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Tourism (Northern Ireland) Order 1992

NORTHERN IRELAND ORDER IN COUNCIL

1992 No. 235 (N.I. 3)

NORTHERN IRELAND

The Tourism (Northern Ireland) Order 1992

Made 11th February 1992

Coming into operation in accordance with Article 1(2)

At the Court at Buckingham Palace, the 11th day of February 1992

The Queen’s Most Excellent Majesty in Council

Whereas a draft of this Order has been approved by a resolution of each House of Parliament:

Now, therefore, Her Majesty, in exercise of the powers conferred by paragraph 1 of Schedule 1 to the Northern Ireland Act 1974 1 and of all other powers enabling Her in that behalf, is pleased, by and with the advice of Her Privy Council, to order, and it is hereby ordered, as follows:—

INTRODUCTORY

Title and commencement

1. —(1) This Order may be cited as the Tourism (Northern Ireland) Order 1992.

(2) This Order (except paragraph 4 of Schedule 3) shall come into operation on such day or days as the Head of the Department may by order appoint.

(3) An order under paragraph (2) may make such transitional provision as appears to the Head of the Department to be necessary or expedient in connection with the provisions brought into operation by the order.

Interpretation

2. —(1) The Interpretation Act (Northern Ireland) 1954 2 shall apply to Article 1 and the following provisions of this Order as it applies to a Measure of the Northern Ireland Assembly.

(2) In this Order—

“assist” includes assist financially;

“the Board” means the Northern Ireland Tourist Board;

“the Department” means the Department of Economic Development;

“directions” means directions issued under Article 5 and “direct” shall be construed accordingly;

“provide” and “maintain”, in relation to any amenity, facility or service, have the meanings assigned to them by section 147 of the Local Government Act (Northern Ireland) 1972 3 ;

“statutory provision” has the meaning assigned to it by section 1( f ) of the Interpretation Act (Northern Ireland) 1954 4 ;

“tourist” means a visitor to Northern Ireland, a person spending his holiday in Northern Ireland or a person travelling for pleasure within Northern Ireland, and “tourism” shall be construed accordingly;

“tourist accommodation” means overnight sleeping accommodation for tourists provided by way of trade or business;

“tourist amenity” means an amenity, facility or service provided primarily for tourists, but does not include tourist accommodation.

(3) Any power of giving directions or making determinations conferred on the Department by any provision of this Order includes power to vary or revoke any directions or determinations given or made under that provision.

THE NORTHERN IRELAND TOURIST BOARD

The Northern Ireland Tourist Board

3. —(1) There shall continue to be a body called the Northern Ireland Tourist Board (in this Order referred to as “the Board”).

(2) Schedule 1 shall have effect in relation to the Board.

Functions of the Board

4. —(1) The functions of the Board shall be—

(a) to encourage tourism;

(b) to encourage the provision and improvement of tourist accommodation and tourist amenities;

(c) to advise the Department generally on the formulation and implementation of its policy in relation to the development of tourism;

(d) such other functions as are conferred on the Board by or under this Order or any other statutory provision.

(2) Without prejudice to the generality of paragraph (1), in the exercise of its functions the Board may—

(a) provide advice and information about travelling to and holidays in Northern Ireland and publicise or advertise holidays in Northern Ireland;

(b) provide or assist any event which appears to the Board likely to encourage tourism;

(c) co-operate with persons or bodies training persons to do work wholly or mainly connected with tourism;

(d) establish or assist in establishing any body in connection with tourism;

(e) trade in any business associated with tourism;

(f) accept gifts and donations and undertake and execute any trusts which may lawfully be undertaken by the Board and may be conducive to its functions;

(g) make known the financial assistance which may be provided under this Order;

(h) make charges for services provided by it and for any certificate or approval granted by it for the purposes of any statutory provision other than this Order;

(i) carry out surveys and collect statistics and information relating to the tourist industry;

(j) generally assist in making Northern Ireland attractive to tourists;

(k) co-operate with or assist any other body or association carrying out activities falling within the functions of the Board.

(3) It shall be the duty of the Board to establish machinery for consulting, and to consult regularly with, bodies appearing to the Board to have an interest in matters falling within the functions of the Board.

(4) The power of the Board under section 19(1)( a )(iv) of the Interpretation Act (Northern Ireland) 1954 5 to acquire, hold, dispose of or charge real property shall not be exercised without the approval of the Department and the Board shall not have power to carry out any building or other physical works on land except with the approval of the Department.

Directions to the Board

5. —(1) The Department may, in accordance with arrangements approved by the Department of Finance and Personnel, issue to the Board—

(a) directions of a general or specific nature as to the exercise by the Board of its functions;

(b) directions as to any matter in relation to which the Department is authorised to issue directions by any other provision of this Order.

(2) The Department may direct the Board to exercise on behalf of the Department any function of the Department connected with or related to the development of tourism, not being a function conferred on the Department by this Order.

(3) Before issuing any directions under this Article the Department shall consult with the Board.

(4) It shall be the duty of the Board to comply with any directions issued to it under this Article.

Estimate of expenditure and income of the Board

6. —(1) The Board shall, on or before such date in each year as the Department may direct, submit to the Department, in such form and containing such particulars as the Department may direct, an estimate of its income and expenditure for the succeeding financial year.

