Using Stata, use the seasonal multiplicative Holt-Winters method to develop a forecast for the...

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Using Stata, use the seasonal multiplicative Holt-Winters method to develop a forecast for the non-seasonally adjusted monthly Total: New Privately Owned Housing Units Started (HOUSTNSA) for January through December 2013. Note: the data is scaled in thousands of units.
Task: Use the tssmooth command with the multiplicative seasonal Holt-Winters method to create a forecast of monthly housing starts for January through December 2013, a monthly seasonal index, the 95% forecast confidence interval, a graph of the results, goodness-of-fit measurements, and a chart of the forecast vs. actual values with upper and lower 95% forecast intervals, all using stata and stata graphs and output screenshots.
Directions: Using the multiplicative Holt-Winters method discussed in class and the non-seasonally adjusted monthly Total: New Privately Owned Housing Units Started (HOUSTNSA) series from the Federal Reserve FRED Economic Data and make a forecast for the next 12 months and provide the following information:
(1) The forecast for each of the 12 months from January 2013 through December 2013.
(2) Be sure to to address the following in your write-up:

The 95% upper and lower forecast confidence interval for each of the forecasted months.

The seasonal index for each of the 12 seasonal periods (months).

The mean squared error, root mean squared error (mean absolute deviation), and percentage error of the in-sample forecast error.

The number and percentage of forecast observations that fall outside of the upper and lower 95% forecast intervals.

A chart of the actual vs. forecasted results including the upper and lower 95% forecast intervals

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Using Stata, use the seasonal multiplicative Holt-Winters method to develop a forecast for the non-seasonally adjusted monthly Total: New Privately Owned Housing Units Started (HOUSTNSA) for January through December 2013. Note: the data is scaled in thousands of units. Task: Use the tssmooth command with the multiplicative seasonal Holt-Winters method to create a forecast of monthly housing starts for January through December 2013, a monthly seasonal index, the 95% forecast confidence interval, a graph of the results, goodness-of-fit measurements, and a chart of the forecast vs. actual values with upper and lower 95% forecast intervals, all using stata and stata graphs and output screenshots. Directions: Using the multiplicative Holt-Winters method discussed in class and the non-seasonally adjusted monthly Total: New Privately Owned Housing Units Started (HOUSTNSA) series from the Federal Reserve FRED Economic Data and make a forecast for the next 12 months and provide the following information: (1) The forecast for each of the 12 months from January 2013 through December 2013. (2) Be sure to to address the following in your write-up: The 95% upper and lower forecast confidence interval for each of the forecasted months. The seasonal index for each of the 12 seasonal periods (months). The mean squared error, root mean squared error (mean absolute deviation), and percentage error of the in-sample forecast error. The number and percentage of forecast observations that fall outside of the upper and lower 95% forecast intervals. A chart of the actual vs. forecasted results including the upper and lower 95% forecast intervals

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David · Accepted Answer

Table of Contents 
Preliminary Work ............................................................................................................................................... 1 
The Output: ........................................................................................................................................................ 2 
Appendix 1 ......................................................................................................................................................... 4 
Appendix2: ....................................................................................................................................................... 17
 

Preliminary Work 
First, we need to check for presence of seasonality in the data. A convinient way of doing so is to find the 
‘Spectral decmpostion’ of the series. We see 80 consecutive days as the periodicity in the given 
data(approximately, one divided by frequency of the longest spike).
Usefulness of the above: 
We get to know the approximate periodicity, or seasonality which is  80-90, interestingly, checking RMSE’s 
of Holt – Winters, would do the same thing but the tool above serves as a basis for using a seasonal model.
The Output: 
 t=75 t=78 t=80 t=82 
alpha 1 1 0.9692 0.9743 
beta 0 0 0 0 
gamma 0.0005 0.0005 1 1 
penalised sum-of-squared residuals 99927.93 86583.51 114895.5 148082.1 
 sum-of-squared residuals 99927.93 86583.51 114895.5 148082.1 
root mean squared error 15.88532 14.78666 17.0335 19.33765
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Frequency
Evaluated at the natural frequencies
'periodogram'
Where alpha is the ‘smoothing constant’, beta the ‘trend constant’, and gamma, ‘the seasonal constant’. 
On the plot below, we see our fits. The horizontal axis contains no of months from start data the 
forecasted values thus occur from point 397.
Percent of outlier forecasts =  6.06%
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no OF mONTHS FROM jAN01, 1982
houstna PO2
Upper CI Lower CI
Holt-Winters Multiplicative Forecast
     outlier         396    .0606061    .2389081          0          1
                                                                      
    Variable         Obs        Mean    Std. Dev.       Min        Max

Appendix 1 
List of seasonal forecasts. 
 
+-------------------------------------------------+ 
period   month        po2        ucl        lcl  
 
------------------------------------------------- 
 1 1       0   84.19238   113.2625   55.12222  
 2 1       0   86.65069   115.7208   57.58052  
 3 1       0   98.67916   127.7493     69.609  
 4 1       1   61.80844    90.8786   32.73827  
 5 1       1   110.6318   139.7019    81.5616  
 
 
------------------------------------------------- 
 6 1       1   106.9511   136.0213   77.88098  
 7 1       2   140.3481   169.4183   111.2779  
 8 1       2   65.66485   94.73501   36.59468  
 9 1       3   52.50322   81.57338   23.43305  
 10 1       3   131.9095   160.9797   102.8394  
 
 
------------------------------------------------- 
 11 1       4   127.5661   156.6362    98.4959  
 12 1       4   77.71767   106.7878   48.64751  
 13 1       5   102.4503   131.5205   73.38015  
 14 1       5    113.762   142.8321    84.6918  
 15 1       6   79.70708   108.7772   50.63692  
 
