Four different groups of recursive tests
Forward recursive tests
Recursively calculated trace tests
Recursively calculated trace tests
Recursively calculated eigenvalues
Recursively calculated eigenvalues
Log transformed eigenvalues
The fluctuations test
A detailed discussion of the test procedure will be given in Chapter 12
The max test of beta.
Tests of known beta. Reference period: full sample
Tests of known beta. Reference period: 1986:1-2003:1
Tests of known beta. Reference period: 1973:2-1986:1
One-step ahead prediction tests
One-step-ahead prediction tests for the system
Prediction tests for each variable: X-form VAR
Prediction tests for each variable. R-form VAR
Backward recursive test of loglikelihood function
Test for Constancy of the Log-Likelihood
1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 19850.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5X(t)
R1(t)
5% C.V. (1.36 = Index)
Backwards recursively calculated trace tests
Backwards calculated log transformed eigenvalues
Backwards calculated fluctuations tests
Eigenv alue Fluctuation Test
Tau(Ksi) = C(T)| |Ksi(t)-Ksi(T)| |
1973 1975 1977 1979 1981 1983 19850.00
0.25
0.50
0.75
1.00X( t )R1( t )5% C. V. (1. 36 = I ndex)
Tau(Ksi(1))
1973 1975 1977 1979 1981 1983 19850.00
0.25
0.50
0.75
1.00X( t )R1( t )5% C. V. (1. 36 = I ndex)
Tau(Ksi(2))
1973 1975 1977 1979 1981 1983 19850.00
0.25
0.50
0.75
1.00X( t )R1( t )5% C. V. (1. 36 = I ndex)
Tau(Ksi(3))
1973 1975 1977 1979 1981 1983 19850.00
0.25
0.50
0.75
1.00X( t )R1( t )5% C. V. (1. 36 = I ndex)
Tau(Ksi(1)+...+Ksi(3))
The max test of parameter constancy
Test of Beta Constancy
1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 19850.00
0.25
0.50
0.75
1.00X(t)R 1(t)5% C .V. (3.92 = Index )
Q(t)
Backward tests of known beta. Reference period ?
Test of Beta(t) = 'Known Beta'
1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 19850.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5X(t)
R1(t)
5% C.V. (16.9 = Index)
Recursively back-casting the system
Recursively back-forecasting each variable. X-form VAR
Back-forecasting each of the variables based on the VAR in R-form
