Tourism was maintained out of the great concerns of the authorities because suspect to only interest most rich people. The statistics of the OMT show with sufficiency the tourism place in the world trade. It seems one of the greatest creators of incomes by his capacity to generate employment.
The tourism is an important factor of the economy of Mali. This sector shows a strong seasonal behavior (the demand is concentrated in July, August, September months).
We want to come out again to rating of the seasonality some economic indicators to explain the demand addressed to the tourist industry of Mali: the price, the income, the supply.
As specification, I keep the structural model of basics with explanatory variables; the approach of Harkey (1990) to estimate the unknown parameters. The procedures based on the method of the maximum likelihood process of inference will be driven. From the diagnostic tests of AIC type procedure of selection and the estimated values of the variances of the different components permit us to identify these components nature.
For modeling the tourist demand we have considerate the transfer function model (MFT) and the specification 'Autoregressive with gradual lags (SARE). We use Malian and Europeans monthly tourism data from January 1991 to December 2003 .
MATERIALS AND METHODS
Specification of the tourist demand: Favorable economic conjuncture,
(yo) auspicious political climate, the political authorities good
Quantification of the tourist demand: Numbers of European tourist entries and how long they have stayed.
Determinants of the tourist demand: The demand (yo) is closely bound to the price (P), to the income (R) and especially to the tourist supply: (yo) (the natural wealth (climate), the capacity of the hotels).
Cost of the stay: Global recipe = Pricexquantities ≡ (recipe of the night)x(number of nights).
Function of the demand: yd = y (P, R, yo) with ∂y/∂P<0; ∂y/∂R>0; ∂y/∂y>0 indicates that the supply induce the demand.
The seasonal unit roots process test by Hylleberg et al. (1990) and its application to the Malian tourist series, one admits extensively that the seasonal shapes fluctuate weakly in the time (Ouerfell and Pichery, 1998).
Construction of the sample
||Short interval of time
||Important size of sample
||Representative ness of the sample.
The sample is provided by the tourism office (156 monthly observations concerning
the French tourists, Germans, English and Italian).
Structural Basic model
Chronological series yt; μt: trend; St: seasonal component
Xt: Vector of k variables; and δ: vector of the unknown parameters
associated to these variables.
Djt are seasonal indicator variables given by
Djt = 1 if t = j, j+s,j+2s,
Djt = 0 if t≠ j, j+s, j+2s,
Djt = -1 if t = s, 2s, 3s,
if t = s, 2s, 3s,
implies that or
if γt is the seasonal effect at time t:
ηt, ξt are independent and non correlated to the component εt.
Kalman filter iterative procedure permits to estimate the values of the unknown parameters.
Approach of Box and Jenkins (1976)
Specification 1: (Transfer Function Model with seasonal indicatory
retrace the dynamics of the model
the dynamics of the disruptions
The Djt is the 11 V.I.S. and λt represent the coefficient of the auto regressive lag associated to the transfer term of i. Li indicates the lag that precedes the impact of the exogenous value xi.
Specification 2: Detects the two aspects of the seasonality: stochastic
and deterministic aspect according to Franses (1991).
where yt and xt are series gotten after elimination of all unit roots to the existing frequencies. a(L) is an auto-regressive polynomial which general expression is given over and β' = (β1, β2, β3) the vector of the coefficients of the explanatory variables.
Specification 3: (Auto regressive distributed Lag Model)
We used (RATS 4.2 software)
Preliminary results and comments
Basis Structural Model estimation
Final equation: (STAMP, version 5.0 program: structural time analyzer
modeler and predictor) elaborated by Koop man
The criteria of selection permitted to keep the specification with a stochastic
trend and a seasonal deterministic component. It has been estimated while using
Kaman filter iterative procedure
μ is a random walk with μt = μt-1 + β
+ ηt and
is relative to the coefficient of month t. (the variables are expressed in logarithm).
||Basic Structural Model
A more refined analysis of these aspects detected for the different components (i.e., the stochastic aspect of the tendency and the seasonality deterministic aspect conduct to the following interpretations:
Knowing that the tendency represents some psychological factors, its stochastic feature implies a volatility of Malian products preferences.
With regard to the seasonality, the deterministic character explains an important part of the variance of the set. The detected deterministic aspect proves that the effort of the professionals of tourism in order to promote a better exhibit of the tourist activity on the year remains henceforth insufficient to the level of the hotel.
Results of the models 1, 2, 3: The evaluations are done while adopting strategies of different selections depending on if about the transfer function model (specification 1) of the specification 2, or of the specification 3.
Specification 1: The valued equation is the following:
is white noise
Specification 2: The valued equation is given by:
εt is a white noise
Specification 3: The equation 3 has the following
εt are a white noise
The variables are expressed in logarithm
|Shart equation 1
|Shart equation 2
|Shart equation 3
The gaps in brackets indicate that the explanatory variables coefficients are significant. The estimated values of the flexibility of the demand are coherent in sign and in module with the economic theory. These variables seem to explain an important part of the dependent variable, having captured the deterministic seasonality, which explains the weak value of the flexibility of the price presumably. This aspect of seasonality presence is distinctly shown by the significant coefficients of the seasonal indicatory variables even while considering the filtered series. These results confirm the mixed character of the seasonality that characterizes the tourist demand and bring up the advantage of the seasonal models esteemed on raw series as suggested by several authors.