TV3, TV1, NTV7, and Astro Prima's Sarapan Dimana. Ba'Kelalan is a collection of nine small towns located in the northeast rural areas of Sarawak, specifically known as the Northern Highlands within Limbang Division. It is inhabited by the Lun Bawang community who are part of the Orang Ulu group.These small towns - Buduk Nur, Long Langai, Long Lemutut, Long Ritan, Long Rusu, Buduk Bui, Long Rangat,Buduk Aru,and Pa'Tawing- are located approximately 3000 feet above sea level and 4 kilometers from the border of East Kalimantan in Indonesia. The name Ba'Kelalan is derived from the Kelalan River and "Ba'" which means moist land in Lun Bawang language. Despite having a population of around 1500 inhabitants, this place is cherished by approximately 8000 individuals who have developed a strong attachment to it and frequently visit due to its cool mountain climate. With an average temperature of 24°C, the climate allows for the cultivation of temperate fruits such as apples,Citrus reticulata oranges,strawberries ,grapes,and vanilla. Ba'Kelalan has been promoted through various mass media platforms including TV3 ,TV1 ,NTV7,and Astro Prima's Sarapan Dimana. Additionally, Ba'kelan enjoys a refreshing mountain climate with an average temperature of 24 degrees Celsius that enables them to cultivate temperate fruits like apples, Citrus reticulata oranges, strawberries ,grapes and vanilla. Rice production and the collection of mountain salt are both significant industries in Ba'Kelalan. Moreover,the region has experienced an increase in tourism due to its 9-hole golf course and its proximity to Kayan Mentarang National Park (KMNP) in Krayan,East-Kaliamantan, Indonesia as well as Pulong Tau National Park (PTNP). Farming is the primary occupation for residents of Ba'Kelalan with paddy cultivation being particularly prominent.However,Ba'Kelalan is renowned as

the only place in Sarawak where apples can be grown effectively.The apples in Ba'Kelalan have become a symbol of the area and its Lun Bawang inhabitants. The Lun Bawang people's cultural practices, including their annual Apple Feast held every May, contribute to Ba'Kelalan's appeal among tourists. Other attractions in the area include Escaped of The Hearth of Borneo, 4WD adventures, and home stay programs. These events draw more tourists and ultimately boost the local population's income.

Forecasting involves predicting future events based on known past values of relevant variables (Makridakis et al., 1998). It entails analyzing current and historical data to determine future trends. Economists often use forecasting techniques to predict future economic trends. Univariate Modeling Techniques analyze data on a single variable at a time, such as Naive Models, Methods of Average, Exponential Smoothing Techniques, and the Box-Jenkins Methodology. Both Double Exponential Smoothing and Holt's Method belong to the Exponential Smoothing Techniques.

Tourism is vital for Malaysia's economic growth, with an increasing number of international tourist arrivals supporting political stability. The Malaysian government has implemented programs and packages to attract more international tourists. This section focuses on the demand for ecotourism in Ba'Kelalan, Sarawak.This study examines the volume, composition, and recent developments of tourist flows by analyzing tourist arrivals between 2000 and 2010. It investigates both international and local demand. The collected data reveals that the highest numbers of international tourists visiting Ba'Kelalan are from the United Kingdom, Indonesia, Brunei, Australia, and Hong Kong. Table 1 presents the tourist arrivals in Ba'Kelalan from 2000 to 2010.

Year

No.

Of Tourist

1999 210
2000 207
2001 217
2002 289
2003 153
2004 64
2005 210
2006 369
2007 800
2008 1650
2009 2150
2010 2750

Beginnings: Visitor Books of Ba'Kelalan and

Borneo Jungle Safari (BJS)

Table displays the arrival numbers of tourists in Ba'Kelalan from Year: 1999-2010. It is evident that the No.

count increased annually during this period. Specifically, there was a rise in tourist arrivals between Year: 2000-202, followed by a two-year decline in Year:*SARS epidemic**. This decline in tourist arrivals could be attributed to the SARS epidemic in *_^i.e.*If condition fulfilled*.

