title: How to sample a SARIMA model with given parameters in R
body: <p>I have a time series in R called jj.</p>
  
  <pre><code>    &gt; jj
       Jan       Feb       Mar       Apr       May       Jun       Jul
    1  2.5625072 2.6864995 2.7760495 2.6864995 2.6176149 2.8472302 2.8889086
    2  2.4733998 2.5853644 2.3614352 2.5548286 2.2392920 2.2698278 2.3614352
    3  2.5833333 1.9444444 2.0092593 2.2222222 2.2222222 2.0092593 2.5446500
    4  2.0092593 1.6666667 1.4351852 2.2222222 2.5000000 2.2962963 2.6260788
    5  2.8703704 2.2222222 1.7222222 1.6666667 1.6666667 1.7222222 2.2222222
    6  2.5259259 1.8333333 1.8944444 1.5277778 2.7500000 2.8897045 2.8703652
    7  2.8703704 1.9444444 2.0092593 1.9444444 1.9444444 2.5833333 2.7288827
    8  2.0092593 1.3888889 1.1481481 1.1111111 1.1111111 1.1481481 2.2222222
    9  1.3777778 1.1111111 0.9185185 0.8888889 1.1111111 1.3777778 0.6666667
    10 1.1481481 1.1111111 1.4351852 1.1111111 1.3888889 1.1481481 1.3888889
    11 1.7222222 1.3888889 1.1481481 1.3888889 1.3888889 1.4351852 2.2222222
    12 2.0092593 1.1111111 0.8611111 1.3888889 1.3888889 1.7222222 2.8286329
    13 1.7222222 2.9517940 2.9416154 2.6666667 2.9517940 2.9517940 2.9416154
    14 2.9517940 2.7777778 2.2962963 2.5000000 1.9444444 1.7222222 2.2222222
    15 2.2962963 1.9444444 2.0092593 2.2222222 1.9444444 2.2962963 2.9426333
    16 2.5833333 1.9444444 1.7222222 1.9444444 1.9444444 2.0092593 2.5000000
    17 1.7222222 1.3888889 1.4351852 1.3888889 1.1111111 1.1481481 1.9444444
    18 1.7222222 1.6666667 1.7222222 2.7777778 2.7777778 2.6861325 2.7604363
    19 2.5833333 1.9444444 1.7222222 2.8286329 2.5000000 2.5833333 2.9253296
    20 2.8703704 2.5000000 1.7222222 1.6666667 2.2222222 2.2962963 2.7237934
    21 2.9277778 2.8968296 2.9517940 2.9517940 2.7777778 2.9314368 2.9416154
    22 2.5833333 1.6666667 2.0092593 1.6666667 1.6666667 2.0092593 2.9049724
    23 2.0092593 1.3888889 2.8703652 2.7807935 2.7064897 2.9039546 2.9273654
    24 2.8703704 1.6666667 2.2962963 2.2222222 2.5000000 2.2962963 2.9517940
    25 2.5833333 1.3888889 2.0092593 2.2222222 1.9444444 2.5833333 2.8388115
    26 2.8703704 1.3888889 2.0092593 1.6666667 1.6666667 2.0092593 2.9517940
    27 2.2962963 1.3888889 2.6861325 1.9444444 1.9444444 2.5833333 2.9517940
    28 2.8703704 1.3888889 2.0092593 2.8286329 2.9202403 2.9517940 2.9517940
    29 2.8703704 1.6666667 1.7222222 1.3888889 1.6666667 1.4351852 2.9517940
    30 1.4351852 1.1111111 0.8611111 1.1111111 1.1111111 1.4351852 2.9517940
    31 1.4351852 1.1111111 0.8611111 1.1111111 1.3888889 1.4351852 2.7777778
    32 1.4351852 1.3888889 0.8611111 2.2222222 2.2222222 2.5833333 2.8479723
    33 2.2962963 1.3888889 2.0092593 2.5000000 2.2222222 2.8703704 2.8347401
    34 2.1513000 2.4921000 2.5453500 2.5027500 2.5347000 2.1300000 2.2684500
    35 1.7892000 2.3430000 2.3749500 2.2258500 2.5134000 1.8744000 2.1726000
    36 1.4590500 2.4921000 2.4814500 2.1619500 1.8424500 2.0341500 1.7253000
    37 1.8424500 1.5549000 1.0330500 0.9904500 0.9265500 0.5751000 0.7668000
    38 0.7348500 0.9904500 2.3749500 2.3004000 2.8222500 2.8648500 2.9500500
    39 2.3536500 2.1513000 2.2684500 1.5229500 0.8946000 0.7774500 1.1715000
    40 0.7029000 1.1608500 0.8839500 0.7881000 0.9478500 2.0448000 1.9276500
    41 1.0330500 1.6507500 2.0235000 2.6092500 2.4388500 2.5666500 2.8861500
    42 1.7679000 2.1300000 2.0661000 2.1832500 2.4175500 2.4388500 2.8435500
    43 1.3845000 2.0661000 2.8861500 2.9517940 2.6518500 2.5453500 2.7370500
    44 2.0874000 2.1087000 2.0661000 2.7051000 1.8531000 1.2673500 2.1619500
    45 1.7276389 2.1373656 1.9451389 1.9963710 1.9757930 1.6044444 1.3500000
    46 0.9780556 1.9094086 2.4434722 2.4868280 2.3836022 2.6620833 2.6272849
    47 2.2038889 2.3560484 2.1755556 2.1993280 1.9193548 2.2468056 2.5161290
    48 1.6276389 1.8481183 2.0204167 2.2172043 1.9631720 1.4890278 1.6551075
    49 0.9380556 1.2758065 2.3233333 2.4397849 2.4451613 2.4405556 2.5103495
    50 1.4444444 2.2043011 1.9166667 1.9086022 1.9489247 2.1111111 1.8682796
    51 2.0139072 2.2568109 2.4786743 1.9108121 2.2756334 1.4880000 1.6814920
       Aug       Sep       Oct       Nov       Dec
    1  2.8828206 2.9262278 2.9162662 2.9030509 2.7553841
    2  2.6973290 2.9262278 2.9162662 2.9030509 2.7553841
    3  2.2962963 2.9517940 2.9517940 2.9517940 2.7777778
    4  2.8416667 2.9517940 2.9517940 2.9517940 2.8703652
    5  2.8129630 2.9517940 2.9517940 2.9517940 2.7777778
    6  2.8642580 2.9517940 2.9517940 2.9517940 2.8622223
    7  2.8713831 2.9517940 2.9517940 2.9517940 2.7777778
    8  2.2962963 2.9517940 2.9517940 2.9517940 1.9444444
    9  1.3777778 1.3333333 2.0000000 1.9682540 1.5555556
    10 2.9436511 2.9517940 2.9517940 2.9517940 2.5000000
    11 2.9182046 2.9517940 2.7777778 2.7678571 1.6666667
    12 2.8754545 2.9517940 2.9517940 2.9517940 1.9444444
    13 2.9314368 2.9517940 2.9517940 2.9009010 2.8296508
    14 2.7879185 2.9517940 2.9517940 2.9517940 2.8286329
    15 2.9416154 2.9517940 2.9517940 2.9517940 2.9120975
    16 2.9039546 2.9517940 2.9517940 2.9216270 2.2222222
    17 2.9517940 2.9517940 2.9517940 2.9517940 2.2222222
    18 2.8703704 2.9517940 2.9517940 2.9517940 2.9314368
    19 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    20 2.9416154 2.9517940 2.9517940 2.9517940 2.9517940
    21 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    22 2.9517940 2.9517940 2.9517940 2.9517940 2.7777778
    23 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    24 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    25 2.9467047 2.9517940 2.9517940 2.9517940 2.9131153
    26 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    27 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    28 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    29 2.9517940 2.9517940 2.9517940 2.9517940 2.5000000
    30 2.9517940 2.9517940 2.9517940 2.9517940 2.5000000
    31 2.9517940 2.9517940 2.9517940 2.9517940 2.5000000
    32 2.9517940 2.9517940 2.9517940 2.9517940 2.7838471
    33 2.9517940 2.9517940 2.9500500 2.9500500 2.6518500
    34 2.8755000 2.9500500 2.9500500 2.7690000 2.2791000
    35 2.8009500 2.9500500 2.9500500 2.7477000 2.0022000
    36 2.9181000 2.9500500 2.4814500 2.0874000 1.7146500
    37 0.9372000 1.1608500 1.6827000 1.4590500 1.0543500
    38 2.8968000 2.8542000 2.8755000 2.8861500 2.5773000
    39 1.6294500 2.1406500 2.1406500 1.9170000 1.2034500
    40 2.7157500 2.9074500 2.9517940 2.0874000 1.1928000
    41 2.7903000 2.9074500 2.9074500 2.9074500 2.7370500
    42 2.9517940 2.9517940 2.9517940 2.9517940 2.3110500
    43 2.9517940 2.9517940 2.9517940 2.9517940 2.9517940
    44 2.9517940 2.9517940 2.9517940 2.7690000 1.8105000
    45 1.9430556 2.5471774 2.4963710 1.8916667 1.4965054
    46 2.6363889 2.6645161 2.6932796 2.6964286 2.6544355
    47 2.6268056 2.6650403 2.5970430 2.5544643 2.1424731
    48 2.2509722 2.2399194 2.2094086 1.8453869 1.3264785
    49 2.6687500 2.8084677 2.8376344 2.7081845 1.9912634
    50 2.4583333 2.8360215 2.8763441 2.6636905 2.0833333
    51 2.0464437 2.0434435 1.8343226 1.7039880 1.3593448
  </code></pre>
  
