Greetings,
I am facing difficulty in determining what AR(p) model to specify for my regression. By trial and error depicted below, it seems to me that an AR(4) model should be specified.
For all it's worth, I attach my ACF and PACF graphs for residuals. 
Any help would be very much appreciated, thank you.
I am facing difficulty in determining what AR(p) model to specify for my regression. By trial and error depicted below, it seems to me that an AR(4) model should be specified.
Code:
. reg r L.r
Source | SS df MS Number of obs = 2,347
-------------+---------------------------------- F(1, 2345) = 854.20
Model | 215.345089 1 215.345089 Prob > F = 0.0000
Residual | 591.179315 2,345 .252102053 R-squared = 0.2670
-------------+---------------------------------- Adj R-squared = 0.2667
Total | 806.524404 2,346 .343787043 Root MSE = .5021
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .5165801 .017675 29.23 0.000 .48192 .5512403
|
_cons | .0002531 .0103641 0.02 0.981 -.0200706 .0205769
------------------------------------------------------------------------------
. actest, robust
Cumby-Huizinga test for autocorrelation
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 | 72.136 1 0.0000 | 1 | 72.136 1 0.0000
-----------------------------------------------------------------------------
Test allows predetermined regressors/instruments
Test robust to heteroskedasticity
. reg r L(1/2).r
Source | SS df MS Number of obs = 2,346
-------------+---------------------------------- F(2, 2343) = 502.98
Model | 242.009015 2 121.004507 Prob > F = 0.0000
Residual | 563.671128 2,343 .240576666 R-squared = 0.3004
-------------+---------------------------------- Adj R-squared = 0.2998
Total | 805.680142 2,345 .343573621 Root MSE = .49049
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .4050162 .0201763 20.07 0.000 .3654511 .4445814
L2. | .2148748 .0201672 10.65 0.000 .1753273 .2544222
|
_cons | .0004264 .0101266 0.04 0.966 -.0194316 .0202844
------------------------------------------------------------------------------
. actest, robust
Cumby-Huizinga test for autocorrelation
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 | 24.707 1 0.0000 | 1 | 24.707 1 0.0000
-----------------------------------------------------------------------------
Test allows predetermined regressors/instruments
Test robust to heteroskedasticity
. reg r L(1/3).r
Source | SS df MS Number of obs = 2,345
-------------+---------------------------------- F(3, 2341) = 350.83
Model | 249.790432 3 83.2634773 Prob > F = 0.0000
Residual | 555.593235 2,341 .237331583 R-squared = 0.3102
-------------+---------------------------------- Adj R-squared = 0.3093
Total | 805.383667 2,344 .343593715 Root MSE = .48717
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .3792806 .0205235 18.48 0.000 .3390345 .4195267
L2. | .166328 .0216949 7.67 0.000 .1237849 .2088712
L3. | .1196588 .0205112 5.83 0.000 .0794368 .1598807
|
_cons | .0004293 .0100602 0.04 0.966 -.0192986 .0201571
------------------------------------------------------------------------------
. actest, robust
Cumby-Huizinga test for autocorrelation
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 | 8.350 1 0.0039 | 1 | 8.350 1 0.0039
-----------------------------------------------------------------------------
Test allows predetermined regressors/instruments
Test robust to heteroskedasticity
. reg r L(1/4).r
Source | SS df MS Number of obs = 2,344
-------------+---------------------------------- F(4, 2339) = 268.14
Model | 253.178313 4 63.2945781 Prob > F = 0.0000
Residual | 552.116947 2,339 .236048289 R-squared = 0.3144
-------------+---------------------------------- Adj R-squared = 0.3132
Total | 805.29526 2,343 .343702629 Root MSE = .48585
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .3706284 .0206157 17.98 0.000 .3302014 .4110555
L2. | .1549074 .0219103 7.07 0.000 .1119418 .1978729
L3. | .0928425 .0219076 4.24 0.000 .0498822 .1358027
L4. | .0720645 .0206045 3.50 0.000 .0316596 .1124695
|
_cons | .0001068 .0100351 0.01 0.992 -.0195718 .0197855
------------------------------------------------------------------------------
