پیش‎بینی ماهانۀ تقاضای گردشگر برای مجموعۀ تاریخی تخت جمشید

Introduction
For efficient organization and effective management of tourism and the pertinent activities,
modeling and forecasting the tourist destination areas are vital issues for good performance. It
helps make a better policy and plan for supplying tourist requirements. The number of tourists is
related to the market supply and demand. Different services are cooperated in supplying tourism
productions, such as reception, entertainment, residential, health and information services. On
the other hand, regarding demand, there are many factors affecting the tourists’ destination. For
example, economic-social conditions, language, culture and motivation that form the request
process tourists. Undoubtedly, demand prediction is a drastic factor especially for activities
related to tourism. In one hand, manager and planners relevant to tourism make attempt to fulfill
tourisms' demands. On the other hand, many of tourisms products like hotel’s rooms, airplane
seats, rent car, museum or cultural plans are not being reserved or stored naturally. A hotel room
that is not reserved for a night, an airplane seat that has no passenger and a restaurant table that
remains empty, are the benefits that have spoiled and they may not be reserved for the future.
Therefore, the tourists demand shall be predicted. Alongside the prediction process and tourism
entry demand model, the governments can organize their strategies better and prepare
appropriate infrastructure for serving the tourists; the private sectors could make appropriate 
marketing strategies for obtaining the maximum benefits from tourist entry increase, as well.
The forecasting of tourism demand is an essential tool for determining the required supply and
the appropriate distribution method of tourism services. When services (like tourism) achieve
desirable market, its current amount and the future potential volume shall be estimated
precisely. Market underestimation or overestimation makes the supplier lose the main part of
his/her interest. Hence, planning and development of tourism require identifying such these
kinds of motivations and demands. Accordingly, what is vitally important for the tourism
management is the amount of accuracy of prediction model that led to development and
diversity of tools and new methods in prediction.
Methodology
In this article, the plan is to forecast the number of tourist arrival for the historical - cultural site
of Perspolis in south Iran. The time series involves monthly data that were collected for both
domestic and international tourists. In order to testify the performance of forecasting method,
the collected data were divided into two sets, training (Farvardin 1376- Esfand 1387) and testing
(Farvardin1388- Esfand 1389). We used seasonal ARIMA model to detect the hidden structure
of data and finally forecast the arrivals for both data sets.
Results and Discussion
Based on the Box & Jenkins approach, both time series data were analyzed. In this approach,
stationarity of time series is a preliminary condition. Therefore, before any attempts, the time
series were made stationary by differencing.
The result of data analysis of Persepolis- domestic tourism
Since the number of visitors in Farvadin (April) of each year has considerable difference from
the other menthes, therefore, it is likely that the forecasting model would be seasonal. The great
amount of autocorrelation function in the lags 12, 24 & 36 confirms the existence of the
seasonal model. Since the seasonal data are not stationary, differencing can help to make a
steady time series. The results showed that, seasonal differencing in order 12, and then first
differencing make the time series in an acceptable stationary form. Thus, we could determine
the seasonal model of ARIMA (p,1,q) (P,1,Q)12 according to the ACF and PACF of the final
series. Exponential decay of PACF in some of the first lags (figure 3, right frame) and the fact
that autocorrelation amount in lag 1,r1,is significantly different from zero, shows no seasonal
moving average model of order 1, MA(1), i.e. p=0, q=1. It is also observed in autocorrelation
function (figure 3, left frame) that the amount of r24 is significant and this means a seasonal MA
(2) (P=0, Q=2). Therefore, the final model of ARIMA (0,1,1) (01,2)12 may be written as the
following:
1) 􁈺1 − 􀜤􁈻􁈺1 − 􀜤12􁈻􀜻􀯧 = 􁈺1 − 􀟠1􀜤􁈻 􁉀1 − 􀟙1􀜤12 − 􀟙􀬶􀜤24􁉁 􀝁􀯧 
2) 􀜻􀯧 − 􀜻􀯧􀬿1 − 􀜻􀯧􀬿24 + 􀜻􀯧􀬿25 = 􀝁􀯧 − 􀟠1􀝁􀯧􀬿1 − 􀟙1􀝁􀯧􀬿12 + 􀟙1􀟠1􀝁􀯧􀬿13 − 􀟙2􀝁􀯧􀬿24 + 􀟙2􀟠1􀝁􀯧􀬿25
The result of data analysis on Persepolis- international tourism
The plot of this time series implies that it is non-stationary. However, seasonality is not obvious
in the last example, but since the amount of r6 and r12 in autocorrelation diagram are located out
of the 95% confidence interval, a seasonal differencing with a six-month course is suggested.
The results show that the six-month seasonal differentiation series is not stationary, but if this
series be re-differencing (first order) we may observe an approximately stationary series.
In order to determine the order and the kind of series in non-seasonal part of ARIMA
(p,1,q)(P,1Q)6, we could consider the amount of autocorrelation as an evidence of damping sine
wave to zero and since the two first amount of partial autocorrelation are significant and
different from zero, the unseasonal autoregressive model, p=2, q=0, is suggested. In the
seasonal part, (P,1,Q), r6, r12,r18,…., are damping to zero and since the amount of partial
autocorrelation in lag 6 is significant, the seasonal AR model with Q=0 & P=1 seems to be more
appropriate. ARIMA (2,1,0)(1,1,0)6 is as the following.
3) 􁈺1 − 􀟚1􀜤 − 􀟚2􀜤2􁈻􁈺1 − 􀟜􀜤6􁈻􁈺1 − 􀜤􁈻􁈺1 − 􀜤6􁈻􀜻􀯧 = 􀝁􀯧
Evaluation of the suggested model was made by comparing real test data versus the
forecasted data. Figures 5 and 9 successfully showed that both real and forecasted values of
tourist arrival have the same variation in different months.
Conclusion
In this research, we conclude that, the tourist arrival time series can be stationary by two
differentiations (seasonal and first order differencing). In other words, the seasonal factor of this
series is the inseparable part of them, with this difference that, the seasonal course for domestic
and foreign visitors is 12 & 6 months, respectively. The results also show that the seasonal
ARIMA model is an appropriate estimation for forecasting the number of tourists.