reading the output from estimation cats

[upani]

Dear Sir,

I want to estimate bivariate cointegration and error correction model for I(1) series.

After i run the model i am getting the following output

MODEL SUMMARY
Sample: 1 to 3484 (3484 observations)
Effective Sample: 9 to 3484 (3476 observations)
Obs. - No. of variables: 3459
System variables: LFP LSP
Constant/Trend: Restricted Constant
Lags in VAR: 8

I(2) analysis not available for the specified model.

The unrestricted estimates:
BETA(transposed)
LFP LSP CONSTANT
Beta(1) 122.564 -122.176 -3.880. Why i am getting two Beta over here? and Which one is my original cointegrating vector
Beta(2) 0.681 -2.124 15.022

ALPHA
Alpha(1) Alpha(2)
DLFP -0.001 0.000
(-3.413) (2.722)
DLSP 0.001 0.000
(6.425) (2.265)

PI
LFP LSP CONSTANT
DLFP -0.073 0.072 0.010
(-3.398) (3.365) (3.490)
DLSP 0.102 -0.103 0.001
(6.438) (-6.464) (0.586)

Log-Likelihood = 33414.312

[TomDoan]

You're doing a restricted constant model. The third element of beta is the constant. If your series are trending, that's the wrong model.

[upani]

Dear Sir,

After i include the trend component, still i am getting two vectors of Beta.

The unrestricted estimates:
BETA(transposed)
LFP LSP TREND
Beta(1) 122.706 -122.653 0.000
Beta(2) 0.245 3.508 -0.001

With sincere regards,
Upani

[TomDoan]

Those are the unrestricted estimates. The first beta is for the linear combination with the most stationary root. If you have one cointegrating vector, you want to do Set Rank of PI to 1 to restrict your attention to just the one.

You probably want DET=CONSTANT, which allows (linear) trends. The model you have would permit quadratic trends.

[upani]

Dear Sir,

I got the following result after modifying the restrictions.

CATS for RATS version 2 - 07/03/2018 02:07

MODEL SUMMARY
Sample: 1 to 3484 (3484 observations)
Effective Sample: 3 to 3484 (3482 observations)
Obs. - No. of variables: 3476
System variables: LFP LSP
Constant/Trend: Restricted Trend
Lags in VAR: 2

The unrestricted estimates:
BETA(transposed)
LFP LSP TREND
Beta(1) 104.880 -104.864 0.000
Beta(2) 2.461 0.962 -0.001

ALPHA
Alpha(1) Alpha(2)
DLFP -0.001 -0.000
(-4.384) (-1.976)
DLSP 0.002 -0.000
(13.853) (-1.426)

PI
LFP LSP TREND
DLFP -0.082 0.081 0.000
(-4.429) (4.366) (1.035)
DLSP 0.193 -0.194 0.000
(13.816) (-13.866) (4.237)

Log-Likelihood = 33329.265



RE-NORMALIZATION OF THE EIGENVECTORS:

THE EIGENVECTOR(s)(transposed)
LFP LSP TREND
Beta(1) 104.880 -104.864 0.000


THE MATRICES BASED ON 1 COINTEGRATING VECTOR:

BETA(transposed)
LFP LSP TREND
Beta(1) 1.000 -1.000 0.000
(.NA) (-377.273) (1.059)

ALPHA
Alpha(1)
DLFP -0.081
(-4.382)
DLSP 0.193
(13.849)

PI
LFP LSP TREND
DLFP -0.081 0.081 -0.000
(-4.382) (4.382) (-4.382)
DLSP 0.193 -0.193 0.000
(13.849) (-13.849) (13.849)

Log-Likelihood = 33327.209


TEST OF WEAK EXOGENEITY
LR-Test, Chi-Square(r), P-values in brackets.

r DGF 5% C.V. LFP LSP
1 1 3.841 18.939 184.629
[0.000] [0.000]

Please suggest me whether the above estimation is correct or not? I am looking for checking the price discovery in both the markets, then checking weak exogeneity for casuality test.

With sincere regards,
Upani

[TomDoan]

Isn't there one and only one sensible cointegrating vector with those data? If it's not (1,-1), couldn't someone make lots of money? Why don't you just impose the obvious value and work off of that?