(2) The Board may at any time submit a supplementary or revised estimate to the Department.

(3) The Department may approve an estimate submitted under paragraph (1) or a supplementary or revised estimate submitted under paragraph (2) either in whole or in part or subject to such modifications or conditions as the Department may think fit.

(4) The Board shall not incur expenditure otherwise than in accordance with an estimate or a supplementary or revised estimate approved under paragraph (3).

Financial provisions relating to the Board

7. —(1) The Department may in each financial year pay to the Board grants of such amount as the Department may determine towards the expenditure incurred or to be incurred by the Board in accordance with an estimate or a supplementary or revised estimate approved under Article 6(3).

(2) The Board may, in accordance with directions, establish reserve funds for such general or special purposes as the Board may think proper.

(3) The Board may borrow or raise money on such terms and on such security and for such purposes as the Department may direct.

(4) The Board may invest the moneys of the Board not immediately required for the purposes of the Board in or upon such investments or securities as the Department may direct.

Accounts and audit

8. —(1) The Board shall—

(a) keep, in such form as the Department may direct, proper accounts of all moneys received and of all moneys paid out by it;

(b) prepare and submit to the Comptroller and Auditor General for Northern Ireland and the Department, on or before such date in each year as the Department may direct, a statement of its accounts in respect of the financial year then last previously occurring, in such form and containing such information as the Department may direct.

(2) The Comptroller and Auditor General shall examine and certify the statement of accounts submitted to him by the Board.

(3) The Department shall lay before the Assembly a copy of the certified statement of accounts and of any report of the Comptroller and Auditor General thereon.

Annual report

9. The Board shall annually on such date and in such form as the Department may direct make to the Department a report on the activities of the Board during the preceding year and a copy of each such report shall be laid before the Assembly.

Power to dissolve the Board

10. —(1) The Department may by order made subject to affirmative resolution make provision for, or in connection with, the winding up and dissolution of the Board.

(2) An order under this Article may—

(a) provide for the transfer of the functions, assets and liabilities of the Board to any other body or person;

(b) contain such incidental, consequential, transitional or supplementary provisions (including the amendment or repeal of any statutory provision (including a provision in this Order)) as appear to the Department to be necessary or expedient for giving full effect to the provisions of the order.

FINANCIAL ASSISTANCE TO TOURIST INDUSTRY

Selective financial assistance

11. —(1) The Board may, in accordance with a scheme under this Article, provide financial assistance to any body or person where in its opinion—

(a) the financial assistance is likely to...

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The Tourism (1992 Order) (Commencement) Order (Northern Ireland) 1992 (Q100072405)

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Application for a Statutory Inspection to allocate a Statutory Category

Article 13 (2)(b) of the Tourism (Northern Ireland) Order 1992

This application requests a statutory inspection of the establishment to be conducted so that it may be allocated to the statutory category specified in this application.

All premises offering tourist accommodation in Northern Ireland must be certified under the Tourism (Northern Ireland) Order 1992. Tourism Northern Ireland (Tourism NI) is required by this legislation to inspect tourist accommodation every 4 years (statutory inspection) to ensure properties comply with the minimum criteria set. You can view the minimum criteria for each category under Guidelines for each category .

To view premises certified by Tourism NI, please visit our website www.discovernorthernireland.com .

If you wish to apply for certification, you can do so by:

• following this link - Apply online for certification OR
• completing an application form available on tourismni.com and posting this, with your fee, to Tourism NI at the address below.

Information on the cost of certification can be found in our Fees Information section in the Information links to the left of this page.

Please note that Tacit Consent will not apply for reasons of public safety, however, on receipt of your application and fee, and any additional necessary paperwork, Tourism NI aims to complete inspections of new tourist accommodation within 8 weeks. Please see New Venture Process in the Information links to the left of this page for more information. You can also contact us at any stage of the process if you have any queries.

If you wish to appeal the decision to refuse certification of your premises, please see our section Reviews & Appeals in the Information links to the left of this page.

If you wish to complain about Tourism NI, please click here .

If you wish to contact Tourism NI, you can email [email protected] , telephone 02890441545, or write to us at Floors 10-12 Linum Chambers, Bedford Square, Bedford Street, Belfast, BT2 7ES.

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Travel and Tourism Spending in the United States: 1992

• News Release

According to the newly developed travel and tourism satellite accounts (TTSA's) released for the first time by the Commerce Department's Bureau of Economic Analysis, spending by U.S. residents and nonresidents traveling in the United States accounted for 5 percent of gross domestic product in 1992. The new accounts provide the best picture yet developed of the importance of travel and tourism spending in the U.S. economy; the data in the new report are based on BEA's 1992 benchmark input-output accounts. In the new accounts, travel and tourism activity is defined as purchases by travelers of air fares, lodging, meals and beverages, recreation, shopping, and other travel activities.

Of the approximately $300 billion in travel and tourism spending, the largest single expenditure was for airline fares ($81 billion), which was followed by lodging ($56 billion) and by meals and beverages (approximately $50 billion). The TTSA's, which designate the industries that are considered travel and tourism industries, show that travel and tourism spending generated employment in these industries that accounted for about 3 percent of total employment.

