Прогнозирование в индустрии гостеприимства и туризма

0,452381        2,21053         7,67477         212,568         0,926203       

0,464286        2,15385         0,879875        213,448         0,930037       

0,47619         2,1             14,0194         227,468         0,991122       

0,488095        2,04878         2,03755         229,505         1,0            

0,5             2,0             0,0000212023    229,505         1,0              
 

The StatAdvisor

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

   This table shows the periodogram ordinates for the residuals.  It

is often used to identify cycles of fixed frequency in the data.  The

periodogram is constructed by fitting a series of sine functions at

each of 43 frequencies.  The ordinates are equal to the squared

amplitudes of the sine functions.  The periodogram can be thought of

as an analysis of variance by frequency, since the sum of the

ordinates equals the total corrected sum of squares in an ANOVA table.

You can plot the periodogram ordinates by selecting Periodogram from

the list of Graphical Options. 
 
 

 

Tests for Randomness of residuals 

Data variable: Occupancy rate

Model: Simple exponential smoothing with alpha = 0,7043

Runs above and below median

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

     Median = 0,194872

     Number of runs above and below median = 44

     Expected number of runs = 43,0

     Large sample test statistic z = 0,109772

     P-value = 0,912585 

Runs up and down

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

     Number of runs up and down = 60

     Expected number of runs = 55,6667

     Large sample test statistic z = 1,00285

     P-value = 0,315933 

Box-Pierce Test

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

     Test based on first 24 autocorrelations

     Large sample test statistic = 23,9981

     P-value = 0,403914 
 
 

The StatAdvisor

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

   Three tests have been run to determine whether or not the residuals

form a random sequence of numbers.  A sequence of random numbers is

often called white noise, since it contains equal contributions at

many frequencies.  The first test counts the number of times the

sequence was above or below the median.  The number of such runs

equals 44, as compared to an expected value of 43,0 if the sequence

were random.  Since the P-value for this test is greater than or equal

to 0.10, we cannot reject the hypothesis that the residuals are random

at the 90% or higher confidence level.  The second test counts the

number of times the sequence rose or fell.  The number of such runs

equals 60, as compared to an expected value of 55,6667 if the sequence

were random.  Since the P-value for this test is greater than or equal

to 0.10, we cannot reject the hypothesis that the series is random at

the 90% or higher confidence level.  The third test is based on the

sum of squares of the first 24 autocorrelation coefficients.  Since

the P-value for this test is greater than or equal to 0.10, we cannot

reject the hypothesis that the series is random at the 90% or higher

confidence level.   
 
 

 
 

Forecasting - Occupancy rate 

Analysis Summary 

Data variable: Occupancy rate 

Number of observations = 84

Start index =  1.97          

Sampling interval = 1,0 month(s)

