Сборник тезисов «Ипак ва зираворлар»

Mamatova N. 
 PhD at Bukhara state university 
PRACTICAL USE OF ADAPTIVE MODELS IN TOURISM 
 
The most important budget-forming branch of many states and regions 
(including the Autonomous Republic of Crimea) is tourism. Today, tourism uses 
about 7% of global capital, and tourism accounts for more than 10% of world trade in 
goods and services [1]. This is due to the fact that the last decades in the tourism 
business, there is an exponential growth of tourists. At the same time, the number of 
international tourists around the world increases by an average of 6% per year [2]. A 
similar pattern is also characteristic of many regions and territories. [3]. Simulation of 
the processes occurring in the tourism business becomes a necessity, as it contributes 
to the study of the factors of stability and growth, allows to carry out forecast 
estimates. The results of modeling are necessary for developing strategies, making 
business decisions and planning in the tourism sector at various levels. 
The main objects of modeling in tourism are the number of arriving tourists 
and indicators related to the seasonality of the leisure industry. Of these, the most 
important role is played by the number of tourists arriving to rest, because is a 
macroeconomic indicator on which all subsequent estimates are based. The purpose 
of this work is to analyze the main directions of modeling the number of arriving 
tourists, develop recommendations on the use of individual techniques. 
The most common in tourism were simple econometric models, the parameters 
of which are estimated using the method of least squares [4,5]. The traditional form 
of such models is different regression equations. Earlier, based on the analysis of the 
number of tourists arriving in different world regions, we have shown that such 
models provide acceptable accuracy and have good predictive qualities [6]. The 
number of tourists arriving is best described by second-order equations. It should be 
noted that the choice of the form of the regression equation is more important than 
the estimation of its parameters. Further research also established that regression 

---

361 
equations are convenient if one has to deal with data that is monotonically increasing 
or decreasing. If the data are characterized by the presence of peak values, then the 
use of regression equations is not so effective, because leads to errors of more than 
20% with short-term forecasts. A number of works [7] note that numerous data 
included in regression equations (prices, revenues, exchange rates, etc.) are 
dynamically changing non-stationary quantities, between which there is 
interdependence. Ignoring the problem of stationarity leads to the fact that parametric 
tests (in particular, t-tests and F-tests) become unreliable and can give erroneous 
results. But, despite the existing limitations, it is inadvisable to completely reject 
regression equations, since under certain circumstances they are the most simple, 
effective and convenient. 
An important issue of mathematical modeling in tourism is the issue of 
achieving equilibrium (saturation) in phenomena, since equilibrium means achieving 
stable prices at which supply and demand are balanced [8]. If we accept the 
hypothesis that equilibrium can be achieved, then we will have to look for models for 
the form of equations with an asymptotic approximation to a certain saturation line. 
However, over the past twenty years, tourism itself and prices (for air travel, hotels, 
etc.) have undergone a significant transformation, there is a steady growth trend, and 
therefore it is wrong to apply the term "saturation" to tourism. 
A promising trend in the modeling of tourism processes is the use of diffusion 
models. Today, diffusion models are used in such diverse areas as marketing, 
management, information technology technologies [9,10]. 
Let f (t) be a function of the probability of a tour being acquired by potential 
tourists at time t, and F (t) is a probability function that describes the share of 
potential tourists in the population at the same time. Then f (t) / [1-F (t)] is the 
conditional probability of arrival of a certain number of tourists at the specified 
moment of time t. It can be assumed that this conditional probability can be described 
by a linear dependence on F (t), i.e. f (t) / [1-F (t)] = a + b • F (t). If we denote by N * 
the total number of potential tourists among the population, then the number of 
tourists arriving at time t will be At = N * • f (t), whereas the number of potential 
tourists Nt = N * • F (t). Simple transformations lead to an expression of the form At 
= a (N * - Nt) + b • Nt (N * - Nt) / N *. Tourist statistics do not allow differentiating 
new tourists and re-arrivals. In the first approximation, it can be assumed that the 
number of repeat tourists is proportional to N *, i.e. Zt = d • Nt. Then the total 
number of tourists arrival 
Yt = At + Zt = a(N* - Nt) + b·Nt(N* - Nt)/N* + d·Nt (1) 
The next stage in the creation of the model is the inclusion of factor attributes 
(variables) in it. The simplest way is to describe N * as a function of factor attributes 
in the logarithmic form 
ln (N*t) = b0 + b1 ln (X1t) + b2 ln (X2t) + ... + bk ln (Xkt) (2) 
We can also write Yt as a quadratic function of Nt-1 
Yt = a·N + (b + d - a)Nt-1 – (b/N*)N2t-1 (3) 
Substituting (2) into (3), we obtain 