The new accounts also distinguish expenditures by type of traveler. U.S. resident households accounted for 45 percent of travel expenditures, government and business accounted for 34 percent, and nonresidents accounted for 21 percent.

Estimates of travel and tourism activities provide a means of comparing them with other activities in the U.S. economy and with such activities in other countries. Satellite accounts provide measures of an economic activity in this case travel and tourism that are consistent with measures of overall economic activity. The new satellite accounts also will facilitate research on the impact of travel and tourism on the economy.

The TTSA's were developed as a prototype by BEA with cooperation and support from the Tourism Industries Office, International Trade Administration, U.S. Department of Commerce.

Additional information about the TTSA's appear in the July 1998 issue of the Survey of Current Business. Information on how to order the Survey of Current Business is provided below.

BEA's major national, regional, and international estimates, the Survey of Current Business (BEA's monthly journal), and BEA news releases are available on BEA's web site: http://www.bea.gov

STAT-USA maintains an electronic bulletin board (EBB) and an Internet site, which contains BEA estimates, BEA news releases, and the Survey of Current Business. The information available through STAT-USA is often more detailed and more timely than that available from other sources. To subscribe to STAT-USA's World Wide Web system, go to http://www.stat-usa.gov. Subscriptions for single-user unlimited access to STAT-USA's Internet information are $50.00 for 3 months or $150.00 for 1 year. For further information, call (202) 482-1986.

The printed Survey of Current Business is available from the Superintendent of Documents, U.S. Government Printing Office, Washington D.C. 20402. First class mail: Annual subscription $69.00 domestic. Second class mail: Annual subscription $35.00 domestic, $43.75 foreign; single issue $11.00, $13.75 foreign.

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Tourism (1992 Order) (Commencement) Order (Northern Ireland) 1992: Tourism (Statutory Rule: 1992: 129 (C. 5)) Paperback – January 1, 1992

• Language English
• Publisher The Stationery Office Books
• Publication date January 1, 1992
• ISBN-10 0337107297
• ISBN-13 978-0337107290
• See all details

Product details

• Publisher ‏ : ‎ The Stationery Office Books (January 1, 1992)
• Language ‏ : ‎ English
• ISBN-10 ‏ : ‎ 0337107297
• ISBN-13 ‏ : ‎ 978-0337107290
• Item Weight ‏ : ‎ 1.11 pounds

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Forecasting Tourist Arrivals in Nepal: A Comparative Analysis of Seasonal Models and Implications

• Research Article
• Open access
• Published: 19 September 2024

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• Tulsi Paudel   ORCID: orcid.org/0000-0002-2934-2640 1 ,
• Wenya Li 1 &
• Thakur Dhakal 2  

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Tourist arrivals play a vital role in the broader tourism ecosystem, substantially contributing to the economy. The global landscape has witnessed significant growth in international arrivals over the years, and Nepal has not been an exception to this trend, experiencing a steady influx of inbound tourists. Although tourist numbers are increasing, the lack of research in forecasting future arrivals is evident, highlighting the pressing need for comprehensive forecasting mechanisms to efficiently manage tourism resources and sustainably accommodate the growing influx of visitors. In order to gain insights into the dynamics of international tourist arrivals in Nepal, we conducted a comparative analysis using two distinct forecasting techniques: Seasonal Autoregressive Integrated Moving Average (SARIMA) and the Exponential Smoothing technique. Our analysis spanned from January 1992 to December 2023, enabling us to formulate forecasts for the upcoming months up to December 2030. The findings of our study underscore the suitability of all three models—namely, SARIMA, Winter Additive, and Winter Multiplicative—as effective tools for projecting international arrivals in Nepal. However, upon careful examination, the Winter Multiplicative model emerged as the most appropriate model for forecasting Nepal's international arrivals. This model aligned strongly with the observed data, enhancing its predictive accuracy. The implications of our research are far-reaching, offering valuable insights for various stakeholders within Nepal's tourism industry. These insights can guide tourism planners, policymakers, and other relevant entities in formulating well-informed strategies to strengthen and sustain the growth of the tourism sector in Nepal. As the nation continues to position itself on the global tourism map, equipped with data-driven forecasts, we believe that our study provides an essential resource for shaping the trajectory of Nepal's tourism industry in a positive direction.

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1 Introduction

Tourism involves the movement of people from one location to another, facilitated by the advancements in transportation that enable easy global travel. The surge in tourist mobility has reflected in various economic, socio-cultural, and environmental consequences in global economies. As reported by WTTC [ 1 ], the tourism sector contributed 10.4% to the global GDP in 2019, generating around 334 million jobs across the globe. The accessibility to different countries has led to an upswing in international arrivals, spurring economic activities worldwide. Therefore, the prediction of international arrivals has emerged as a captivating field of research for both tourism scholars and stakeholders. Accurate forecasting raises confidence in authorities, allowing them to formulate effective strategies to manage future influxes. However, the susceptibility and volatility of tourist arrivals have been exacerbated by unforeseen crises such as natural disasters, pandemics, and political upheavals. Particularly, the recent COVID-19 pandemic dealt a severe blow to the global tourism industry resulting in a nearly 74% decline in worldwide arrivals [ 1 ].

