VAR() or dynlm() or lm()

Question

Can anybody tell me something about the difference between the functions VAR() and dynlm()? I thought I could do my VAR with OLS also with the lm() function, but found out that I can not include lags. This problem is solved by using dynlm(). I tried VAR() and dynlm() with the same data and also changed the type of the VAR function ("const" / "trend" /"none" / "both"), but in none of the cases the results were the same. Does anybody know the difference?

Data Example (only 100 rows of my time series with over 1000 rows):
  Price Open_Interest_All

1992-10-06 -0.781222672        1.63119379
1992-10-13 -0.226928010        4.05849973
1992-10-20 -0.314059754        0.74296670
1992-10-27  0.427535236        4.69469707
1992-11-03 -0.066975848       -8.97727509
1992-11-10 -1.105733849       13.60848986
1992-11-17 -0.033504156       -0.86606938
1992-11-24  0.132090521        3.09942608
1992-12-01  0.451677760       -6.96875467
1992-12-08  0.059010297        1.45547915
1992-12-15  0.018143072        2.47922886
1992-12-22  0.415489498        0.11104701
1992-12-29  0.281748150       -0.01741099
1993-01-05  1.264093684        0.75242942
1993-01-12 -1.765301997       -0.16864140
1993-01-19  0.352909608        1.23869888
1993-01-26  0.152561942        5.16469475
1993-02-02 -0.306023610       -1.88288581
1993-02-09  0.371154802       -0.22569400
1993-02-16 -0.096699431        0.72290467
1993-02-23 -0.216939288       -1.03640733
1993-03-02 -0.692525272        7.32922042
1993-03-09  0.148512407       -0.83248916
1993-03-16  0.053258877       -9.34412387
1993-03-23  0.282899028       -2.27865356
1993-03-30 -0.348375291       -0.68304626
1993-04-06 -0.701583175        5.13726283
1993-04-13 -0.643717452        7.49539668
1993-04-20 -2.315215806        6.78579388
1993-04-27  0.728123084       -7.89513692
1993-05-04 -0.401917826        1.93334817
1993-05-11 -0.820260275       -0.41889123
1993-05-18 -0.136744342        0.17780875
1993-05-25  0.851391229        5.73901054
1993-06-01 -1.030441814        2.02329734
1993-06-08  0.622336509       -0.47102737
1993-06-15  0.188830476        1.12995553
1993-06-22  0.425932387        3.25510238
1993-06-29  0.094860323       -1.15090784
1993-07-06  0.690949433       -3.84819577
1993-07-13 -0.555562379       -0.79792963
1993-07-20 -0.003165141        0.26002615
1993-07-27  0.303670755       -2.04747741
1993-08-03  0.173833160        0.14447390
1993-08-10 -0.361775029        4.78484100
1993-08-17  0.384427420       -3.66029272
1993-08-24  0.427606006        0.68034298
1993-08-31 -0.138889246       -7.61964095
1993-09-07  0.336480002       -2.54707323
1993-09-14 -1.121502023        5.46051062
1993-09-21 -1.763129531       13.11181789
1993-09-28  0.039080472        0.86031698
1993-10-05 -0.966905912       -4.20461016
1993-10-12  0.218149112       -2.12196119
1993-10-19 -0.817582360       -1.80785218
1993-10-26 -0.077143308        4.02653854
1993-11-02  0.079626855        0.64359810
1993-11-09  0.451802406        6.08728086
1993-11-16 -0.305816356        4.74542449
1993-11-23  0.217000320        4.48037134
1993-11-30 -0.188669087       -1.17994159
1993-12-07  0.747784520        5.22816662
1993-12-14  0.636011468       -2.22521990
1993-12-21  0.373247064       -0.52307968
1993-12-28  0.046941753       -0.95758768
1994-01-04 -0.810928287       -1.05574558
1994-01-11  0.490505014       -2.23947004
1994-01-18  0.699126287        1.47016108
1994-01-25  0.420702924       -5.33040334
1994-02-01 -0.034364270        1.03293264
1994-02-08  0.178692037        7.82838866
1994-02-15 -0.763248370       -4.77697912
1994-02-22  0.834492829       -4.39362728
1994-03-01 -0.319921226       -5.77740405
1994-03-08  0.428953703        6.08511360
1994-03-15  0.293429418        3.33746465
1994-03-22  0.212134960        8.28017661
1994-03-29  0.015434084       -3.84063215
1994-04-05 -0.819101724      -12.37463070
1994-04-12 -0.241797314       -6.35085378
1994-04-19 -0.110199011       -0.52875672
1994-04-26  0.292877781        8.25096506
1994-05-03  0.769091229        8.93992009
1994-05-10  1.335381796       -3.14410505
1994-05-17  1.218414811       -6.21162283
1994-05-24  0.915342249       -1.06778949
1994-05-31 -0.899495962        3.65817336
1994-06-07 -0.033983195       -4.82433827
1994-06-14  1.561915814        4.23026763
1994-06-21 -0.066335053       -1.33347133
1994-06-28 -0.385756193       -5.93684313
1994-07-05  0.991119380       -5.67886504
1994-07-12 -0.398792460       -8.50476149
1994-07-19  0.232917128        6.45658144
1994-07-26  0.382266943       -9.35866297
1994-08-02 -1.190583357       -0.50190110
1994-08-09  0.364675303       -5.42680501
1994-08-16 -0.070737617        1.57683454
1994-08-23 -0.167435051       -3.93086516
1994-08-30  0.928324476        5.51263721
VARexample <- VAR(example, p=5, type="const")
lmexample <- lm(example$Price[6:100]~example$Price[5:99]+example$Price[4:98]+example$Price[3:97]+example$Price[2:96]+example$Price[1:95]+example$Open_Interest_All[5:99]+example$Open_Interest_All[4:98]+example$Open_Interest_All[3:97] + example$Open_Interest_All[2:96] + example$Open_Interest_All[1:95])
dynlmexample <- dynlm(example$Price~L(example$Price,1:5) + L(example$Open_Interest_All,1:5))
VARcoeffsexample <- as.data.frame(coef(VARexample)$Price[c(11,1,3,5,7,9,2,4,6,8,10),1])
lmcoeffsexample <- as.data.frame(coef(lmexample))
dynlmcoeffsexample <- as.data.frame(coef(dynlmexample))
compare <- data.frame(VARcoeffsexample[,1], lmcoeffsexample[,1], dynlmcoeffsexample[,1])
rownames(compare) <- rownames(VARcoeffsexample)
Output: 
> compare
                     VARcoeffsexample...1. lmcoeffsexample...1. dynlmcoeffsexample...1.
const                         0.0162815782         0.0162815782             0.016408246
Price.l1                     -0.0233716524        -0.0233716524            -0.062759716
Price.l2                      0.1262282115         0.1262282115             0.050038501
Price.l3                      0.1444267851         0.1444267851             0.103449318
Price.l4                     -0.0806846153        -0.0806846153             0.005414185
Price.l5                     -0.0197842734        -0.0197842734            -0.048802520
Open_Interest_All.l1         -0.0176241595        -0.0176241595            -0.022186654
Open_Interest_All.l2          0.0166671079         0.0166671079            -0.008759684
Open_Interest_All.l3          0.0205802095         0.0205802095            -0.007958906
Open_Interest_All.l4         -0.0384040280        -0.0384040280            -0.003796186
Open_Interest_All.l5          0.0006342804         0.0006342804            -0.029456337