Length of seasonality = 12 

Forecast Summary

---------------- 

Forecast model selected: ARIMA(3,0,2)x(3,0,2)12 with constant

Number of forecasts generated: 24

Number of periods withheld for validation: 0 

            Estimation      Validation

Statistic   Period          Period

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

RMSE        1,66846                        

MAE         1,20884                        

MAPE        2,80188                        

ME          0,189659                       

MPE         0,393969                         

                           ARIMA Model Summary

Parameter           Estimate        Stnd. Error     t               P-value

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

AR(1)               -0,181615       0,135409        -1,34123        0,184004

AR(2)               0,0152056       0,139689        0,108854        0,913617

AR(3)               0,550154        0,118119        4,65762         0,000014

MA(1)               -0,811644       0,0938311       -8,65006        0,000000

MA(2)               -0,822767       0,0924359       -8,90095        0,000000

SAR(1)              0,958282        0,188335        5,08817         0,000003

SAR(2)              -0,308114       0,181564        -1,697          0,093957

SAR(3)              0,339545        0,124208        2,73368         0,007854

SMA(1)              1,01597         0,169718        5,98626         0,000000

SMA(2)              -0,384302       0,130704        -2,94025        0,004390

Mean                57,5939         14,8685         3,87355         0,000232

Constant            0,365119       

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

Backforecasting: yes

Estimated white noise variance = 3,06678 with 73 degrees of freedom

Estimated white noise standard deviation = 1,75122

Number of iterations: 20 
 

The StatAdvisor

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

   This procedure will forecast future values of Occupancy rate.  The

data cover 84 time periods.  Currently, an autoregressive integrated

moving average (ARIMA) model has been selected.  This model assumes

that the best forecast for future data is given by a parametric model

relating the most recent data value to previous data values and

previous noise.  Each value of Occupancy rate has been adjusted in the

following way before the model was fit:

You can select a different forecasting model by pressing the alternate

mouse button and selecting Analysis Options. 

   The output summarizes the statistical significance of the terms in

the forecasting model.  Terms with P-values less than 0.05 are

statistically significantly different from zero at the 95% confidence

level.  The P-value for the AR(3) term is less than 0.05, so it is

significantly different from 0.0.  The P-value for the MA(2) term is

less than 0.05, so it is significantly different from 0.0.  The

P-value for the SAR(3) term is less than 0.05, so it is significantly

different from 0.0.  The P-value for the SMA(2) term is less than

0.05, so it is significantly different from 0.0.  The P-value for the

constant term is less than 0.05, so it is significantly different from

0.0.  The estimated standard deviation of the input white noise equals

1,75122.   

   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.   
 
 

 

Forecast Table for Occupancy rate 

Model: ARIMA(3,0,2)x(3,0,2)12 with constant

Period           Data                Forecast             Residual           

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

1.97            29,0                27,9184              1,08162            

2.97            36,0                36,1943              -0,194298          

3.97            38,0                37,357               0,643              

4.97            39,0                40,1401              -1,14011           

5.97            45,0                45,7092              -0,709246          

6.97            49,0                47,8382              1,1618             

7.97            40,0                43,3304              -3,33038           

8.97            55,0                51,8065              3,19348            

9.97            53,0                51,4202              1,57984            

10.97            47,0                46,2408              0,759243           

11.97            42,0                42,6701              -0,670127          

12.97            33,0                31,6039              1,3961             

1.98            31,0                31,1722              -0,172239          

2.98            39,0                38,2008              0,799226           

3.98            38,0                38,3821              -0,382069          

4.98            40,0                41,6581              -1,65811           

5.98            46,0                46,3473              -0,347341          

6.98            45,0                47,8291              -2,82908           

7.98            43,0                42,3448              0,655243           

8.98            52,0                51,2559              0,744128           

9.98            49,0                50,5836              -1,58361           

10.98            42,0                42,8515              -0,851506          

11.98            38,0                37,7039              0,296142           

12.98            29,0                29,2337              -0,233667          

1.99            30,0                28,601               1,39902            

2.99            35,0                35,948               -0,94805           

3.99            37,0                36,9308              0,0691882          

4.99            41,0                40,8847              0,115281           

5.99            47,0                46,6498              0,35016            

6.99            52,0                50,7403              1,25974            

7.99            48,0                46,3427              1,65727            

8.99            54,0                55,0925              -1,09248           

9.99            54,0                52,9861              1,01385            

10.99            46,0                44,7723              1,22768            

11.99            42,0                41,7381              0,261897           

12.99            30,0                32,8496              -2,84955           

1.00            28,0                28,7932              -0,793177          

2.00            36,0                35,028               0,972026           

3.00            37,0                37,5866              -0,586583          

4.00            45,0                40,4073              4,59272            

5.00            50,0                48,8499              1,1501             

6.00            52,0                53,8607              -1,86071           

7.00            46,0                45,1808              0,8192             

8.00            52,0                54,3569              -2,35686           

9.00            51,0                52,1869              -1,18694           

10.00            41,0                43,2492              -2,24918           

11.00            38,0                37,3167              0,683345