 
------------------------------------------------- 
 16 1       6   93.98825   123.0584   64.91809  
 17 1       7     107.99   137.0601    78.9198  
 18 1       7   107.4195   136.4896   78.34931  
 19 1       7   58.45941   87.52957   29.38925  
 20 1       8   39.17584     68.246   10.10568  
 
 
------------------------------------------------- 
 21 1       8   110.5678    139.638   81.49768  
 22 1       8    109.742   138.8121   80.67182  
 23 1       9   32.91262   61.98278   3.842458  
 24 1       9    96.3163   125.3865   67.24614  
 25 1       9   103.2312   132.3013     74.161  
 
 
------------------------------------------------- 
 26 1      10    102.603   131.6732   73.53284  
 27 1      10   88.20161   117.2718   59.13145  
 28 1      10   34.67025   63.74041   5.600087  
 29 1      11   37.35618   66.42634   8.286016  
 30 1      11    82.1524   111.2226   53.08224  
 
 
------------------------------------------------- 
 31 1      11   91.96389    121.034   62.89373  
 32 1      12   51.68585   80.75601   22.61569  
 33 1      12   60.25751   89.32767   31.18735  
 34 1      12   86.14713   115.2173   57.07697  
 35 2       0   71.03852   100.1087   41.96836  
 
 
------------------------------------------------- 
 36 2       0   84.78593   113.8561   55.71577  
 37 2       0   47.35707   76.42723   18.28691  
 38 2       1   72.74835   101.8185   43.67819  
 39 2       1   80.67303   109.7432   51.60287  
 40 2       1   90.69836   119.7685    61.6282  
 
 
------------------------------------------------- 
 41 2       2   73.53631   102.6065   44.46614  
 42 2       2   153.9202   182.9904     124.85  
 43 2       2   70.92025   99.99041   41.85009  
 44 2       3   71.46632   100.5365   42.39616  
 45 2       3   142.6417   171.7119   113.5715  
 
 
------------------------------------------------- 
 46 2       4   119.0085   148.0786    89.9383  
 47 2       4   50.18007   79.25023   21.10991  
 48 2       5   101.2701   130.3403   72.19997  
 49 2       5   120.2602   149.3304   91.19003  
 50 2       6   104.1375   133.2077   75.06738  
 
 
------------------------------------------------- 
 51 2       6   94.42115   123.4913   65.35099  
 52 2       7   81.08655   110.1567   52.01638  
 53 2       7   110.3299   139.4001   81.25974  
 54 2       8   60.76142   89.83158   31.69126  
 55 2       8   108.1014   137.1715   79.03121  
 
 
------------------------------------------------- 
 56 2       8   109.2448    138.315   80.17465  
 57 2       9   47.06644    76.1366   17.99628  
 58 2       9   106.5071   135.5772    77.4369  
 59 2       9   115.2835   144.3536    86.2133  
 60 2      10   102.1355   131.2057   73.06538  
 
 
-------------------------------------------------
61 2      10   38.95092   68.02109   9.880761  
 62 2      10    88.3746   117.4448   59.30444  
 63 2      11   117.5754   146.6456   88.50526  
 64 2      11   88.58399   117.6542   59.51383  
 65 2      11   41.91729   70.98745   12.84713  
 
 
------------------------------------------------- 
 66 2      12   89.82561   118.8958   60.75544  
 67 2      12   31.58798   60.65815    2.51782  
 68 2      12   90.41979     119.49   61.34963  
 69 3       0   108.9009   137.9711   79.83076  
 70 3       0   109.3552   138.4253   80.28502  
 
 
------------------------------------------------- 
 71 3       0   45.19092   74.26108   16.12076  
 72 3       1   94.02459   123.0947   64.95443  
 73 3       1   90.33701   119.4072   61.26684  
 74 3       1   59.10841   88.17857   30.03825  
 75 3       2   94.03553   123.1057   64.96537  
 
 
------------------------------------------------- 
 76 3       2   134.8445   163.9147   105.7744  
 77 3       2    109.208   138.2782   80.13786  
 78 3       3   78.08234   107.1525   49.01218  
 79 3       3   151.8805   180.9506   122.8103  
 80 3       3   83.63026   112.7004   54.56009  
 
 
------------------------------------------------- 
 81 3       4    155.414   184.4841   126.3438  
 82 3       4   82.13277   111.2029   53.06261  
 83 3       5   137.5537   166.6239   108.4836  
 84 3       5   64.31081   93.38097   35.24065  
 85 3       6   83.98737   113.0575    54.9172  
 
 
------------------------------------------------- 
 86 3       6   106.0254   135.0956   76.95524  
 87 3       7    94.1508    123.221   65.08064  
 88 3       7   132.1213   161.1914   103.0511  
 89 3       8    98.5415   127.6117   69.47134  
 90 3       8   118.2077   147.2779   89.13755  
 
 
------------------------------------------------- 
 91 3       9   135.1048    164.175   106.0346  
 92 3       9   116.0287   145.0989   86.95856  
 93 3       9   68.57684     97.647   39.50667  
 94 3      10   135.2715   164.3416   106.2013  
 95 3      10   131.5888   160.6589   102.5186  
 
 
------------------------------------------------- 
 96 3      10    61.0023   90.07246   31.93214  
 
97 3      11   118.4093   147.4794   89.33911  
 98 3      11   43.93303   73.

Using Stata, use the seasonal multiplicative Holt-Winters method to develop a forecast for the non-seasonally adjusted monthly Total: New Privately Owned Housing Units Started (HOUSTNSA) for January...

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