Our study focuses on Nepal, renowned for its abundant natural beauty and rich cultural diversity. Nepal is the Himalayan nation with the world's tallest peak, Everest, and over a dozen mountains 8,000 m high and surrounded by diverse flora and fauna. Nepal's abundant dense forests, winding rivers, awe-inspiring mountains, and serene valleys collectively weave a captivating tapestry that beckons nature enthusiasts and travellers alike. In a heartwarming synergy, Nepal's tourism sector not only unveils these natural treasures but also contributes significantly to nurturing the nation's economy. Drawing global visitors lays the foundation for a cycle of prosperity, empowering investors and entrepreneurs to thrive through income, employment opportunities, and substantial revenue streams.

Nepal's travel and tourism industry stands tall as one of the pillars supporting the nation's financial well-being. Its resounding impact resonates across the economy, making it a vital contributor to Nepal's GDP. On a more intimate level, it holds the key to livelihoods, offering substantial employment opportunities within local communities. Over time, Nepal has experienced a positive growth trajectory in terms of international tourist arrivals. Notably, 2019 marked a peak in arrivals, with 1,197,191 international tourists visiting Nepal [ 2 ]. Nonetheless, the Nepalese tourism sector has frequently grappled with various crises. The devastating earthquake of 2015 significantly impacted the industry, resulting in substantial losses and decreasing arrivals by nearly 31.8% [ 2 ].

The recent COVID-19 pandemic has damaged Nepal's tourism industry even more. In 2020, international tourist arrivals witnessed an unprecedented decline of 80.7%, totalling just 230,085 visitors. Echoing this trend, 2021 experienced a further reduction, dwindling to 150,962 [ 3 ]. Accurate prediction of tourist arrivals is instrumental in assisting tourism planners with effective planning and preparation. The significant fluctuations in arrival numbers substantially impact various sectors such as accommodation, food and beverage, and transportation. Given this, forecasting tourist arrivals becomes necessary, enabling tourism planners and stakeholders to devise strategies to handle future arrival fluctuations.

Considering the significant impact of accurate forecasting, there is a promising avenue for the current study due to the relatively limited research on international arrivals in Nepal. Existing literature has primarily focused on predicting arrivals or incorporating other variables for impact analysis. However, the comparison of forecasting models in the context of tourism arrivals has not been explored by researchers. To fill this gap this study employs the Exponential Smoothing and Seasonal Autoregressive Integrated Moving Average (SARIMA) models to analyse historical monthly tourist arrival data, thereby discerning patterns and projecting future arrivals. The main research questions our study aims to answer are: (a) Which forecasting model, Exponential Smoothing or SARIMA, should be employed for accurate predictions of tourist arrivals in Nepal, and how does this forecasting assist tourism planners and stakeholders? (b) How can insights gained from historical tourist arrival data in Nepal inform the development of strategies to promote a resilient and thriving tourism industry in the country?

The anticipated outcomes of this study are poised to yield substantial benefits for various stakeholders, including tourism policymakers, governmental authorities, entrepreneurs, and other vested parties within Nepal. By providing insights into the anticipated trends and patterns of tourist arrivals, this research equips these stakeholders with the essential knowledge needed to devise informed strategies that can foster a resilient and thriving tourism industry in Nepal.

2 Literature Review

Forecasting tourist arrivals using time series analysis is widely adopted in tourism demand research. Researchers have harnessed various forecasting models to predict tourist arrivals, including ARIMA, Exponential Smoothing, and Neural Network techniques. Chhorn and Chaiboonsri [ 4 ] employed the ARIMA-GARCH model to predict monthly arrivals in Cambodia, asserting the suitability of a hybrid ARIMA approach for such predictions. The popularity of ARIMA as a forecasting method is evident in the works of Chu [ 5 ], Unhapipat and Unhapipat [ 6 ] and Jere et al. [ 7 ], who employed ARIMA models for tourist arrival predictions, while Sun et al. [ 8 ] showcased the utilisation of machine learning models for the same purpose.

In the domain of Exponential Smoothing models, Lim and McAleer [ 9 ] stood out by forecasting quarterly tourist arrivals to Australia from various source countries such as Hong Kong, Malaysia, and Singapore. Their findings indicated that the Holt-Winters Additive and Multiplicative models effectively predict tourist arrivals, further establishing the versatility and suitability of these models in the realm of tourism forecasting. Numerous other researchers have investigated and forecasted future tourist arrivals in various countries by analysing time series data. For instance, Tularam et al. [ 10 ] delved into arrivals in Australia, utilising both ARIMA and VAR methodologies considering data spanning from 1956 to 2010. Intarapak et al. [ 11 ] studied in case of Thailand, employing the Box-Jenkins approach and the Winter Multiplicative model to predict arrivals. Their findings highlighted the superior performance of the Winter Multiplicative model in this context. Roshan and Jahufer [ 12 ] utilised the SARIMA model and the Holt-Winters forecasting method to predict international arrivals in Sri Lanka. They concluded that the SARIMA model was the most suitable for forecasting tourist arrivals in the Sri Lankan context.