So lm() and VAR() are the same coefficients, but dynlm() is different...

If you make lags manually (e.g. using the function embed), you can use them in lm. (This does not answer your question, so I am only posting this as a comment.) — Richard Hardy, Mar 01 '21 at 08:51

Christoph Hanck · Accepted Answer · 2021-03-02T11:23:10.797

Without seeing your code, it is hard to spell out the difference in results. But it sure is possible to get the same results in either package, as - as you correctly point out - all three commands ultimately just run OLS regressions.

It is with different degrees of ease, though, reflecting the purpose of the packages. lm is, of course, for all sorts of regressions, while the other two explicitly have time series regressions in mind, and vars even multivariate ones.

Here is an example.

library(dynlm)
library(vars)
x <- ts(rnorm(100)) # ts is relevant for dynlm, see discussion in comments below!
y <- ts(rnorm(100))
at a glance
all.equal(c(coef(dynlm(x ~ L(x, 1:3) + L(y, 1:3))), coef(dynlm(y ~ L(x, 1:3) + L(y, 1:3)))),
          c(coef(VAR(cbind(x,y), p = 3, type = "const"))$x[c(7,1,3,5,2,4,6),1], coef(VAR(cbind(x,y), p = 3, type = "const"))$y[c(7,1,3,5,2,4,6),1]),
          c(coef(lm(x[4:100]~x[3:99]+x[2:98]+x[1:97]+y[3:99]+y[2:98]+y[1:97])), coef(lm(y[4:100]~x[3:99]+x[2:98]+x[1:97]+y[3:99]+y[2:98]+y[1:97]))),
          check.attributes=F)
dynlm(x ~ L(x, 1:3) + L(y, 1:3))
dynlm(y ~ L(x, 1:3) + L(y, 1:3))
VAR(cbind(x,y), p = 3, type = "const")
lm(x[4:100]~x[3:99]+x[2:98]+x[1:97]+y[3:99]+y[2:98]+y[1:97])
lm(y[4:100]~x[3:99]+x[2:98]+x[1:97]+y[3:99]+y[2:98]+y[1:97])

