l1     prod.l1       rw.l1        U.l1        e.l2     prod.l2 
-0.14816907  1.09880604  0.01519072 -0.57736715  0.23300094 -0.21942106 
      rw.l2        U.l2       const       trend 
-0.09343379  0.89061470 -2.16644760  0.06728750 


Estimated coefficients for equation rw: 
======================================= 
Call:
rw = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const + trend 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
 -0.24395401  -0.13327924   0.85895095  -0.08786974   0.21384463  -0.05272931 
       rw.l2         U.l2        const        trend 
  0.07838534  -0.25444874 133.30872014   0.06805925 


Estimated coefficients for equation U: 
====================================== 
Call:
U = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const + trend 

        e.l1      prod.l1        rw.l1         U.l1         e.l2      prod.l2 
 -0.57610104  -0.08790304   0.01181620   0.60018959   0.38095481   0.04320519 
       rw.l2         U.l2        const        trend 
  0.04661948  -0.09492249 180.98536416   0.01275563 

vars documentation built on May 1, 2019, 8:23 p.m.