In the case of Hong Kong, Xie et al. [ 13 ] found that the Decomposition-ensemble approach effectively facilitated the prediction of arrivals from nine different countries. Artificial neural networks (ANN) and deep learning methods have also emerged as popular techniques for projecting international tourist arrivals. Alamsyah and Ayastri Friscintia [ 14 ] used ANN to forecast tourism demand in Indonesia, incorporating variables such as GDP, CPI, and exchange rates in their analysis. For the context of Morocco, Laaroussi et al. [ 15 ] discovered that long short-term memory (LSTM) and gated recurrent unit (GRU) deep learning models outperformed support vector regression (SVR) and ANN models in predicting arrivals. In a study of tourism demand in Sweden, Hopken et al. [ 16 ] found that the ANN approach outperformed the ARIMA model when analysing monthly data on inbound tourists from Denmark, Finland, Norway, Russia, and the UK.

In Nepal's specific context, there have been limited efforts to anticipate future tourism demand. Subedi [ 17 ] introduced a distinct approach to forecasting arrivals by combining ARIMA with a polynomial function. Paudel et al. [ 18 ] delved into forecasting international tourist arrivals in Nepal by utilising the Gompertz model. Furthermore, they engaged the system dynamics approach to explore various scenarios, thus providing a comprehensive perspective on potential outcomes. Upadhayaya [ 19 ] applied the ARIMA model to predict yearly tourist arrivals in Nepal until 2029, contributing to a long-term projection of the tourism landscape. Neupane et al. [ 20 ] adopted a time series analysis to scrutinise monthly arrivals in Nepal to uncover associated risks and highlight the inherent volatility characterising tourist arrivals. Shrestha and Shrestha [ 21 ] employed the ARIMA model to predict yearly arrivals while exploring the trends prevalent in tourist arrivals over time.

These diverse research efforts collectively contribute to an enriched understanding of tourism demand forecasting within Nepal, offering valuable insights into the array of methods and approaches researchers have employed to project tourist arrivals and navigate the intricate landscape of the tourism sector. Indeed, most studies concerning tourist arrivals in Nepal have been conducted before the COVID-19 era, often concentrating on yearly data. The disruptive impact of COVID-19 has led to a significant transformation in tourist arrivals.

This study addresses this imperative by forecasting and contrasting the monthly arrivals up to December 2025. The study employs two distinct Exponential Smoothing models alongside the Seasonal Autoregressive Integrated Moving Average (SARIMA) model to identify the best forecasting model. The decision to focus on SARIMA and exponential smoothing models for tourism demand forecasting stems from their proven effectiveness, suitability for our research objectives, and widespread adoption. SARIMA models capture seasonal patterns effectively, while exponential smoothing models offer simplicity and adaptability. VAR and GARCH models are more complex and may not directly apply to our context. ANN and LSTM models, though flexible, require extensive resources. Therefore, SARIMA and exponential smoothing strike a balance between accuracy and practical feasibility for our study. By adopting these forecasting methodologies, this research aims to capture Nepal's evolving dynamics of tourist arrivals. This comprehensive examination of recent trends and predictions holds the potential to provide critical insights that can guide stakeholders, planners, and policymakers in effectively responding to the transformed landscape of Nepal's tourism sector.

3 Materials and Methods

The primary objective of this study is to investigate the monthly patterns of tourist arrivals in Nepal and subsequently predict the trajectory of upcoming monthly arrivals. To achieve this, we acquired a comprehensive dataset from the Ministry of Culture, Tourism, and Civil Aviation covering the period from January 1992 to December 2023 [ 2 ]. This dataset comprises a total of 384 months of arrival data. The time-series data was transformed into a stationary format by applying a natural logarithmic transformation to facilitate meaningful analysis. Subsequently, three distinct methodologies were employed to project forthcoming arrival figures: the Seasonal Autoregressive Moving Average (SARIMA), Holt-Winter Multiplicative and Holt-Winter Additive techniques. Given the seasonality in tourist arrival data, the study incorporated a seasonal decomposition process to comprehend the underlying patterns more effectively. Moreover, the dataset's autocorrelation (ACF) and partial autocorrelation (PACF) were examined closely to verify the validity of the chosen approaches. The optimal order (which varies from 0 to 3) that minimizes a selected criterion, such as the AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion), was found through a grid search over possible parameter combinations for the SARIMA model. This grid search involves fitting multiple SARIMA models with different combinations of parameters and selecting the one with the lowest AIC or BIC value. Grid search is a simpler and more interpretable approach, suitable for smaller search spaces.

3.1 Autoregressive Integrated Moving Average Modelling (ARIMA)

In the 1970s, George Box and Gwilym Jenkins introduced a systematic approach to handling time series data in business and economics, now widely recognised as the Box-Jenkins approach. This approach encompasses three fundamental stages: model identification, estimation of model parameters, and validation of the fitted model, as outlined by Hyndman and Athanasopoulos [ 22 ]. For integrated time series data to become stationary, it typically involves two terms: autoregressive (AR) and moving average (MA). Combining these elements forms the autoregressive integrated moving average model (ARIMA), a widely embraced technique for analysing and predicting time series data. Notably, researchers within the field of tourism extensively employ ARIMA models to explore and forecast international arrivals.