Output:

> dynlm(x ~ L(x, 1:3) + L(y, 1:3))
Time series regression with "ts" data:
Start = 4, End = 100
Call:
dynlm(formula = x ~ L(x, 1:3) + L(y, 1:3))
Coefficients:
(Intercept)   L(x, 1:3)1   L(x, 1:3)2   L(x, 1:3)3   L(y, 1:3)1   L(y, 1:3)2   L(y, 1:3)3

   -0.14797     -0.13608      0.04310     -0.14119      0.03736     -0.20556     -0.07980
> dynlm(y ~ L(x, 1:3) + L(y, 1:3))
Time series regression with "ts" data:
Start = 4, End = 100
Call:
dynlm(formula = y ~ L(x, 1:3) + L(y, 1:3))
Coefficients:
(Intercept)   L(x, 1:3)1   L(x, 1:3)2   L(x, 1:3)3   L(y, 1:3)1   L(y, 1:3)2   L(y, 1:3)3

   0.001093     0.008268     0.101429    -0.122984     0.039118     0.060185    -0.194614
> VAR(cbind(x,y), p = 3, type = "const")
VAR Estimation Results:
Estimated coefficients for equation x:
Call:
x = x.l1 + y.l1 + x.l2 + y.l2 + x.l3 + y.l3 + const
   x.l1        y.l1        x.l2        y.l2        x.l3        y.l3       const 

-0.13608446  0.03735653  0.04310129 -0.20555950 -0.14119156 -0.07980048 -0.14797419
Estimated coefficients for equation y:
Call:
y = x.l1 + y.l1 + x.l2 + y.l2 + x.l3 + y.l3 + const
    x.l1         y.l1         x.l2         y.l2         x.l3         y.l3        const 

0.008267836  0.039117666  0.101428691  0.060184617 -0.122984226 -0.194613595  0.001093310
> lm(x[4:100]~x[3:99]+x[2:98]+x[1:97]+y[3:99]+y[2:98]+y[1:97])
Call:
lm(formula = x[4:100] ~ x[3:99] + x[2:98] + x[1:97] + y[3:99] + 
    y[2:98] + y[1:97])
Coefficients:
(Intercept)      x[3:99]      x[2:98]      x[1:97]      y[3:99]      y[2:98]      y[1:97]

   -0.14797     -0.13608      0.04310     -0.14119      0.03736     -0.20556     -0.07980
> lm(y[4:100]~x[3:99]+x[2:98]+x[1:97]+y[3:99]+y[2:98]+y[1:97])
Call:
lm(formula = y[4:100] ~ x[3:99] + x[2:98] + x[1:97] + y[3:99] + 
    y[2:98] + y[1:97])
Coefficients:
(Intercept)      x[3:99]      x[2:98]      x[1:97]      y[3:99]      y[2:98]      y[1:97]

   0.001093     0.008268     0.101429    -0.122984     0.039118     0.060185    -0.194614

I added the data. You helped me with the lm() function and I now get the same results for VAR() and lm(), but not for dynlm()... — Anna, Mar 02 '21 at 10:07
It will be related to you not declaring the variables as ts objects. Something like this works for me: `library(vars) library(dynlm)
my_data <- read.table(file = "clipboard", sep = "\t", header=F, dec=",") example <- data.frame(my_data) example$Price <- ts(example$V1) example$Open_Interest_All <- ts(example$V2) example$V1 <- NULL example$V2 <- NULL

VARexample <- VAR(example, p=5, type="const") dynlmexample <- dynlm(example$Price~L(example$Price,1:5) + L(example$Open_Interest_All,1:5))` — Christoph Hanck, Mar 02 '21 at 10:26
Needed to create two separate variables ('x <- xts_to_ts(example$Price)' & 'y <- xts_to_ts(example$Open_Interest_All)' ) and then it worked and all three functions created the same coefficients. Interesting, that the function lm() doesn't know we have a ts when str(example) is a xts object. Thanks for the help! — Anna, Mar 02 '21 at 11:03
@ChristophHanck, this is off topic here, but I have been struggling with some time series questions that you might be able to answer. So if you find the time and interest, here is the last one, and some other ones are linked in it. Thank you! — Richard Hardy, Mar 04 '21 at 13:59

VAR() or dynlm() or lm()

1 Answers1

at a glance

VAR Estimation Results:

Estimated coefficients for equation x:

Estimated coefficients for equation y: