Vector auto-regressive model with 1 dependent variable that does not has lags

Hi,

I would like to estimate the following VAR model: z(t)=a+Bx(t-1)+e(t)

with z(t)'=[ r(t) , x(t) ] and x(t) = [ NPY(t), TB(t), DEF(t) ]' e(t)~ iid N(0,sig)

Note that r(t) lags does not appear in the system of equations. I would like to output the matrix of coefficients B and the variance co-variance matrix of errors. How can I do that?

Here is my data:

if true
 date    t    MKTrf    NPY    TB    DEF    L1_NPY    L1_TB    L1_DEF
31mar1953    1    -1.52    -1.99486    2.36    .42            
30apr1953    2    -2.91    -1.9914    2.48    .44    -1.99486    2.36    .42
31may1953    3    .54    -1.98652    2.45    .46    -1.9914    2.48    .44
30jun1953    4    -1.85    -1.97217    2.38    .58    -1.98652    2.45    .46
31jul1953    5    2.38    -1.97788    2.28    .61    -1.97217    2.38    .58
31aug1953    6    -4.58    -1.96153    2.2    .59    -1.97788    2.28    .61
30sep1953    7    .15    -1.95691    1.79    .66    -1.96153    2.2    .59
31oct1953    8    4.58    -1.96923    1.67    .64    -1.95691    1.79    .66
30nov1953    9    2.75    -1.96342    1.66    .61    -1.96923    1.67    .64
31dec1953    10    -.05    -1.99034    1.41    .65    -1.96342    1.66    .61
31jan1954    11    5.14    -2.00099    1.14    .66    -1.99034    1.41    .65
28feb1954    12    1.68    -2.00127    1.13    .65    -2.00099    1.14    .66
31mar1954    13    3.65    -2.00536    .96    .62    -2.00127    1.13    .65
30apr1954    14    4.2    -2.01369    .85    .59    -2.00536    .96    .62
31may1954    15    3.11    -2.01669    .82    .59    -2.01369    .85    .59
30jun1954    16    1.09    -2.01725    .84    .61    -2.01669    .82    .59
31jul1954    17    4.99    -2.03005    .88    .62    -2.01725    .84    .61
31aug1954    18    -2.3    -2.01893    1.03    .58    -2.03005    .88    .62
30sep1954    19    6.34    -2.03151    1.17    .59    -2.01893    1.03    .58
31oct1954    20    -1.69    -2.0246    1.14    .56    -2.03151    1.17    .59
30nov1954    21    9.47    -2.03259    1.21    .55    -2.0246    1.14    .56
31dec1954    22    5.45    -2.11241    1.39    .52    -2.03259    1.21    .55
31jan1955    23    .62    -2.11376    1.57    .54    -2.11241    1.39    .52
28feb1955    24    3.04    -2.13234    1.59    .46    -2.11376    1.57    .54
31mar1955    25    -.21    -2.12995    1.75    .48    -2.13234    1.59    .46
30apr1955    26    3.13    -2.1314    1.9    .46    -2.12995    1.75    .48
31may1955    27    1.05    -2.12635    1.91    .46    -2.1314    1.9    .46
30jun1955    28    6.48    -2.13513    2.02    .46    -2.12635    1.91    .46
31jul1955    29    1.93    -2.1639    2.37    .45    -2.13513    2.02    .46
31aug1955    30    .27    -2.15558    2.36    .46    -2.1639    2.37    .45
30sep1955    31    -.36    -2.15148    2.39    .49    -2.15558    2.36    .46
31oct1955    32    -2.75    -2.14876    2.48    .48    -2.15148    2.39    .49
30nov1955    33    6.99    -2.14527    2.73    .47    -2.14876    2.48    .48
31dec1955    34    1.46    -2.16469    2.58    .49    -2.14527    2.73    .47
31jan1956    35    -3.02    -2.15226    2.49    .5    -2.16469    2.58    .49
end

Thanks!

Answer 1

[Harry Vancao]

It doesn't look like MATLAB supports generating auto-regressive models that have some lags of 0. It does support any number or combination of positive lags. If you think about it, it doesnt make much sense to perform an auto-regression without lags either.

It looks like you are trying to estimate some 3 factor model. And it looks like x(t) are your factors and r(t) is your returns. Please correct me if I am wrong. I think it would be simpler to just generate two separate models. One normal regression for r(t) and one auto-regressive one for x(t). I will show you how to generate the VAR for x(t). Of course, I am assuming that x(t) is not dependent on r(t).

MATLAB has a neat function called varm in the econometrics toolbox. To generate the auto-regressive model, you would use the following commands. (change your data to be comma separated and this should work)

data = importdata('data.txt')
data = data.data;
x = data(:, 3:5);

model = varm(3, 1); 
[model, EstSE,logL,E] = estimate(model, x)

The first line generates a skeleton vector auto-regressive model that is modeling 3 time series with one lag at t-1. The second line takes that model and your training data and then populates the model. the member AR is a cell that holds a matrix for each time lag which in this case, is B. The model also contains your covariance matrix and EstSE stands for estimate standard error.

You can even predict with this model using the function forecast. Here is a link with more documentation on varm. and here is a link on forecast