A Time Series Approach to Assess the Impact of the COVID-19 Pandemic on the South African Tourism Sector

Abstract

The chapter examines tourism flows all over the world with a special case of all foreign tourists to South Africa (SA) from January 2009 to December 2023. A time series approach is used, and the model obtained is used to forecast and evaluate the effects of COVID-19 on total tourist arrivals in SA. The model forecasts are used in comparison with actual tourist arrivals after February 2020 when COVID-19 restrictions were employed. Monthly data on arrivals of all tourists to SA was considered. The ARIMA (0,1,1)(0,1,1)₁₂ model was obtained considering its lowest value of the Bayesian Information Criterion (BIC) through the Box and Jenkins methodology. The forecasting power of the model is evidenced by its Mean Absolute Percentage Error (MAPE) of 1.934579. The effects of COVID-19 are realized form the difference in forecasts made and actual figures recorded from March 2020 when COVID-19 restrictions were effected. This study gives an overview of the contribution being realized from tourism receipts through an analysis of tourist arrivals before, during and after the COVID-19 pandemic. This helps inform various tourism stakeholders on how best the tourism sector may be revived through informative forecasts, good planning and policy formulation strategies.

1. Introduction

The tourism industry has developed to be a major driving force in any host country’s economic, social, cultural, political, environmental and legal sectors due to its spillover effects. The tourism sector is immensely contributing towards foreign currency earnings, infrastructure, foreign direct investments (FDI) and technological development, as examples, in a manner that has gained the attention of many researchers globally. As travel facilitates a vibrant tourism sector, an analysis of the movement of tourist arrivals is of great importance for planning, informed decision making and forecasting for the implementation of necessary and sufficient strategies and policies that help in informative forecasting. An analysis of tourist arrivals is vital as tourist arrivals are among the key indicators for measuring progress towards economic growth, considering the complex nature of the tourism industry and its interconnectivity with other sectors of the economy. The fragile nature of the tourism industry can be evidenced by the recent effects of the COVID-19 pandemic. The COVID-19 pandemic has had a significant impact on the global tourism industry, with far-reaching effects on tourist arrivals. This, therefore, necessitates the need to consider the modelling of tourist arrivals to a host country a necessity for ensuring sustainable development of the tourism sector.

Accurate and informative forecasts of international tourist arrivals are important for the detailed planning of different tourism products that enable utilisation of various decision-making strategies [1, 2, 3, 4, 5]. This is so since tourism flow forecasts facilitate effective description, planning and budgetary control for industries that provide tourism products and services such as accommodation, game reserves, food retail and airlines [6, 7, 8]. Therefore, tourism demand forecasting is critical in the description, planning and policy formulation of the tourism business in avoiding over or under utilisation of tourism resources, according to [9].

The tourism industry has demonstrated its importance over the past few years, and this is shown through the contribution tourism has made globally and to the host country in employment creation, infrastructure development, cultural preservation and foreign currency earnings as examples. Ref. [10] pointed out that, after petroleum, tourism is indeed a major export for developing countries and the most substantial source of foreign exchange earnings. The tourism industry contributed 5% of direct gross domestic product (GDP) globally and 235 million jobs as of 2018, as pointed out by Ref. [11]. In 2020, Ref. [12] pointed out that the Travel and Tourism sector contributed to the creation of 334 million jobs (direct, indirect and induced) and was responsible for 1 in every 4 of all new jobs generated from 2014 to 2019 and US$ 10.3 trillion of global GDP which translates to 10.4%. Ref. [13] highlighted that tourism supports the creation of jobs and encourages notable developments in a country’s foreign currency earnings and technological and infrastructure development. With these statistics, tourism is therefore crucial to the host country and globally as it facilitates a sound legal system, stable political environment, good human security policies, good economic environment, good infrastructure and digitalisation, among others.

Ref. [14] highlighted the importance of tourism research, as tourism is considered a key determinant of business profitability. Modernisation and digitalisation have contributed to increased globalisation, which has led the tourism sector to be among the fastest-growing industries globally as its effects trickle down in tackling, political, legal, cultural, social, environmental and economic development. Ref. [15] highlighted that tourism development is an important tool in promoting economic growth, food security advancement and poverty alleviation. Ref. [16] pointed out that tourism development effectively alleviates poverty and not just a catalyst for economic growth. This, therefore, validates the importance of ensuring long-lasting employment creation and foreign currency earnings, as shown by examples from the tourism industry. Ref. [17] also highlighted on the importance of sustainable tourism as it ensures a reliable stream of income for economic development. With this, informative tourism forecasts ensure a strong foundation for community engagement strategies and optimal usage of tourism resources through collective support from all sectors of the economy, which will ultimately improve the skills development of locals as they try engaging in various income-generating projects.