ARIMA models comprise components for autoregression, differencing, and moving averages. These components collectively aid in characterising autocorrelations within the data. The fundamental principle underlying ARIMA is the projection of future data by utilising a linear amalgamation of historical values of the variable within an autoregressive framework. Thus, the autoregressive equation of order p, often referred to as AR(p), can be expressed as follows [ 22 ]:

where c is the constant, \({\mathrm{\varnothing }}_{{\text{k}}}\) is the autoregressive coefficient at lag k, \({x}_{t-p}\) are lagged values from time t to p and \({\varepsilon }_{t}\) is termed white noise. On the other hand, a Moving Average model uses prior prediction errors rather than historical values of the forecast variable. The Moving average equation of model MA (q) model with order \(q\) is expressed as [ 22 ]:

where c is the constant,  \({\varepsilon }_{t}\)  is error and \({\theta }_{k}\) is the moving average coefficient at lag k. In this model, the lags of \({\varepsilon }_{t}\) are used as predictors. If we combine AR(p) and MA(q), we will get the following equation, which is expressed as the nonseasonal ARIMA model [ 22 ].

where \({x}_{t}^{\mathrm{^{\prime}}}\)   is the differentiated form of \({x}_{t}\) . This model is called the ARIMA (p, d, q) model. The order of the autoregressive part, the degree of difference, and the order of the moving average part are p, d, and q, respectively. The nonseasonal ARIMA model can be noted with the backshift operator as [ 22 ]:

where B is the backshift operator, is \(\left(1-{\mathrm{\varnothing }}_{{\text{p}}}{B}^{{\text{p}}}\right)\) AR (p),  \({\left(1-B\right)}^{d}{x}_{t}\) is a differencing term, \(\left(1+{\theta }_{{\text{q}}}{B}^{{\text{q}}}\right){\upvarepsilon }_{t}\) and is MA (q). The backshift operator B is used to express the lags in time series, i.e., \({\text{B}}{x}_{t}={x}_{t-1}\)

The earlier equation does not account for the inherent seasonality in time series data. In order to accommodate this seasonality, a modification is applied to the ARIMA model, leading to the development of Seasonal ARIMA (SARIMA). This enhanced model integrates the original ARIMA structure with the consideration of seasonal patterns. SARIMA introduces three additional seasonal parameters—P, D, and Q—while also introducing the parameter "m" to represent the specific number of periods that constitute a season. It is important to note that seasonal parameters are denoted in uppercase letters, while nonseasonal components retain lowercase letters. Therefore, the formulation of the seasonal ARIMA model, which is applicable for a given seasonal period "m," is as follows:

Where p, d, and q are nonseasonal parameters, and P, D, and Q are seasonal parameters. Further, the SARIMA equation with backshift notation is expressed as [ 22 ]:

3.2 Holt-Winter Exponential Smoothing Model

The exponential smoothing method was first introduced by Robert G. Brown in the 1950s and then modified by Charles C. Holt and Peter Winter in 1960 [ 23 ]. Exponential Smoothing (ES) uses an exponentially weighted moving average (EWMA) for each component of time series data, such as level, trend, and seasonality, with past observations receiving diminishing weights [ 24 ]. The forecast is generated by computing weighted averages of previous observations while considering the progressively decreasing weights assigned to these observations, as outlined by Hyndman and Athanasopoulos [ 22 ]. The Holt-Winters model encompasses two distinct variations: the additive and multiplicative models. Both versions incorporate the consideration of seasonality while forecasting time series data. Three essential parameters are considered within the Holt-Winters exponential smoothing model framework: the value, the trend, and the seasonality. This amalgamation of parameters gives rise to what is referred to as the Triple Exponential Smoothing model, owing to its incorporation of three distinct components to enhance forecasting accuracy.

In the Winter Additive model, the forecasted data is the sum of baseline, trend and seasonality components. The Winter Additive model consists of three smoothing expressions for level, trend, seasonality, and forecasting equations as follows [ 22 ]:

where, \({L}_{t}\) is for level, \({{\text{B}}}_{t}\) is for trend, \({S}_{t}\) is for seasonality with corresponding smoothing parameters \(,\beta\) , and  \(\gamma\) . The seasonality period is denoted by p, and m is the number of forecasts in the future.

In the Multiplicative model, the forecasted data is the product of its baseline, trend and seasonality components. Similar to the Winter Additive model, the Multiplicative model consists of three smoothing equations for level, trend and seasonality as follows [ 22 ]:

where, \({L}_{t}\) is for level, \({B}_{t}\) is for trend \({S}_{t}\) is for seasonality with corresponding smoothing parameters \(,\beta\) , and \(\gamma\) . The seasonality period is denoted by p, m is the number of forecasts in the future, and the term, \({S}_{t+m-p}\) is a seasonal component for the same period as the previous year.

The time series plot in Fig.  1 illustrates the monthly international arrivals to Nepal, encompassing January 1992 to December 2023. The plot distinctly showcases a nonlinear arrival pattern intertwined with evident seasonality. The data exhibits numerous upward surges and downward troughs throughout this time frame. Amidst these fluctuations, an overarching growth trend is perceptible in international tourist arrivals over 384 months. Notwithstanding a few pronounced dips in the graph, the general trajectory demonstrates a robust increase. Notably, the plot reflects the impact of significant events on tourist arrivals. The seismic occurrence of the earthquake in 2015 and the unprecedented outbreak of COVID-19 in 2020 have contributed to the distinctive downward spikes in international arrivals. According to the analysis presented by the World Travel & Tourism Council (WTTC) in 2021, it is evident that tourist arrivals encountered a steep decline due to these impactful events. In 2015, tourist arrivals experienced a substantial drop of approximately 35%, and in 2020, this decline was even more pronounced, reaching a staggering 80%. The intricate interplay of these events and the corresponding fluctuations in tourist arrivals underscore Nepal's tourism sector's dynamic and resilient nature within the context of global events and their aftermath. We have employed the COVID impact as an intervention factor in tourist arrivals in our analysis.

