Прогнозирование в индустрии гостеприимства и туризма

            Estimation      Validation

Statistic   Period          Period

--------------------------------------------

RMSE        1,72215                        

MAE         1,26657                        

MAPE        2,95827                        

ME          0,122105                       

MPE         0,182382                         
 

The StatAdvisor

---------------

   This procedure will forecast future values of Occupancy rate.  The

data cover 84 time periods.  Currently, a simple exponential smoothing

model has been selected.  This model assumes that the best forecast

for future data is given by an exponentially weighted average of all

previous data values.  Each value of Occupancy rate has been adjusted

in the following way before the model was fit:

(1) A multiplicative seasonal adjustment was applied. 
 

   The table also summarizes the performance of the currently selected

model in fitting the historical data.  It displays:

   (1) the root mean squared error (RMSE)

   (2) the mean absolute error (MAE)

   (3) the mean absolute percentage error (MAPE)

   (4) the mean error (ME)

   (5) the mean percentage error (MPE)

Each of the statistics is based on the one-ahead forecast errors,

which are the differences between the data value at time t and the

forecast of that value made at time t-1.  The first three statistics

measure the magnitude of the errors.  A better model will give a

smaller value.  The last two statistics measure bias.  A better model

will give a value close to 0.0.   
 
 

 

Model Comparison

----------------

Data variable: Occupancy rate

Number of observations = 84

Start index =  1.97          

Sampling interval = 1,0 month(s)

Length of seasonality = 12 

Models

------

(H) Simple exponential smoothing with alpha = 0,7043

(L) Winter's exp. smoothing with alpha = 0,3136, beta = 0,0876, gamma = 0,5632

(M) ARMA(0,0) SARMA(0,0)

(N) ARMA(1,0) SARMA(1,0)

(O) ARMA(2,1) SARMA(2,1)

(P) ARMA(3,2) SARMA(3,2)

(Q) ARMA(4,3) SARMA(4,3) 

Estimation Period

Model  RMSE         MAE          MAPE         ME           MPE          SBIC

-------------------------------------------------------------------------------------

(H)    1,72215      1,26657      2,95827      0,122105     0,182382     1,13989     

(L)   2,34026      1,76564      4,17822      -0,250179    -0,645721    1,85877     

(M)   7,92509      6,63095      16,508       3,38354E-16  -3,69663     4,19282     

(N)   2,34188      1,74024      4,05966      0,123703     0,0796252    1,86015     

(O)   1,86524      1,35401      3,16279      0,233571     0,512876     1,61601     

(P)   1,66846      1,20884      2,80188      0,189659     0,393969     1,60403     

(Q)   1,1915       0,738663     1,69042      0,17732      0,44224      1,14164       

Model  RMSE         RUNS  RUNM  AUTO  MEAN  VAR

-----------------------------------------------

(H)    1,72215       OK    OK    OK    OK   OK  

(L)    2,34026       OK    ***   OK    OK   OK  

(M)    7,92509       ***   ***   ***   OK   OK  

(N)    2,34188       OK    OK    *     OK   OK  

(O)    1,86524       OK    OK    OK    OK   OK  

(P)    1,66846       OK    OK    OK    OK   OK  

(Q)    1,1915        OK    OK    **    OK   ***   

Key:

RMSE = Root Mean Squared Error

RUNS = Test for excessive runs up and down

RUNM = Test for excessive runs above and below median

AUTO = Box-Pierce test for excessive autocorrelation

MEAN = Test for difference in mean 1st half to 2nd half

VAR = Test for difference in variance 1st half to 2nd half

OK = not significant (p >= 0.05)

* = marginally significant (0.01 < p <= 0.05)

** = significant (0.001 < p <= 0.01)

*** = highly significant (p <= 0.001) 
 
 

The StatAdvisor

---------------

   This table compares the results of fitting different models to the

data.  The model with the lowest value of the Schwarz Bayesian

Information Criterion (SBIC) is model H, which has been used to

generate the forecasts.   

   The table also summarizes the results of five tests run on the

residuals to determine whether each model is adequate for the data.

An OK means that the model passes the test.  One * means that it fails

at the 95% confidence level.  Two *'s means that it fails at the 99%

confidence level.  Three *'s means that it fails at the 99.9%

confidence level.  Note that the currently selected model, model H,

passes 5 tests.  Since no tests are statistically significant at the

95% or higher confidence level, the current model is probably adequate

for the data.   
 
