Actest for time series

[Bill Smith]

Using Stata 13.1 under Windows 7E. I'm looking at the actest module (see: http://econpapers.repec.org/software...de/s457668.htm) and trying to decipher the output. My understanding id that it is supposed to help understand the correlational structure of time series data, but the output is a confusing array of six hypotheses and two columns of results that has me wondering what to do. Here's some output from the example with the module:

Cumby-Huizinga test for autocorrelation (Breusch-Godfrey)
  H0: variable 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  |     15.242      1    0.0001 |   1 |     15.242      1    0.0001
   1 -  2  |     15.255      2    0.0005 |   2 |      3.300      1    0.0693
   1 -  3  |     15.325      3    0.0016 |   3 |      1.192      1    0.2749
   1 -  4  |     15.896      4    0.0032 |   4 |      0.000      1    0.9880
   1 -  5  |     16.057      5    0.0067 |   5 |      1.113      1    0.2914
   1 -  6  |     16.078      6    0.0133 |   6 |      2.051      1    0.1521
   1 -  7  |     16.087      7    0.0243 |   7 |      1.902      1    0.1679
   1 -  8  |     16.211      8    0.0395 |   8 |      1.579      1    0.2090
   1 -  9  |     16.932      9    0.0498 |   9 |      1.582      1    0.2085
   1 - 10  |     19.571      10   0.0336 |  10 |      2.411      1    0.1205
   1 - 11  |     20.095      11   0.0441 |  11 |      2.264      1    0.1324
   1 - 12  |     22.640      12   0.0309 |  12 |      1.619      1    0.2032
-----------------------------------------------------------------------------
  Test allows predetermined regressors/instruments
  Test requires conditional homoskedasticity

Baum and Schaffer provide extensive comment here: http://fmwww.bc.edu/EC-C/S2014/823/UKSUG2013.pdf. On p. 17 they state that examples from previous pages are univariate time series like the from the module example above. Judging by their comments on p. 15, are the tests on the left side cumulative? So the first row tests:

H₀: No correlation
H₁: cigsales and cigsales_t-1 are correlated

The next row tests:

H₀: No correlation
H₁: cigsales and cigsales_t-1, cigsales_t-2 are correlated

and so on, correct?

For the right side, it's not clear what the null hypothesis is. According to p. 15 in the presentation, it involves lag-1 as shown, but the meaning in terms of the hypothesis escapes me. The alternates appear to be testing cigsales_t-1, cigsales_t-2, etc. individually against this null, whatever it is. Furthermore, it's not entirely clear how to use both columns. P. 25 of the presentation offers advice that when the cumulative tests are significant, but the individual tests are not, one should be cautious about including too many lags. Anybody else have any other insights they can share about the interpretation and use of these output? Thx.

[Steven Kassakian]

Bump, same question

[Jesse Wursten]

I don't know if you still need an answer, but the way I understand it, you are correct about the left hand side. On the right, the H0 is that serial correlation only starts appearing from order(q). E.g. for q = 2, the H0 allows first order serial correlation (t, t-1). For q = 3, it allows up to 2nd order serial correlation (t, t-2).