Obtaining a SE for the sum of predictions, following a regression model

[evank23]

Hi all

Is anyone familiar with a user-written package or a well documented approach to calculate a reliable confidence interval for a sum of predictions?
Imagine a time series (say monthly) and predictions for a few months. The predict command will provide out of sample predictions for these months and SEs.
Is there a reliable way to combine them into an estimate? Adding up the SEs from predict (assuming zero covariances)? I've tried bootstrapping but because it is a time series it gets messsy and again not supported as standard by Stata commnands (Block bootstrap etc). I tried margins and then mutliplying the estimate by the number of months, and doing the same for the SEs, as I saw in another thread here, but I am not convinced this is entirely appropriate. I contacted Stata but there was no official suggestion - I was advised to use simulate. But surely there must be a straightforward parametric way to obtain the confidence interval for the quantity of interest!

Best

Evan

[Andrew Musau]

Consider using margins and lincom. You may hit limits on the length of the expression, so check if xlincom from SSC by Wouter Wakker allows a lengthier expression. I seem to recall something to that effect.

webuse grunfeld, clear
keep if company<=5
regress invest mvalue kstock
margins, expression(predict(xb)) over(company year) post
local coefs
forval company= 1/5{
    forval year= 1935/1954{
        local coefs "`coefs' `company'.company#`year'.year +"
    }
}
local coefs `coefs'0
lincom `coefs'

Res.:

. lincom `coefs'

 ( 1)  1bn.company#1935bn.year + 1bn.company#1936.year + 1bn.company#1937.year +
       1bn.company#1938.year + 1bn.company#1939.year + 1bn.company#1940.year +
       1bn.company#1941.year + 1bn.company#1942.year + 1bn.company#1943.year +
       1bn.company#1944.year + 1bn.company#1945.year + 1bn.company#1946.year +
       1bn.company#1947.year + 1bn.company#1948.year + 1bn.company#1949.year +
       1bn.company#1950.year + 1bn.company#1951.year + 1bn.company#1952.year +
       1bn.company#1953.year + 1bn.company#1954.year + 2.company#1935bn.year + 2.company#1936.year
       + 2.company#1937.year + 2.company#1938.year + 2.company#1939.year + 2.company#1940.year +
       2.company#1941.year + 2.company#1942.year + 2.company#1943.year + 2.company#1944.year +
       2.company#1945.year + 2.company#1946.year + 2.company#1947.year + 2.company#1948.year +
       2.company#1949.year + 2.company#1950.year + 2.company#1951.year + 2.company#1952.year +
       2.company#1953.year + 2.company#1954.year + 3.company#1935bn.year + 3.company#1936.year +
       3.company#1937.year + 3.company#1938.year + 3.company#1939.year + 3.company#1940.year +
       3.company#1941.year + 3.company#1942.year + 3.company#1943.year + 3.company#1944.year +
       3.company#1945.year + 3.company#1946.year + 3.company#1947.year + 3.company#1948.year +
       3.company#1949.year + 3.company#1950.year + 3.company#1951.year + 3.company#1952.year +
       3.company#1953.year + 3.company#1954.year + 4.company#1935bn.year + 4.company#1936.year +
       4.company#1937.year + 4.company#1938.year + 4.company#1939.year + 4.company#1940.year +
       4.company#1941.year + 4.company#1942.year + 4.company#1943.year + 4.company#1944.year +
       4.company#1945.year + 4.company#1946.year + 4.company#1947.year + 4.company#1948.year +
       4.company#1949.year + 4.company#1950.year + 4.company#1951.year + 4.company#1952.year +
       4.company#1953.year + 4.company#1954.year + 5.company#1935bn.year + 5.company#1936.year +
       5.company#1937.year + 5.company#1938.year + 5.company#1939.year + 5.company#1940.year +
       5.company#1941.year + 5.company#1942.year + 5.company#1943.year + 5.company#1944.year +
       5.company#1945.year + 5.company#1946.year + 5.company#1947.year + 5.company#1948.year +
       5.company#1949.year + 5.company#1950.year + 5.company#1951.year + 5.company#1952.year +
       5.company#1953.year + 5.company#1954.year = 0

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   25374.22   1309.402    19.38   0.000     22775.42    27973.02
------------------------------------------------------------------------------




. margins,  expression(predict(xb)) over(company year) post

Predictive margins                              Number of obs     =        100
Model VCE    : OLS