. actest, robust
Cumby-Huizinga test for autocorrelation
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 | 1.225 1 0.2684 | 1 | 1.225 1 0.2684
-----------------------------------------------------------------------------
Test allows predetermined regressors/instruments
Test robust to heteroskedasticity
. **ACTEST COMMAND SUGGESTS AR(4)**
. reg r L(1/4).r
Source | SS df MS Number of obs = 2,344
-------------+---------------------------------- F(4, 2339) = 268.14
Model | 253.178313 4 63.2945781 Prob > F = 0.0000
Residual | 552.116947 2,339 .236048289 R-squared = 0.3144
-------------+---------------------------------- Adj R-squared = 0.3132
Total | 805.29526 2,343 .343702629 Root MSE = .48585
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .3706284 .0206157 17.98 0.000 .3302014 .4110555
L2. | .1549074 .0219103 7.07 0.000 .1119418 .1978729
L3. | .0928425 .0219076 4.24 0.000 .0498822 .1358027
L4. | .0720645 .0206045 3.50 0.000 .0316596 .1124695
|
_cons | .0001068 .0100351 0.01 0.992 -.0195718 .0197855
------------------------------------------------------------------------------
. estat bgodfrey
Breusch-Godfrey LM test for autocorrelation
---------------------------------------------------------------------------
lags(p) | chi2 df Prob > chi2
-------------+-------------------------------------------------------------
1 | 7.146 1 0.0075
---------------------------------------------------------------------------
H0: no serial correlation
. reg r L(1/5).r
Source | SS df MS Number of obs = 2,343
-------------+---------------------------------- F(5, 2337) = 217.60
Model | 253.895887 5 50.7791773 Prob > F = 0.0000
Residual | 545.359929 2,337 .233358977 R-squared = 0.3177
-------------+---------------------------------- Adj R-squared = 0.3162
Total | 799.255815 2,342 .34127063 Root MSE = .48307
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .3662664 .0205618 17.81 0.000 .3259452 .4065876
L2. | .1551372 .0218684 7.09 0.000 .1122537 .1980207
L3. | .0937314 .022019 4.26 0.000 .0505525 .1369103
L4. | .0703822 .0218659 3.22 0.001 .0275036 .1132607
L5. | .0109803 .0205456 0.53 0.593 -.0293091 .0512698
|
_cons | -.0010002 .0099799 -0.10 0.920 -.0205707 .0185702
------------------------------------------------------------------------------
. estat bgodfrey
Breusch-Godfrey LM test for autocorrelation
---------------------------------------------------------------------------
lags(p) | chi2 df Prob > chi2
-------------+-------------------------------------------------------------
1 | 22.015 1 0.0000
---------------------------------------------------------------------------
H0: no serial correlation
. reg r L(1/6).r
Source | SS df MS Number of obs = 2,342
-------------+---------------------------------- F(6, 2335) = 181.23
Model | 251.154059 6 41.8590099 Prob > F = 0.0000
Residual | 539.330146 2,335 .230976508 R-squared = 0.3177
-------------+---------------------------------- Adj R-squared = 0.3160
Total | 790.484206 2,341 .33766946 Root MSE = .4806
------------------------------------------------------------------------------
r | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
r |
L1. | .3555388 .0205829 17.27 0.000 .3151761 .3959014
L2. | .1525293 .0218011 7.00 0.000 .1097778 .1952809
L3. | .0918417 .0219918 4.18 0.000 .0487162 .1349672
L4. | .0658227 .0219911 2.99 0.003 .0226985 .1089468
L5. | -.00477 .0218076 -0.22 0.827 -.0475342 .0379943
L6. | .0498962 .0204418 2.44 0.015 .0098103 .0899821
|
_cons | -.0019319 .009931 -0.19 0.846 -.0214064 .0175426
------------------------------------------------------------------------------
. estat bgodfrey
Breusch-Godfrey LM test for autocorrelation
---------------------------------------------------------------------------
lags(p) | chi2 df Prob > chi2
-------------+-------------------------------------------------------------
1 | 2.459 1 0.1169
---------------------------------------------------------------------------
H0: no serial correlation
** B-G LM test suggests AR(6)**
Any help would be very much appreciated, thank you.