Sustainability of the tourism sector during and after the COVID-19 era has caught the attention of many academics, researchers and policymakers among the general populace as the pandemic crippled many households’ livelihoods. Ref. [1] pointed out that sustainability is a crucial element in every factor as it ensures continuity. The authors developed a tourism sustainability model for SA, as they try highlight the importance of every sector of a host country in promoting tourist arrivals and optimal utilisation of available resources. The tourism sustainable model by Ref. [1] highlighted the contribution of digitalisation, culture, ecosystem (natural/man-made), community engagement, social, economic, political, legal, infrastructural development and accessibility (air/roads/visas) contribution towards tourist arrivals to a host country. The ecosystem is another variable that promotes the tourism sector; hence, there is a need to consider the varying climatic conditions for a thriving ecosystem that draws more tourists. The model also pointed out the influence of the various components on tourism description, planning, budgetary control, and forecasting. Sustainable tourism guarantees a reliable stream of income for economic development as locals may end up gaining skills such as of weaving baskets and or painting various products for sale to the tourists. This, therefore, validates tourism’s vital contribution towards the achievement of SDGs all around the globe. Ref. [18] pointed out that tourism is a significant economic activity that links with sectors like agriculture, animal husbandry, handicrafts, building, transportation and entertainment and thus ultimately shows the need for sustainable tourism initiatives in avoidance of harsh spillover effects.

Data on tourist arrivals was obtained for this study. The datasets were obtained from monthly reports published by the South African Tourism and Migration statistical release P0351 (http://www.statssa.gov.za/publications/P0351). The data is collected by the Department of Home Affairs (DHA) immigration officers at different ports of entry/exit. In this study, total arrivals data on tourists is used as this has an influence on infrastructure development, employment creation, community engagement, optimal utilisation of resources and sustainability of the tourism sector. This study also validates the need to use tourist arrivals for informative description, planning, budgetary control, forecasting and policy formulation in the presence or non-presence of rare events such as COVID-19.

This chapter is structured as follows: Section 2 provides the literature review, Section 3, the methodology, Section 4, the results and discussions and Section 5 concludes and recommends.

2. Literature review

The volatility of the tourism industry and its interconnectivity with other sectors have been more realised recently during the COVID-19 pandemic, which started in Wuhan, China, in December 2019. COVID-19 spread like wildfire all around the globe, and this saw the World Health Organisation (WHO) declaring it a pandemic and possible measures communicated in containing the virus. The different measures taken in curbing the virus saw movement restrictions being employed, thus negatively affecting tourist arrivals around the world from February 2020 to May 2022 when COVID-19 was declared a non-health emergency. According to Ref. [19], they outlined the massive drop in overnight foreign tourist arrivals from 1464 million to 407 million in 2020 compared to 2019, thus showing the negative effects of global lockdowns and widespread travel restrictions on the tourism sector. Ref. [12] postulated that during the pre-COVID-19 era, the Travel and Tourism sector contributed to 10.5% of all jobs, as well as 10.4% of global GDP. The easing of the travel restrictions on tourist arrivals saw a slight increase in tourist arrivals but remained lower compared with 2019 levels by 69%, according to Ref. [19]. The report points out that global tourist arrivals doubled in 2022 due to strong demand for travel and the easing of travel restrictions, compared to 2021 statistics, but still below the 2019 levels by 34%. Ref. [20] highlighted the contribution made to global GDP of 9.1% from the Travel and Tourism sector, which is an increase of 23.2% from 2022 but below the 2019 level by 4.1%. International visitor spending also increased by 33.1% in 2023, but still below the 2019 figures by 14.4%. These statistics are an indication of how COVID-19 has negatively impacted the tourism sector and ultimately global development.