  <p>I have decided that the best SARIMA fit is SARIMA(1, 0, 0)x(0, 1, 2)12.  So I used (from astsa package) sarima(jj, 1, 0, 0, 0, 1, 2, 12) to fit the model.  I get the following results:</p>
  
  <pre><code>    Coefficients:
               ar1     sma1     sma2  constant
            0.7456  -0.7469  -0.1032    -6e-04
      s.e.  0.0272   0.0405   0.0429     8e-04
  
      sigma^2 estimated as 0.1201:  log likelihood = -223.17,  aic = 456.33
  
      $AIC
      [1] -1.106286
  
      $AICc
      [1] -1.102856
  
      $BIC
      [1] -2.077418
  </code></pre>
  
  <p>Now I would like to generate a new SARIMA(1, 0, 0)x(0, 1, 2)12 model, feed it the variance and parameters I just found, plus the first few values of my time series, then simulate say 500 values, in order to compare the simulated data to the real data in terms of mean, variance, skewness, etc.  Is there a function in R to do this?  Or am I going about things the wrong way?  I thought about using Arima from the forecast package to create the model, then feeding it new starting values (say the first 24 values of my original time series data), then having it predict future values.  But I am concerned this does not preserve my variance, and I want to do it as if I didn{t have all the data, just the 24 starting values and the parameters of the model.  Thanks!</p>