Expression   : Linear prediction, predict(xb)
over         : company year

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
company#year |
     1 1935  |   301.7139    26.0024    11.60   0.000     250.1063    353.3214
     1 1936  |   501.9952   36.55419    13.73   0.000     429.4452    574.5451
     1 1937  |   614.6596   40.32774    15.24   0.000     534.6202     694.699
     1 1938  |   320.7424   18.79546    17.06   0.000     283.4386    358.0462
     1 1939  |   499.3968   30.15797    16.56   0.000     439.5416    559.2521
     1 1940  |   539.5384   32.85264    16.42   0.000      474.335    604.7418
     1 1941  |   540.8703   31.11196    17.38   0.000     479.1217    602.6189
     1 1942  |    398.501   19.91162    20.01   0.000      358.982    438.0201
     1 1943  |   484.2307   26.80819    18.06   0.000     431.0239    537.4376
     1 1944  |   506.7638   30.74471    16.48   0.000     445.7441    567.7835
     1 1945  |   577.6948   33.40658    17.29   0.000      511.392    643.9976
     1 1946  |   619.9897   31.73589    19.54   0.000     557.0027    682.9766
     1 1947  |   549.3628   21.41554    25.65   0.000     506.8589    591.8668
     1 1948  |    558.439   23.80148    23.46   0.000     511.1997    605.6784
     1 1949  |   636.2603    27.3973    23.22   0.000     581.8843    690.6364
     1 1950  |   663.0578   29.60409    22.40   0.000     604.3019    721.8137
     1 1951  |   818.5404   35.96751    22.76   0.000     747.1548     889.926
     1 1952  |   886.5679   41.87612    21.17   0.000     803.4554    969.6804
     1 1953  |   1131.472   55.59411    20.35   0.000     1021.133     1241.81
     1 1954  |   1169.871   67.70605    17.28   0.000     1035.493    1304.249
     2 1935  |   111.5453   17.82875     6.26   0.000     76.16012    146.9304
     2 1936  |   163.3676   18.54704     8.81   0.000     126.5569    200.1783
     2 1937  |   283.6505   20.32358    13.96   0.000     243.3139    323.9872
     2 1938  |   216.5351   14.00041    15.47   0.000     188.7481     244.322
     2 1939  |   248.4052   13.58933    18.28   0.000     221.4341    275.3762
     2 1940  |   262.4892   15.03627    17.46   0.000     232.6464    292.3321
     2 1941  |   285.3702   15.60736    18.28   0.000     254.3939    316.3465
     2 1942  |   269.8401   14.24684    18.94   0.000     241.5641    298.1162
     2 1943  |   248.9021   13.75448    18.10   0.000     221.6033    276.2009
     2 1944  |   222.8037   13.76931    16.18   0.000     195.4754     250.132
     2 1945  |    210.355   14.81621    14.20   0.000     180.9489    239.7611
     2 1946  |    215.289   17.15355    12.55   0.000     181.2439     249.334
     2 1947  |    217.099    13.9326    15.58   0.000     189.4466    244.7513
     2 1948  |   207.6559   13.45162    15.44   0.000     180.9581    234.3536
     2 1949  |   223.8718   13.20715    16.95   0.000     197.6592    250.0843
     2 1950  |   226.8219   13.18385    17.20   0.000     200.6556    252.9882
     2 1951  |   295.2902    14.1378    20.89   0.000     267.2306    323.3498
     2 1952  |    306.068   13.42988    22.79   0.000     279.4134    332.7225
     2 1953  |   336.9083   15.63254    21.55   0.000      305.882    367.9346
     2 1954  |   358.7043   16.56908    21.65   0.000     325.8192    391.5893
     3 1935  |   100.1141   16.89354     5.93   0.000     66.58513    133.6431
     3 1936  |   201.9094   17.69742    11.41   0.000      166.785    237.0339
     3 1937  |   298.6663   21.06466    14.18   0.000     256.8588    340.4738
     3 1938  |   218.0256   16.49519    13.22   0.000     185.2872     250.764
     3 1939  |   247.8733   16.89876    14.67   0.000      214.334    281.4127
     3 1940  |   236.7779   16.11495    14.69   0.000     204.7942    268.7616
     3 1941  |   210.2691   14.66157    14.34   0.000       181.17    239.3683
     3 1942  |   198.2802   13.62474    14.55   0.000     171.2389    225.3216
     3 1943  |   225.6288    13.3383    16.92   0.000      199.156    252.1017
     3 1944  |   218.6211    13.3312    16.40   0.000     192.1624    245.0799