Tourist arrivals are prejudiced by numerous push/pull factors, and these factors may lead to the extinction of tourism resources when not properly managed. The push factors refer to the conditions that encourage people to travel, such as the desire for a change of scenery, relaxation, or cultural experiences, according to Ref. [21]. On the other hand, the pull factors refer to the characteristics of a destination that attract tourists, such as natural beauty, cultural attractions, or favourable weather conditions [22]. Therefore, tourist arrivals and the effect of COVID-19 on the tourism sector are considered for the South African case in this chapter. SA is a country found in Sub-Saharan Africa. The country occupies the southernmost part of the African continent, and it stretches from the Limpopo River in the north to Cape Agulhas in the south. Ref. [23] postulates that tourism accounts for around 55% of the export component of the services sector in Sub-Saharan Africa compared to the 29% it accounts for other non-Sub-Saharan countries. The report also points out that 36 million tourists were received in Sub-Saharan Africa, with SA receiving 26.4% (9.5 million) of the total tourists. SA prides itself on a vast number of natural resources such as gold, copper, platinum, coal, timber, sugar, wildlife, sea and marine resources, iron ore and fish. SA promotes tourism initiatives, as shown by the different strategies it has employed since its independence on 27 April 1994 from the apartheid era. According to Ref. [24], earnings from tourism were among the leading five sources of foreign currency earning export revenue for 69 developing countries, SA included for the 1995 to 1998 period. Ref. [25] points out that SA is recorded among the top ten countries that had more jobs created from tourism in 2017, thus validating the significance of tourism in human capital and the income status of locals.

Though SA do not substantially depend on tourism for its growth, the contribution of tourism to SA can never be underestimated due to the contribution tourism has made towards SA’s overall economic growth. Ref. [26] highlights the contribution made by travel and tourism, citing that R189.402 billion (in nominal terms) was contributed towards the GDP of SA from tourism activities in 2009. SA recorded a growth in GDP, which outperformed other sectors due to massive direct travel in 2016 [27]. According to Ref. [28], tourist exports increased by 14% to 245,074 Overseas tourists in January 2017 in relation to January 2016. The SA’s tourism is more popular among other developing countries due to its cultural diversity, infrastructure, competitive prices and natural beauty. Examples of intriguing areas of interest are the national parks, Table Mountain in Cape Town, Victoria, and Alfred waterfront. In 2002, an International Tourism growth strategy was organised based on intensive market segmentation. This strategy increased the visibility of the SA’s tourism industry, and this contributed to a sharp rise in tourist arrivals from the Overseas and African markets by 11.1% to 6.4 million. The Department of Environmental Affairs and Tourism (DEAT), Department of Trade and Industry (DTI) and South African Tourism initiated a competitiveness study in 2004 in their quest to develop products, infrastructure, services and strategies that attract and accommodate tourists for more acceptance and visibility.

SA prides itself on its tourism pull factors, which are rich cultural diversity, historical attractions, outdoor adventures, beach destinations, wildlife safaris, Winelands, urban centres, and ecotourism as well as its developed tourism infrastructure and favourable exchange rates have made SA a more interesting tourist destination. This Sub-Saharan country also boasts of hosting some notable events, including the 2010 soccer Federation Internationale de Football Association (FIFA) World Cup, and this was the largest event of them all. These notable events promoted the growth of SA’s economy and boosted the tourism sector’s visibility. Hence, revamping tourism facilities increases adaptability, visibility and acceptability from the global community, which results in a subsequent increase in tourist arrivals. The economic contribution of SA’s tourism sector was predicted to be R124.4 billion in the year 2020 compared to R91.2 billion in 2015 [29]. From this strategy, it was shown that a 15.4% increase in tourist arrivals was realised in the first half months of 2016, validating the thrust towards fulfilling the 2015 tourism contributions’ projections. The sector also claimed to be massive enough to create more job vacancies and contribute towards SA’s GDP, considering its high unemployment and poverty rates experienced during the apartheid era. According to Ref. [30], SA’s GDP rose 1.3% in 2017 and 0.8% in 2018.

SA is one of the most affected countries in Sub-Saharan Africa affected by the COVID-19 pandemic, crippling tourism activities due to travel restrictions, thus affecting SA tourism’s pull factors. Ref. [31] highlighted that COVID-19 travel restrictions and lockdowns created a significant push factor as this limited tourist travel as the emergence of new variants and the potential for future outbreaks created a sense of uncertainty and caution among travellers. According to Ref. [32], SA recorded 4,016,157 cases and 102,146 deaths from COVID-19 as of September 2022. Despite SA having high rates of COVID-19 cases, the SA government initiated ways of boosting the economy through the recovery of the tourism, hospitality, leisure and entertainment industries, according to Ref. [33]. According to Ref. [34], SA’s ‘Tourism Recovery Plan’ initiated in 2021 aimed to sustain jobs and livelihoods, provide new jobs, match demand and supply as well as strengthen the transformation of the tourism industry.

