Interpreting actest results

[Scott Rick]

Hi. I am using the Cumby-Huizinga method (actest) to test for autocorrelation in my data. Post this, I will be accounting for autocorrelation structure in my panel interrupted time series model (xtset).

Below are the results of the actest, where I have significant results at lag 7, 14, 21 and 28; but not at other points. I am unsure about how to account for this in the regression - would the lag be at 7/14/21/28 or not at all? Any help would be much appreciated.

actest resid, lags(30) robust

Cumby-Huizinga test for autocorrelation
  H0: disturbance is MA process up to order q
  HA: serial correlation present at specified lags >q
-----------------------------------------------------------------------------
  H0: q=0 (serially uncorrelated)        |  H0: q=specified lag-1
  HA: s.c. present at range specified    |  HA: s.c. present at lag specified
-----------------------------------------+-----------------------------------
    lags   |      chi2      df     p-val | lag |      chi2      df     p-val
-----------+-----------------------------+-----+-----------------------------
   1 -  1  |      0.265      1    0.6065 |   1 |      0.265      1    0.6065
   1 -  2  |      0.651      2    0.7221 |   2 |      0.385      1    0.5351
   1 -  3  |      1.548      3    0.6711 |   3 |      0.899      1    0.3431
   1 -  4  |      2.087      4    0.7197 |   4 |      0.604      1    0.4371
   1 -  5  |      2.369      5    0.7961 |   5 |      0.282      1    0.5957
   1 -  6  |      2.768      6    0.8373 |   6 |      0.397      1    0.5286
   1 -  7  |     18.624      7    0.0095 |   7 |     27.274      1    0.0000
   1 -  8  |     18.662      8    0.0168 |   8 |      0.305      1    0.5808
   1 -  9  |     18.669      9    0.0282 |   9 |      0.107      1    0.7433
   1 - 10  |     19.061      10   0.0395 |  10 |      0.320      1    0.5716
   1 - 11  |     19.868      11   0.0472 |  11 |      0.841      1    0.3592
   1 - 12  |     26.093      12   0.0104 |  12 |      1.558      1    0.2120
   1 - 13  |     26.383      13   0.0151 |  13 |      0.358      1    0.5494
   1 - 14  |     28.868      14   0.0109 |  14 |      8.916      1    0.0028
   1 - 15  |     28.965      15   0.0163 |  15 |      0.204      1    0.6514
   1 - 16  |     29.830      16   0.0189 |  16 |      0.954      1    0.3286
   1 - 17  |     30.854      17   0.0208 |  17 |      0.499      1    0.4801
   1 - 18  |     33.490      18   0.0146 |  18 |      0.841      1    0.3590
   1 - 19  |     33.503      19   0.0210 |  19 |      1.092      1    0.2959
   1 - 20  |     33.774      20   0.0277 |  20 |      0.446      1    0.5043
   1 - 21  |     40.950      21   0.0057 |  21 |      4.893      1    0.0270
   1 - 22  |     52.016      22   0.0003 |  22 |      2.005      1    0.1568
   1 - 23  |     52.445      23   0.0004 |  23 |      2.060      1    0.1513
   1 - 24  |     52.484      24   0.0007 |  24 |      1.253      1    0.2629
   1 - 25  |     52.487      25   0.0010 |  25 |      0.840      1    0.3595
   1 - 26  |     52.500      26   0.0016 |  26 |      0.003      1    0.9586
   1 - 27  |     53.325      27   0.0018 |  27 |      1.736      1    0.1876
   1 - 28  |     60.059      28   0.0004 |  28 |      3.903      1    0.0482
   1 - 29  |     60.947      29   0.0005 |  29 |      1.612      1    0.2042
   1 - 30  |     61.000      30   0.0007 |  30 |      1.100      1    0.2943
-----------------------------------------------------------------------------

[Nick Cox]

If the data are daily, then a weekly (7-day) cycle doesn't seem surprising -- but what do the data mean? Interpretation is often best when (social) scientific as well as statistical.

[Scott Rick]

Nick Cox The data refers to the number of teleconsultations done by doctors per day in a two year study period. So, each row/single observation refers to the number of teleconsults done by a particular doctor on a particular day, e.g. row 1 = # teleconsults done by Dr A on 01jan2022; row 2 = # consults by Dr B on 01jan2022; row 3 = # consults by Dr A on 03jan2022. I am attempting to assess the impact of certain interventions designed to increase the number of teleconsults using an interrupted time series single group study design

If I understand correctly, then including a lag of 7 makes sense? However, this is an unbalanced panel, i.e. not all doctors do teleconsults on all days of the study period. Is there still anyway for me to account for the autocorrelation then?

Thanks a lot!

[Nick Cox]

Being unbalanced doesn't, I think, affect my simple point. If consultations are more or less common on particular days, then there's a weekly cycle likely and it's secondary which particular doctors are or are not active if there is a dominant shared pattern.

That said, autocorrelation sounds inevitable and whether a test makes more sense than just a measurement is for panel data experts to comment.

[Scott Rick]

Nick Cox You are right, there is a weekly cycle, i.e. consultations are more or less common on particular days. To address this, I include a day of the week fixed effect. I assume this would address the weekly cycle, right?

However, within each doctors, autocorrelation seems inevitable and will need to be addressed. Does it then make sense to manually generate lagged variables at lag 7, 14, etc? Or just a lagged variable at lag 1?

[Nick Cox]

Again, you need advice from a panel data expert who knows about interrupted time series analysis. That's not me.