     3 1945  |    256.144   13.61018    18.82   0.000     229.1316    283.1565
     3 1946  |   286.6734   13.84702    20.70   0.000     259.1909    314.1559
     3 1947  |   249.6589   13.57476    18.39   0.000     222.7168    276.6011
     3 1948  |   265.7782   14.89358    17.85   0.000     236.2186    295.3379
     3 1949  |   264.5463   17.06143    15.51   0.000      230.684    298.4085
     3 1950  |   293.1744   17.10724    17.14   0.000     259.2212    327.1275
     3 1951  |   324.0456   17.10084    18.95   0.000     290.1051     357.986
     3 1952  |   368.9295   18.01027    20.48   0.000     333.1841    404.6749
     3 1953  |   422.5318   19.73504    21.41   0.000     383.3632    461.7004
     3 1954  |   491.2446   22.22106    22.11   0.000      447.142    535.3473
     4 1935  |  -11.47091   20.42346    -0.56   0.576    -52.00582      29.064
     4 1936  |   38.23102   19.28012     1.98   0.050    -.0346735    76.49672
     4 1937  |   49.97465   18.65386     2.68   0.009     12.95189     86.9974
     4 1938  |    1.53771   19.63789     0.08   0.938    -37.43806    40.51348
     4 1939  |   33.38164   18.57574     1.80   0.075    -3.486067    70.24934
     4 1940  |   39.79657   18.38153     2.17   0.033     3.314314    76.27882
     4 1941  |   31.90168   18.50465     1.72   0.088    -4.824924    68.62827
     4 1942  |   3.366881   19.45023     0.17   0.863    -35.23643     41.9702
     4 1943  |   23.28652   18.82851     1.24   0.219    -14.08287     60.6559
     4 1944  |   34.62179   18.58744     1.86   0.066    -2.269132     71.5127
     4 1945  |   50.63718   18.31522     2.76   0.007     14.28653    86.98783
     4 1946  |   63.99668   17.62137     3.63   0.000     29.02315    98.97022
     4 1947  |   29.79059   18.40189     1.62   0.109    -6.732066    66.31325
     4 1948  |   46.91865   17.77971     2.64   0.010     11.63085    82.20645
     4 1949  |   44.10668   17.71581     2.49   0.014     8.945699    79.26766
     4 1950  |   60.38167   17.11008     3.53   0.001      26.4229    94.34045
     4 1951  |   84.39714   16.25557     5.19   0.000     52.13433    116.6599
     4 1952  |   97.02453   16.28807     5.96   0.000     64.69722    129.3518
     4 1953  |   143.7699   15.04322     9.56   0.000     113.9132    173.6265
     4 1954  |   126.0859    17.1877     7.34   0.000     91.97305    160.1987
     5 1935  |   2.052923   19.75366     0.10   0.917    -37.15263    41.25848
     5 1936  |   8.595707   19.62734     0.44   0.662    -30.35913    47.55055
     5 1937  |    19.7639   19.43182     1.02   0.312    -18.80288    58.33067
     5 1938  |   29.76229   19.80235     1.50   0.136    -9.539898    69.06448
     5 1939  |   41.92543   19.73788     2.12   0.036     2.751202    81.09965
     5 1940  |   46.58703   19.93646     2.34   0.022     7.018667    86.15539
     5 1941  |    54.3355   20.05177     2.71   0.008     14.53829    94.13272
     5 1942  |   63.27015   20.57191     3.08   0.003      22.4406    104.0997
     5 1943  |   63.70969    21.1127     3.02   0.003     21.80682    105.6126
     5 1944  |   79.16375    21.5054     3.68   0.000     36.48148     121.846
     5 1945  |   89.85068   21.81273     4.12   0.000     46.55845    133.1429
     5 1946  |   101.0855   22.35491     4.52   0.000      56.7172    145.4538
     5 1947  |   111.1996   22.90225     4.86   0.000     65.74499    156.6542
     5 1948  |   115.6588   23.71883     4.88   0.000     68.58352    162.7341
     5 1949  |   126.4337   24.47515     5.17   0.000     77.85726    175.0101
     5 1950  |   134.6904   25.22209     5.34   0.000     84.63157    184.7493
     5 1951  |    150.558    25.1571     5.98   0.000     100.6281    200.4879
     5 1952  |   166.0039   26.15841     6.35   0.000     114.0867    217.9211
     5 1953  |   182.1644   27.16756     6.71   0.000     128.2443    236.0845
     5 1954  |   186.1397   28.28615     6.58   0.000     129.9996    242.2799
------------------------------------------------------------------------------