Literature Review

During the past three decades, numerous studies have been conducted by both tourism researchers and practitioners to forecast international tourism demand.The literature on modeling and predicting tourism demand is vast, with researchers employing various types of empirical analysis. While some use cross-sectional data, most utilize forecasting methods to analyze tourism demand. The rapid expansion of the global tourism industry has fueled the growing interest in studying tourism demand, especially as the economy becomes more stable. Over the past forty years, significant progress has been made in studying tourism demand, with diverse research interests, strong theoretical foundations, and advancements in research methodologies. Two main focuses of these studies are analyzing the effects of various factors and accurately predicting future demand. Time-series models are commonly used for this purpose – they explain a variable based on its past and random perturbations. It is crucial to explore historical trends and patterns like seasonality in time series data to forecast future demand effectively. These models are cost-effective as they only require historical observations of a variable. Tourism demand or visits can occur due to reasons such as vacations, business trips, visiting friends and relatives (VFR), conferences, or pilgrimages. In essence, according to Hong Kong Tourism Demand Forecasting System, tourism demand refers to the quantity of the

tourism product for a specific destination.
The text discusses the concept of tourism demand and factors that influence it. Tourism demand refers to the combination of goods and services that consumers are willing to pay for within a specific period, under certain conditions (e.g., month, quarter or year). Various factors impact the quantity of tourism demanded, including destination prices (including cost of living and travel expenses), availability of prices for competing destinations, consumer incomes, advertising expenditures, consumer preferences in their home countries, as well as other social cultural geographical political factors. Evaluating tourism demand is crucial in tourism research and has attracted attention from both scholars and industry professionals.

A study conducted by Li et al (2005) identified 420 published studies between 1960 and 2002 that focused on modeling and predicting tourism demand using qualitative and quantitative techniques for different destinations. The objective was to establish prediction rules to assist practitioners in selecting suitable techniques. However, previous attempts at forecasting tourism demand have not been successful. Witt and Song (2000) as well as Li et al.(2005) noted that the accuracy of prediction models varies based on factors such as data frequencies, destination-origin pairs, and prediction timeframes.The text discusses various articles that have reviewed tourism demand forecasting, such as those by Crouch (1994), Li et al.(2005), Lim (1997a, 1997b, and 1999), and Witt and Witt (1995). These reviews cover studies conducted from 1960 to 2000, with additional studies from 2000 to 2004 included in Li et al.'s review specifically focused on the econometric approach. In contrast to previous efforts, this paper aims to present demand modeling and prediction using univariate models like naive forecast, mean change model, exponential

smoothing, and Holt's Method. The objective is to find the most accurate model for predicting tourism demand by considering the model with the smallest RMSE. To assess the best theoretical model, various criteria such as ME, MAE, MPE, MSE, and RMSE must be considered when comparing results from each method. While ME and MPE are not commonly used as measures of prediction accuracy due to potential offsetting of large positive and negative mistakes, MAE, MAPE, MSE,and RMSE are preferred options for comparing prediction models in a given series. Typically,RMSE is focused on evaluating the accuracy of different calculation methods as it is easily interpretable and similar to standard deviation concept.Hence,it is one of the most commonly used measures of prediction accuracy.This section briefly explains the statistical techniques employed in analyzing data collected from Ba'Kelalan's Visitor Book and Borneo Jungle Safari.
The Univariate Modeling Technique was used to forecast future values of ecotourism demand based on past observations in the time series. This involved fitting a model to the collected information, which included data on tourist numbers visiting the survey country between 2000 and 2010. These data were crucial for determining an appropriate model for analysis purposes.

Time series analysis and forecasting models were used to predict the demand for ecotourism in Ba'Kelalan. Four types of forecasting models were employed: Naive with Trend Model, Average Change Model, Exponential Smoothing, and Holt's Method.

The Naive with Trend Model assumes that future forecasts can be set as the observed value in the most recent time period. It relies on the trend measurement represented by Yt/Yt-1; if Yt is greater than Yt-1, it indicates an upward trend and vice versa. The one

step ahead forecast is denoted as (1), where Yt represents the actual value at time T and Yt-1 represents the actual value in the preceding period.

