# [R] Forecasting using VECM

Preetam Pal lordpreetam at gmail.com
Tue Feb 14 13:18:26 CET 2017

```Hi,

I have attached the historical dataset (titled data) containing numerical
variables GDP, HPA, FX and Y - I am interested to predict Y given some
future values of GDP, HPA and FX.

- Some variables are non-statioanry as per adf.test()
- I wanted to implement a VECM framework for modeling cointegration, so
I have used *result = VECM(data, lag = 3, r = 1)* , and I get the output
below showing that cointegration relationship does exist between these 4
variables:
- My question is: How do I get predictions of Y given
externally-generated future values of the other variables (for say,
upcoming 10 time points), using this result programmatically?

Regards,
Preetam
#############
Model VECM
#############
Full sample size: 25 End sample size: 22
Number of variables: 4 Number of estimated slope parameters 40
AIC 23.84198 BIC 70.75681 SSR 156.5155
Cointegrating vector (estimated by ML):
GDP      HPA        FX           Y
r1   1 2.171994 -6.823215 -0.07767563

ECT                 Intercept           GDP -1
Equation GDP 0.0612(0.0436)      0.0141(0.0687)      -0.4268(0.2494)
Equation HPA -0.6368(0.2381)*    0.1858(0.3749)      3.1656(1.3609)*
Equation FX  0.1307(0.0874)      -0.0039(0.1377)     0.1739(0.4997)
Equation Y   -0.0852(0.4261)     0.3219(0.6711)      -5.0248(2.4359).
HPA -1              FX -1               Y -1
Equation GDP -0.0910(0.0790)     0.1988(0.2261)      0.0413(0.0299)
Equation HPA 0.4891(0.4311)      -2.2140(1.2337).    -0.3206(0.1631).
Equation FX  -0.2108(0.1583)     -0.2536(0.4530)     -0.0303(0.0599)
Equation Y   -0.3686(0.7716)     0.5234(2.2083)      -0.9638(0.2920)**
GDP -2              HPA -2              FX -2
Equation GDP -0.2892(0.2452)     -0.0622(0.0563)     0.0598(0.1352)
Equation HPA -0.7084(1.3379)     0.1877(0.3069)      -0.2231(0.7377)
Equation FX  -0.1773(0.4913)     -0.0170(0.1127)     -0.2486(0.2709)
Equation Y   -3.8521(2.3948)     -0.4559(0.5494)     1.1239(1.3205)
Y -2
Equation GDP 0.0411(0.0279)
Equation HPA -0.2447(0.1521)
Equation FX  -0.0102(0.0559)
Equation Y   -0.1696(0.2723)
-------------- next part --------------
GDP	        HPA	        FX      	Y
0.514662421	0.635997077	1.37802145	1.773342598
0.936722	3.127683176	1.391916535	3.709809052
0.101482324	1.270555421	0.831157511	0.226267793
0.017548634	2.456061547	1.003945759	9.510258161
0.236462416	0.988324147	0.223682679	5.026671536
0.372005149	2.177631629	0.904226065	4.219235789
0.153915709	4.620341653	0.033410743	3.17396006
0.524887329	1.050861084	0.518201484	7.950098612
0.776616937	0.503349512	0.666089868	3.320938471
0.760074361	3.635853456	0.470220952	6.380945175
0.802986662	1.260738545	0.452674872	1.036040804
0.375145127	0.20035625	1.837306306	6.486871565
0.002568896	3.532359526	0.556752154	8.536594244
0.754309276	3.952381767	0.247402168	8.559081716
0.585966577	4.01463047	1.184382133	0.148121669
0.39767356	1.553753452	0.983129422	5.378373676
0.859898623	4.73191381	0.828795696	3.367809329
0.741376169	4.993350692	1.758051281	5.516460988
0.329240391	3.465836416	1.701655508	1.249497907
0.078661064	3.298298811	0.04575857	5.132921426
0.270971873	0.46627043	1.739487411	4.94697541
0.731072625	0.940642982	0.728747166	7.583041122
0.385038046	3.51048946	0.021866584	7.361148458
0.530760376	1.204422978	0.415530715	1.163503483
0.555323667	4.777712592	1.844184811	8.596644394
```