(Source: MOCTCA)

Monthly Arrival of International Tourists

Given the non-stationary and strongly seasonal nature of the monthly arrival data, a series of analyses were conducted to validate the presence of seasonality and ensure stationarity. Seasonal decomposition and spectral analysis were performed to illuminate these aspects. The outcomes of the seasonal decomposition have been documented in Table  1 , providing a comprehensive breakdown of the distinct seasonal components. These components effectively highlight the patterns inherent in the data across various months.

An insightful observation drawn from the seasonal factors is that tourists prefer travelling to Nepal from October to November and February to April. These windows exhibit a notable surge in tourist arrivals, underscoring their preference for these timeframes. Conversely, the period from May to July is the least favourable for arrivals, indicating a comparatively lower influx of tourists during these months (Fig.  2 ). Together, these analyses provide a comprehensive understanding of the seasonal and stationary characteristics of the data, contributing valuable insights into the patterns and trends governing tourist arrivals in Nepal across different periods.

Monthly Tourist Arrival Distribution

To confirm the stationarity of the data, we conducted three distinct tests: the Augmented Dickey-Fuller test, the Kwiatkowski-Phillips-Schmidt-Shin test (KPSS), and the Phillips-Perron test (PP). We then compared the statistical significance of first-order differentiation and natural logarithmic transformation (Table  2 ). Taking into account the results from all three tests, the logarithmic transformation generally outperformed the first differentiation in achieving stationarity. It consistently yields higher statistical values and, in some cases, lower p -values, indicating a more significant departure from non-stationarity.

Figure  3 illustrates the autocorrelation and partial autocorrelation functions (ACF and PACF) of the tourist arrival data. In the ACF plot, a notable spike is observed at lag 2, indicating a significant correlation between observations at lag 2 intervals. Similarly, the PACF plot exhibits a similar pattern, further confirming the strong correlation at lag 2.

Autocorrelation and Partial Autocorrelation plots

We observed notable differences in the performance of three forecasting models—SARIMA, Winter Additive, and Winter Multiplicative—evaluated using Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) (Table  3 ). The Winter Additive and Winter Multiplicative models exhibited superior performance over SARIMA in both metrics, with lower MSE values of 1.375 and 1.334, respectively, compared to SARIMA's MSE of 2.765. Similarly, in terms of MAPE, the Winter Additive and Winter Multiplicative models outperformed SARIMA, with MAPE values of 0.099 and 0.098, respectively, as opposed to SARIMA's higher MAPE of 1.131. These results indicate that both the Winter Additive and Winter Multiplicative models offer improved accuracy and better fit for the forecasting task, with the Winter Multiplicative model showing a slightly enhanced performance over the Winter Additive model. Table 4 has details of optimal model parameters for all three models and Fig.  4 shows the prediction of all three models in graphical representation.

Model Prediction SARIMA, Holtwinter Additive and Multiplicative

Figure  5 depicts the forecasting plot generated by the Winter Multiplicative model, which exhibited superior performance compared to alternative models considered in the analysis. The plot provides a visual representation of the forecasted international tourist arrivals until the year 2030.

Forecasted plot for Holt-Winter Multiplicative model

Table 5 presents the forecasted international tourist arrivals until 2030, utilizing the Winter Multiplicative model, which was identified as the most suitable for this analysis. Notably, the predictions highlight October and March as the months with the highest anticipated arrivals in the upcoming years. Conversely, it is anticipated that the winter and summer months will experience relatively lower arrival numbers. These insights provide valuable guidance for stakeholders in the tourism industry, allowing them to strategize and allocate resources effectively to accommodate the expected fluctuations in tourist traffic throughout the year. By leveraging this forecasted data, tourism authorities and businesses can tailor their marketing efforts, infrastructure development plans, and service offerings to optimize the visitor experience and capitalize on peak arrival periods. Ultimately, this proactive approach can contribute to the sustainable growth and success of the tourism sector.

5 Discussions and Conclusions

Tourism is significant in Nepal's economic landscape, serving as a crucial driving force for its economic prosperity. The magnitude of tourist arrivals directly influences tourism consumption patterns, thus holding the potential to shape the nation's economic trajectory. Notably, in 2019, the tourism sector's contribution to Nepal's Gross Domestic Product (GDP) reached an impressive 6.7%, a testament to its substantial impact (as reported by WTTC in 2021). In Nepal, the tourism industry is the fourth largest employment sector, underscoring its role in generating livelihoods for its populace. Remarkably, in 2019, the tourism sector engendered employment for approximately 1,042,100 individuals, constituting 6.9% of the overall employment landscape of the country (according to WTTC in 2021).

