How to determine the number of lags in time series

[Adrian Cernescu]

Hi I am running the following model:

reg CSAD RtnMrktPort AbsRtnMrktPort SquDiffRtnMrktPort
predict residual, r

Below you can see the partial auto correlation of the residual for this model.

How would I test for how many lags of CSAD should I be using on the RHS of my regression in order to remove auto correlation from the model? I know that one may use the

varsoc

command, but I am unsure whether I need to use

varsoc CSAD

or

varsoc CSAD RtnMrktPort AbsRtnMrktPort SquDiffRtnMrktPort

to determine the number of lags.



Also, it will help me a lot if you could tell me other alternative tests I could run in Stata and how to read them.

Thank you.

[Oscar Ozfidan]

basically in your chart the gray area is a good indicator how many lags are significant. I think it is based on ljung box statistics if i remember correctly
so the first lag is sky high and must be included. after you include it relook at the PACF and is you see 2nd lag sticking out include that too. then redo PACF and check 3rd lag etc until the rest of the lags are about the same height. and check the significant of acoeffcients of lags. it would be ok to have no 2nd lag but include 4th. i.e. you would have 1st, 2nd, 4th, but not third if that turns out to be the case

[Sebastian Kripfganz]

What you probably want to estimate is an ARDL model. You can use our ardl command from SSC:

• ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

ssc describe ardl

The command obtains the optimal lag orders with the Akaike or Schwarz/Bayesian information criterion. For more information, please see my 2018 London Stata Conference presentation:

• Kripfganz, S. and D. C. Schneider (2018). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Proceedings of the 2018 London Stata Conference.

[Adrian Cernescu]

What you probably want to estimate is an ARDL model. You can use our ardl command from SSC:

• ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

ssc describe ardl

The command obtains the optimal lag orders with the Akaike or Schwarz/Bayesian information criterion. For more information, please see my 2018 London Stata Conference presentation:

• Kripfganz, S. and D. C. Schneider (2018). ardl: Estimating autoregressive distributed lag and equilibrium correction models. Proceedings of the 2018 London Stata Conference.

Hi, I have computed the results using the method you just mentioned and I also looked over the slides and added the options for 'aic' and 'bic' my dependent variable is 'CSAD' and the rest are the independent variables. I am unsure of how to interpret the results table. However, I used a max lag of 15 and I see that for CSAD the lags stop at 8, would this be infomative of the fact that I should be using 8 lags of my dependent variable to reduce autocorrelation. Could you please tell me if my interpretation is correct?

. ardl CSAD RtnMrktPort SquDiffRtnMrktPort AbsRtnMrktPort, aic bic maxlag(15) 
> matcrit(data)

ARDL(8,0,1,0) regression

Sample:        17 -      1152                   Number of obs     =      1,136
                                                F(  12,   1123)   =     229.23
                                                Prob > F          =     0.0000
                                                R-squared         =     0.7101
                                                Adj R-squared     =     0.7070
Log likelihood =  3683.1831                     Root MSE          =     0.0095

------------------------------------------------------------------------------
        CSAD |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        CSAD |
         L1. |   .3665477   .0257583    14.23   0.000     .3160078    .4170876
         L2. |   .0721833   .0258589     2.79   0.005     .0214462    .1229204
         L3. |    .062255   .0258824     2.41   0.016     .0114716    .1130384
         L4. |   .0217986   .0259814     0.84   0.402     -.029179    .0727761
         L5. |   .0816112   .0259944     3.14   0.002     .0306082    .1326142
         L6. |   .0088785   .0259251     0.34   0.732    -.0419885    .0597455
         L7. |   .0480239   .0257391     1.87   0.062    -.0024783    .0985261
         L8. |   .0883302    .024115     3.66   0.000     .0410147    .1356458
             |
 RtnMrktPort |   .0937725   .0065156    14.39   0.000     .0809884    .1065567
             |
SquDiffRtn~t |
         --. |   .2399237   .1010571     2.37   0.018     .0416418    .4382057
         L1. |  -.1841277    .056281    -3.27   0.001    -.2945554   -.0737001
             |
AbsRtnMrkt~t |   .1465559   .0172538     8.49   0.000     .1127026    .1804091
       _cons |   .0012414    .000633     1.96   0.050    -5.51e-07    .0024833
------------------------------------------------------------------------------

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |          N   ll(null)  ll(model)      df        AIC        BIC
-------------+---------------------------------------------------------------
           . |      1,136   2979.874   3683.183      13  -7340.366  -7274.908
-----------------------------------------------------------------------------

[Sebastian Kripfganz]

First of all, only use either aic or bic, not both options together. In your case, the bic option dominates the aic option. Thus, the optimal lag order is obtained with the Bayesian information criterion.

Yes, according to the BIC, 8 lags of the dependent variable (and 1 lag of of SquDiffRtnMrktPort) are deemed sufficient to account for the serial correlation.

[Adrian Cernescu]

First of all, only use either aic or bic, not both options together. In your case, the bic option dominates the aic option. Thus, the optimal lag order is obtained with the Bayesian information criterion.

Yes, according to the BIC, 8 lags of the dependent variable (and 1 lag of of SquDiffRtnMrktPort) are deemed sufficient to account for the serial correlation.

Thank you Sebastian, this has been very helpful, I appreciate the patience and help tremendously.