This model is highly sensitive to changes in actual values, so any sharp increase or sudden drop will significantly impact the forecast. Additionally, using this model results in losing the first two observations in the series and it is only suitable for short time series.The Average Change Model, also known as the moving average approach, assumes that the forecast value is equal to the real value in the current period plus the average absolute changes experienced up until that point. The one step ahead forecast is given by:

(2)

This model is useful when analyzing historical data with consistent period-to-period changes. However, it tends to lag behind turning points and gives equal weight to all periods regardless of their importance. The simple moving average forecast equation is:

(3)

Where: Ft+1 = forecast value for the next period Xt = real value at period T K = number of terms in the moving average.

Exponential Smoothing:
Simple exponential smoothing, like moving average, uses past values of a time series to predict future values when there is no trend or seasonality present. It aims to estimate the current level which is then used as the forecast for future values. Exponential smoothing continuously revises this estimation based on recent experiences.This text describes a method of averaging or smoothing past values of a series using exponential smoothing. The most recent observation is given the largest weight, while subsequent observations receive smaller weights based on a smoothing constant (0 < I± < 1). The formula for exponential

smoothing is shown formally as (5), with ? representing the forecast value for the next period, I± representing the smoothing constant, Xt representing the actual value in period T, and Ft representing the smoothed forecast value for period T.

The choice of I± depends on the behavior of the series. A value close to 0 should be chosen when there is a lot of random fluctuation, while a value close to 1 should be chosen if recent changes strongly influence forecast values. The root mean squared error (RMSE) is commonly used to select an appropriate smoothing constant, with smaller RMSE values indicating a better fit. In simple exponential smoothing, smaller I± values generally yield more accurate forecasts.

Holt's Method is an extension of smoothing models that smooths both trend and slope by using different variables. It offers more flexibility in selecting parameter values to track these components. This model involves three equations and two smoothing variables.The equations for Holt's Method are as follows: Exponential smoothed series:

(6)

Trend estimation:

(7)

Therefore, the one step ahead forecast is:

(8)

Where: Ft+1 = Smoothed value for period t+1 ? = Smoothing variable for the level (0 < ? < 1) Ct = Actual value at period t Ft = Forecasted The text discusses the use of a univariate prediction model to forecast the demand for ecotourism in the first quarter of 2011. The estimation is based on data from the first quarter of 2000 to the fourth quarter of 2010. The Measure of Root Mean Square Error (RMSE) is used to quantify the difference between the forecasted and actual values during this estimated period at a specific location. Several studies

have employed RMSE for this purpose. Comparing RMSE values among different prediction models allows for measuring discrepancies between predicted and observed values, with a smaller RMSE indicating higher accuracy.

Evaluating the accuracy across multiple periods helps identify which model performs best, using various criteria including ME, MAPE, MSE, and RMSE. Throughout this research, emphasis has been placed on using RMSE as a measure to assess relative accuracy. The calculation for RMSE can be determined using the following formula: [RMSE formula ].

Table 3 presents a comparison of different forecasting techniques, including Naive with Forecast, Average Change Model, Exponential Smoothing, and Holt's Method.Based on the results, the Average Change Model has the smallest RMSE value of 29.85, making it the most suitable for forecasting ecotourism demand. This model is preferred because it minimizes the impact of temporary fluctuations in data, enhances data fit by smoothing the trend, and highlights values that deviate from the trend.

Table 3: RMSE Values by type of model
Type of model Naive Forecast Average Change Model Exponential Smoothing Holt's Method
RMSE = 123.60 RMSE = 29.85 RMSE = 110.51 RMSE = 97.50

The first method discussed is the Naive with Trend Model which utilizes Microsoft Excel to analyze all available data and estimate forecast values. The simplest naive prediction model assumes that the forecast value (Ft) equals the previous observed value (At-1). Mathematically represented as Ft = At-1 (10). However, considering solely the most recent observation may not sufficiently consider how we arrived at this latest observation; hence additional factors should be considered in determining forecasts.