However, the advent of the COVID-19 pandemic had far-reaching consequences for the global tourism industry. An unprecedented decline of approximately 80% in tourist arrivals was reported worldwide, effectively shaking the very foundation of the tourism ecosystem. This cascading effect reverberated through national and global economies, highlighting the intricate interdependencies and vulnerabilities of the tourism sector. This crisis has underscored the importance of tourism to Nepal's economy while emphasising the need for resilience and innovation within the sector to safeguard against future disruptions.

This study employed three forecasting models to project Nepal's monthly international tourist arrivals. The dataset spans from January 1992 to December 2023 and is subjected to analysis using the SARIMA, Winter Additive, and Winter Multiplicative models. These models are particularly suitable for predicting time-series data characterised by inherent seasonality. The observed arrival pattern in Nepal during this period unveils a series of fluctuations, encompassing both peaks and troughs. Notably 1992, October witnessed the highest recorded arrivals, totalling 42,647 visitors. This figure underwent a significant transformation by 2019, surging to 134,096 arrivals, marking an impressive threefold growth.

However, 2015 recorded a stark contrast, depicting a reduced number of arrivals attributed to the earthquake that struck Nepal during that period. Furthermore, the years 2020 and 2021 deviated from the norm due to the global outbreak of COVID-19, which severely impacted worldwide tourism. The results derived from this study hold optimistic prospects for the future of tourist arrivals in Nepal. Forecasts suggested an overall positive growth trajectory in the forthcoming months. This positive projection, analysing historical patterns, contributes valuable insights to stakeholders, policymakers, and researchers within Nepal's tourism industry.

Among the three forecasting models applied in this study, the Winter Multiplicative model was the most favourable fit based on assessing the MSE and MAPE values. Also, this model yielded projections of a large number of arrivals in the upcoming months. Regarding model performance, SARIMA and Winter Additive both exhibited comparable predictions for the patterns of tourist arrivals. The decisive preference for the Winter Multiplicative model, as indicated by the favourable MSE and MAPE values and the enhanced forecasted figures, underscores its efficacy in capturing the inherent complexities of the dataset's seasonality and variations. This conclusion enables stakeholders and researchers to make informed decisions in Nepal's tourism industry, backed by robust modelling techniques. The results of this study further underscore the significance of accurate tourist arrival predictions, particularly within developing economies. Accurate forecasting plays a pivotal role in providing policymakers with a comprehensive understanding of future arrival trends, thereby enabling the formulation of strategic initiatives aligned with these projections. Given the inherent seasonality of tourist arrival data, any forecasting approach must effectively incorporate seasonal components.

In our study context, both Seasonal Autoregressive Integrated Moving Average (SARIMA) and Exponential Smoothing models have demonstrated their suitability for forecasting tourist arrivals. These models adeptly capture the intricate interplay of seasonal patterns and variations, offering valuable insights into future trends. The findings of this study suggest a gradual increment in tourist arrivals in Nepal. This projection carries essential implications for various sectors, particularly hotels, restaurants, trekking, and transportation. These sectors should proactively gear their resources towards accommodating the anticipated surge in tourism demand. By recognising and capitalising on these forecasts, Nepal can effectively harness its tourism potential, driving economic growth and enhancing the overall tourism experience for visitors.

Indeed, this study offers a foundational exploration of the Nepalese tourism industry, yet it reveals a significant scope for future research. A crucial avenue for future research involves examining the microeconomic impact of the tourism industry, integrating findings from SARIMA, Holt-Winters additive, and multiplicative methods used to forecast tourist arrivals using monthly data. This outcome entails a comprehensive analysis of the intricate interdependencies and dynamics that underlie the tourism economy, considering the limitations such as data availability and model assumptions. To prevent spurious regression with multiple macroeconomic variables, methods like the Ghouse equation (GE) can be useful for the accurate forcasting [ 25 ]. Such an analysis could shed light on the ground realities, providing insights into how the industry resonates within the broader economic context. Additionally, given the nonlinear nature of arrivals, alternative machine learning approaches may prove beneficial, indicating opportunities to improve forecasting precision and resilience in future research initiatives.

Furthermore, the potential for an in-depth qualitative study with primary data acquisition holds immense promise. Interviews conducted with key stakeholders within the tourism sector could yield qualitative insights that complement and enrich quantitative findings. This qualitative dimension would provide a deeper understanding of the challenges, opportunities, and intricacies that influence Nepal's tourism landscape. In essence, future research efforts could extend beyond the scope of this study to encompass a multifaceted examination of various tourism indicators, microeconomic implications, and qualitative insights drawn from direct interactions with stakeholders. Such holistic research endeavours would contribute towards a more comprehensive comprehension of Nepal's tourism industry and its impact on the overall economy.

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Authors are thankful to the editor and anonymous reviewers for their insightful comments and feedback.

The authors gratefully acknowledge the financial support from Sanming University (grant number 23YG19S).

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Conceptualisation: T.P.; Methodology: T.P, W.L and T.D.; Software: T.P and T.D; Formal anlaysis: T.P and W.L; Data Curation: T.D.; Writing- original draft preparation T.P, W.L, and T.D.; Review and editing T.P,W.L and T.D.; Resource: W.L.; Supervision: W.L

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Paudel, T., Li, W. & Dhakal, T. Forecasting Tourist Arrivals in Nepal: A Comparative Analysis of Seasonal Models and Implications. J Stat Theory Appl (2024). https://doi.org/10.1007/s44199-024-00079-7

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