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(MAximum Likelihood COintegration analysis of Linear Models)
The theory and practice of cointegration analysis in RATS
by Rocco Mosconi
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As any RATS procedure, MALCOLM has to be compiled in each RATS session where you want to use it. This takes just a few seconds. Once MALCOLM is compiled, you have a new RATS instruction, @MALCOLM. The syntax of in the instruction @MALCOLM is the following:
Syntax  @MALCOLM(options) Start End Mod 
#<supp.card> endogenous variables in regression format (do not include constant) 
#<supp.card> exogenous variables in regression format (only with option EXOG
#<supp.card> intervention dummies in regression format (only with option IDUM
  • Start End: The range to analyze. This defaults to the maximum common range for endogenous, exogenous and dummy variables.
  • Mod: This is a 6 dimensional VEC[INT] describing the model. If Mod is not supplied, Menu 2 of MALCOLM may be used to choose a model. Non expert users are encouraged to use Menu 2 instead of Mod. The elements of Mod have the following meaning:
    • Mod(1) = 0/1/2/3 describes the constant (0 no constant, 1 constant in sp(a), 2 constant in sp(a , a^1), 3 unrestricted constant).
    • Mod(2) = 0/1/2/3 describes the trend (0 no trend, 1 trend in Sp(a), 2 trend in sp(a ,a^1), 3 unrestricted trend).
    • Mod(3) = 0/1/2 describes the seasonality (0 for no seasonality, 1 for quarterly dummies, 2 for monthly dummies).
    • Mod(4) = (any positive integer) is the maximum lag.
    • Mod(5) = (any integer between 0 and the number of endogenous variables) is the cointegration rank r.
    • Mod(6) = (any integer between 0 and the number of endogenous variables minus r) is the cointegration rank s. 
  • EXOG/[NOEXOG] To allow for exogenous variables. The exogenous are included both in levels, with coefficients restricted to be in Sp(a), and in differences (current and lagged, up to lag=Mod(4)).
  • IDUM/[NOIDUM] To allow for intervention dummies. The dummies are simply included in levels, with unrestricted coefficients. If EXOG and IDUM are both present, the supplementary card for exogenous has to come first. 


1) The following example analyses the series Y1, Y2, Y3 and Y4, all regarded as endogenous, from 83:5 to 92:3. The model will be defined within the MALCOLM session using Menu 2:
@MALCOLM 83:5 92:3
# Y1 Y2 Y3 Y4

2) The following example analyses the series Y1, Y2, Y3 and Y4, with Y4 regarded as exogenous, from 83:1 to 94:12, including a dummy for 85:1 (say DUM851, which is supposed to be created in advance), starting with a VAR(3), restricted constant, no trend, r=2, s=1, and no seasonality. The model may be changed within the MALCOLM session using Menu 2:
COM MYMOD=||1,0,0,3,2,1||
# Y1 Y2 Y3
# Y4
# DUM851

3) Of course, IDUM may be used also to include any variable, no matter if dummy or not, which you may want to include just in the levels (with no lags). The following example:
@MALCOLM(IDUM) 83:5 92:3
# Y1 Y2 Y3
# Y4

is different from example 1 in that Y4 is included just in the levels, with no rank restrictions.


Copyright © 1996-99 Rocco Mosconi. All Rights Reserved.



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