If we have a decreasing series up until the latest point, it may be reasonable to

assume a further decrease. Conversely, if we have only observed an increase, it may make sense to incorporate a further increase into our forecast. This adjustment can be made in the second naive prediction model, which considers a proportion of the most recently observed rate of change in the series.

The model can be represented algebraically as follows: Ft = At-1 + (At-1 - At-2) (11).In this equation, Ft represents the forecast for time period T, At-1 is the actual observation at period t-1, and At-2 is the observed value at period t-2. Therefore, to calculate the demand of ecotourism in Ba'Kelalan for the first quarter of 2011 (BKM0111), we use the observed value for the fourth quarter of 2010 (BKM0410) and adjust it by incorporating some information from recent trends. According to equation (11), BKM0111 equals BKM0410 plus (BKM0410 minus BKM0310). Table 4 displays the Naive Forecast 2 Method with details on year, quarter, number of arrivals, Naive Trend Forecast, mistake, square error, absolute error,% mistake,% absolute error for each entry. The data for 2010 presents values of 1 ,708 ,263 ,445 ,198025 ,445 ,0.63,and 0.63 respectively under these categories. Similarly,in 2011,the data shows321.The calculation for BKM0111 in this case would be532 plus(532 minus743)=532 plus(-211)=321.This study compares Naive Forecast 1 and Naive Forecast 2 to determine the better value of RMSE. It concludes that Naive Forecast 1 has a lower RMSE of 123.60 compared to Naive Forecast 2 with an RMSE of196.65 indicating that Naive Forecast 1 is better choice.Additionally,the study applies average change model by using mean of all data for calculations.This approach known as "moving average," typically involves applying three-and five-quarter moving averagesThe

study in Ba'Kelalan utilizes three- and five-moving averages to determine the most precise trend for projecting tourism demand and forecasting future tourist flow.This application utilizes equation (2) to calculate the mean of the norm, similar to a naive prognosis measurement. Table 5 displays various data including Year, Quarter, No.Of Arrival, 5 Qtr MA, Forecast 5 Qtr MA, Mistake, Square Error, Absolute Error, % Mistake, and Absolute % Mistake. Additionally,< h21>   

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In this study, it is found that the five-quarter moving average outperforms the three-quarter moving average with an RMSE of 49.52 compared to the smallest RMSE of 29.85 for the five-quarter moving average.The Exponential Smoothing Method can be executed in Microsoft Excel along with the naive and mean change models.However,Eviews provides more convenience for analyzing data.We can utilize Eviews by solving or calculating equation (5). The following are results obtained from using Eviews for the Exponential Smoothing Method: Table 6: Exponential Smoothing Method: Parameters: - Alpha: 0.478 - Sum of Squared Residuals: 537351.2 - Root Mean Squared Error:110.5103 By employing the smoothing constant alpha (±), we can continue calculations utilizing this methodThe exponential smoothing method calculates the forecast value at any given time by taking a weighted average of all previous values. The RMSE for this method is determined to be 110.51. Using Eviews, Holt's method can also be applied and yields the following results: Table

7: Holt's Method Method: Holt-Winter No Seasonal Parameters: - Alpha: 0.11 - Beta: 1 - Sum of Squared Residuals: 418306.8 - Root Mean Squared Error: 97.50371 The analysis demonstrates that utilizing Holt's method with an alpha value of 0.11 and beta value of 1 leads to an RMSE of 97.50. This approach offers the advantage of assigning greater importance to recent observations compared to older ones. Based on the assessment of one step ahead forecasts, it can be concluded that the Average Change model is the most suitable technique for forecasting quarterly demand in ecotourism.Decision-makers should consider exploring additional forecasting methods specifically tailored for longer periods of demand in ecotourism.The Univariate Modelling Technique relies on a single variable and utilizes historical data to generate forecast values.Consideration should be given to employing this technique when evaluating forecasting alternatives.This model assumes that forecast values are solely dependent on past patterns within the data series