---

362 
(4) 
If we introduce the notation α = a • exp (b0), β = (b + d - a) and γ = b / exp 
(b0), we obtain the following final expression 
(5) 
It is impossible to estimate the parameters a, b, and d based on the values of α, 
β and γ because of the problem of determining b0. To evaluate the parameters of the 
model obtained, methods used in the case of regression equations are not applicable. 
there is a parametric nonlinearity. In this case, nonlinear methods should be used, 
which greatly complicates the work with the model. The main advantage of the 
model written in this form is its complete consistency in conditions of nonstationary 
data. 
An alternative form of models, which has recently attracted the attention of 
researchers, is the neural network [11]. This model is characterized by the use of a 
significant number of factor attributes, which are independent variables, and one 
target variable. It does not directly describe the form of the dependence of the target 
variable as a function of factor characteristics, but uses a significant number of 
intermediate variables, and often not one set of them can be used. The model 
performs an internal evaluation of the interdependence of variables. The form of 
interdependence can be both linear and non-linear. The experience of using neural 
networks for modeling processes in tourism does not yet allow us to state that such an 
approach can solve all problems. This is explained by the fact that this approach does 
not allow to completely abandon the regression equations that are necessary for 
evaluating the internal interrelation of variables, and the fact that a significant amount 
of retrospective tourism data is required, i.e. With a limited database, the model is not 
effective. 
A significant problem in using the models considered in practice is the 
selection of factor attributes. It is specific for each region and is determined by the 
surrounding areas, the level of development of the region itself, the level of service, 
etc. For example, for Australia [12], the dominant factors are real income level, 
openness to trade, import attractiveness, relative price level, recreation and 
entertainment and The set of factor attributes will always be characterized by 
incompleteness. Another major problem is the use in models of diverse natural 
indicators, the nature of the changes which are often unpredictable and which are 
interdependent. All this imposes serious restrictions on tourism models, in particular, 
their predictive quality may not be high enough. 
We have investigated the question of the possibility of applying adaptive 
statistical models to obtain estimates of the number of arriving tourists. For such 
models it is typical to use statistical data on the number of tourists arrived for some 
retrospective period. The advantage of this approach, from our point of view, is the 
fact that the statistics reflect the effect of absolutely all any significant factors. 
Moreover, these models have good predictive qualities, because they take into 
account the inertia and delay in the influence of factor characteristics. According to 

---

363 
the totality of features, adaptive statistical models can be assigned to dynamic 
forecast models. 
The initial analysis of the retrospective data on the number of tourists arriving 
in different regions shows that the nature of the data change corresponds to linearly 
additive types of trends. Therefore, Holt's model and Brown's adaptive smoothing 
model were chosen for the study [13]. 
In the linear additive model of the trend, it is assumed that the average value of 
the predicted parameter ft varies according to the linear time function ft = μ + λ • t + 
εt, where μ is the process average; λ - rate of growth / decrease; εt is a random error. 
Holt's method is based on an estimation of a parameter - to the extent of the degree of 
linear growth or the decrease of the indicator in time. In this case, the growth factor λ 
is estimated by the coefficient bt, which in turn is calculated as an exponentially 
weighted average of the differences between the current exponentially weighted 
averages of the process ut and their previous values ut-1. A characteristic feature of 
this method is the calculation of the current value of the exponentially weighted 
average ut includes the calculation of the previous growth rate bt-1, thus adapting to 
the previous value of the linear trend. The model can be written in the following form 
ut = A·dt + (1 - A)(ut-1 + bt-1), bt = B·(ut – ut-1) + (1 - B)·bt-1 (6) 
where A and B are coefficients that determine the nature of data smoothing, dt 
is the actual value of the data. 
The method of adaptive smoothing of Brown is based on the idea that it is 
possible to specify a parameter γ such that the weighted sum of deviations between 
the observed and expected values becomes minimal 
(7) 
Brown showed that ut = ut-1 + bt-1 + (1-γ2) • et, where et = dt - ft, ft is the 
predicted value, bt = bt-1 + (1- γ) 2 • et. The value of γ Brown recommends taking 
approximately equal to 0.7-0.8. 
The forecast in these models is determined by summing the estimate of the 
average current value of ut and the expected growth rate bt multiplied by the period 
of anticipation τ, that is, ft + τ = ut + bt • τ. 
To verify the predictive properties of the Holt model and the adaptive 
smoothing model, we performed a numerical comparative analysis. The WTO 
information on regional tourism development was used as a retrospective database 
[14]. Analyzed indicators for the arrival of tourists and on the receipt of funds from 
tourism for the main world regions (according to the classification of the WTO), 
namely: Europe, America, East Asia and the Pacific, the Middle East, Africa and 
South Asia. 
Data were collected for the period from 1985 to 1996, and based on them, 
predictions were made for 1997 and 1998 on previously obtained regression 
equations [6], as well as Holt and Brown models. The results of calculations were 
compared with the actual data for 1997 and 1998 [15], given in Table 1. 

---

364 
Preliminarily, the tuning of the models under investigation was performed, 
which consisted in selecting the smoothing coefficients A and B for the Holt model 
and the coefficient γ for the Brown model on the test problems. It was found that the 
most acceptable values are A = 0.3, B = 0.4 and γ = 0.7.