 

 

Estimated Autocorrelations for residuals 

Data variable: Occupancy rate

Model: Simple exponential smoothing with alpha = 0,7043

                                              Lower 95,0%       Upper 95,0%      

Lag       Autocorrelation   Stnd. Error       Prob. Limit       Prob. Limit

----------------------------------------------------------------------------------

1         -0,013809         0,109109          -0,21385          0,21385          

2         0,0744767         0,10913           -0,213891         0,213891         

3         -0,106439         0,109733          -0,215073         0,215073         

4         -0,252986         0,110955          -0,217469         0,217469         

5         -0,0128943        0,117622          -0,230536         0,230536         

6         -0,0259049        0,117639          -0,230569         0,230569         

7         -0,118581         0,117707          -0,230702         0,230702         

8         -0,000901013      0,119121          -0,233472         0,233472         

9         0,0573048         0,119121          -0,233473         0,233473         

10        -0,0606539        0,119448          -0,234115         0,234115         

11        0,157264          0,119814          -0,234832         0,234832         

12        -0,148652         0,122247          -0,2396           0,2396           

13        -0,00520587       0,12438           -0,243782         0,243782         

14        0,0531173         0,124383          -0,243787         0,243787         

15        0,00111586        0,124653          -0,244315         0,244315         

16        -0,0774865        0,124653          -0,244316         0,244316         

17        -0,0974508        0,125225          -0,245437         0,245437         

18        -0,145287         0,126125          -0,2472           0,2472           

19        0,152848          0,128101          -0,251075         0,251075         

20        0,219246          0,130255          -0,255295         0,255295         

21        0,0747522         0,134576          -0,263765         0,263765         

22        -0,019244         0,13507           -0,264732         0,264732         

23        0,0333537         0,135102          -0,264796         0,264796         

24        -0,134053         0,1352            -0,264988         0,264988           
 

The StatAdvisor

---------------

   This table shows the estimated autocorrelations between the

residuals at various lags.  The lag k autocorrelation coefficient

measures the correlation between the residuals at time t and time t-k.

Also shown are 95,0% probability limits around 0.0.  If the

probability limits at a particular lag do not contain the estimated

coefficient, there is a statistically significant correlation at that

lag at the 95,0% confidence level.  In this case, one of the 24

autocorrelation coefficients is statistically significant at the 95,0%

confidence level, implying that the residuals may not be completely

random (white noise).  You can plot the autocorrelation coefficients

by selecting Residual Autocorrelation Function from the list of

Graphical Options. 
 
 

 

Periodogram for residuals 

Data variable: Occupancy rate

Model: Simple exponential smoothing with alpha = 0,7043

                                                Cumulative      Integrated     

Frequency       Period          Ordinate        Sum             Periodogram    

--------------------------------------------------------------------------------

0,0                             1,55789E-27     1,55789E-27     6,78803E-30    

0,0119048       84,0            1,68327         1,68327         0,00733436     

0,0238095       42,0            1,74214         3,42542         0,0149252      

0,0357143       28,0            2,86663         6,29204         0,0274157      

0,047619        21,0            3,59356         9,8856          0,0430735      

0,0595238       16,8            12,0593         21,9449         0,0956185      

0,0714286       14,0            1,8318          23,7767         0,1036         

0,0833333       12,0            0,120269        23,897          0,104124       

0,0952381       10,5            25,1207         49,0177         0,21358        

0,107143        9,33333         7,0743          56,092          0,244404       

0,119048        8,4             2,4575          58,5496         0,255112       

0,130952        7,63636         8,48899         67,0385         0,2921         

0,142857        7,0             6,1288          73,1673         0,318805       

0,154762        6,46154         16,4885         89,6559         0,390648       

0,166667        6,0             0,489193        90,145          0,39278        

0,178571        5,6             0,00375281      90,1488         0,392796       

0,190476        5,25            4,23671         94,3855         0,411257       

0,202381        4,94118         18,3285         112,714         0,491118       

0,214286        4,66667         1,24095         113,955         0,496525       

0,22619         4,42105         2,2119          116,167         0,506162       

0,238095        4,2             1,02668         117,194         0,510636       

0,25            4,0             0,387054        117,581         0,512322       

0,261905        3,81818         5,76044         123,341         0,537422       

0,27381         3,65217         0,928316        124,269         0,541467       

0,285714        3,5             1,55601         125,825         0,548246       

0,297619        3,36            0,819327        126,645         0,551816       

0,309524        3,23077         6,06532         132,71          0,578244       

0,321429        3,11111         0,0870613       132,797         0,578623       

0,333333        3,0             0,297391        133,094         0,579919       

0,345238        2,89655         2,28342         135,378         0,589869       

0,357143        2,8             23,8678         159,246         0,693865       

0,369048        2,70968         8,37424         167,62          0,730353       

0,380952        2,625           8,87059         176,49          0,769004       

0,392857        2,54545         3,71859         180,209         0,785207       

0,404762        2,47059         8,18305         188,392         0,820862       

0,416667        2,4             0,728399        189,121         0,824036       

0,428571        2,33333         7,76723         196,888         0,857879       

0,440476        2,27027         8,00581         204,894         0,892762