Understanding the dynamics of COVID-19 or rare events and their impact on tourist arrivals is crucial for tourism stakeholders, policymakers and industry leaders to develop effective strategies for recovery and resilience in the post-pandemic era. Ref. [35] highlighted that tourism is indeed a driver for prosperity and a reducer of poverty when the author studied the contribution of tourism to SA. Key indicators used in monitoring the progress of the tourism sector were also considered in tracking the progress of the tourism sector recovery process, and these indicators are the number of tourist arrivals, revenue for key tourism industries as well as their contribution to GDP and employment according to 2020/21 State of Tourism Report (STR). Given that the number of tourist arrivals to SA is one of the key indicators of measuring tourism progress, this data is to be used in model development of a time series model for tourist arrivals from various places around the globe to SA.

Seasonality refers to the regular pattern that occurs on a yearly basis, and its effect plays a crucial role in tourism earnings. As tourist arrivals depend on various factors, [36] pointed out some drivers of seasonality that affect tourist arrivals as often driven by factors such as weather, school holidays and cultural events. Research has shown that tourist arrivals tend to peak during certain seasons, such as summer or holiday periods, and decline during other times of the year [37]. According to Ref. [38], seasonality can have significant impacts on tourism-dependent economies, as it can lead to fluctuations in revenue, employment and infrastructure utilisation. Therefore, seasonality, occurrence of rare events such as COVID-19 and the contribution of tourism to a host country’s foreign currency earnings has attracted a lot of attention from academia and beyond. Qualitative and quantitative research have been carried out with the thrust of gaining a deeper understanding of the tourism sector, which has proven to be a critical contributor to economic development worldwide and mostly to countries that depend on tourism-related business. Models that have been used by various researchers for forecasting purposes are regression, econometric, time series, judgemental and artificial intelligence-based models [39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]. The contribution towards forecasting tourist arrivals aims to ensure the development of methodologies that can best be adopted for improved tourism service delivery and, ultimately, growth.

Univariate time series approaches to modelling encompass deterministic and stochastic models, which have been widely used in forecasting tourist arrivals as they only require information on the past behaviour of a variable over time. Deterministic time series approaches consist of extrapolation techniques such as smoothing techniques, trend models and seasonally adjusted models as examples. Ref. [51] highlighted the four types of stochastic time series models, which are the Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA). Seasonal deterministic models and stochastic seasonal models were also considered due to their applicability in addressing seasonally influenced variables. Forecasting tourism demand through tourist arrivals has seen the extensive application of Holt’s additive and multiplicative smoothing models, ARIMA and Vector autoregressive (VAR) models. However, Refs. [46, 52] postulated on the seasonal ARIMA (SARIMA) models and their ability to perform better with some variables as compared to ARIMA models due to their ability to consider the seasonality component that tends to prevail in some tourism data sets.

Various research has been carried out investigating the association that exists among tourism development in relation to economic growth, especially for economies that depend largely on tourism [1, 2, 5, 46, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61]. Univariate time series have been used all around the globe in their quest for an in-depth analysis of tourism demand. SARIMA models have proved to be more popular and reliable using monthly or quarterly time series datasets [1, 57, 62, 63, 64, 65, 66, 67].

In this chapter, a univariate time series approach to modelling total tourist arrivals to SA will be considered.

3. Materials and methods

A time series approach to modelling helps to give the behaviour of a variable over time together with an innovative term. These models have been popular for tourism demand analysis due to their efficacy in forecasting tourist arrivals. In this section, ARIMA and SARIMA models established by Box and Jenkins are explained.

3.1 ARIMA (p,d,q) model

ARIMA models have been adopted in modelling and forecasting of time series data. These ARIMA models are integrated with the Autoregressive Moving Average (ARMA) process. For non-stationary time series data, such as the distribution of tourist arrivals, the Box-Cox transformation is employed in determining the best data transformation for use until the data is made stationary in the mean. Popular data transformation methods are square root, inverse and logarithmic transformation. A time series $H_t$ follow an ARIMA model if the $d^{\mathit{th}}$ difference ${∆}^d{H}_t=W_t$ is a stationary ARMA process.

The ARIMA $\left(p,d,q\right){\left(P,D,Q\right)}_S$ or SARIMA is of the form:

$${\phi }_p\left(B\right){\mathrm{\Phi }}_{\mathrm{P}}\left(\mathrm{B}\right){\mathrm{\Delta }}^{\mathrm{d}}{\mathrm{\Delta }}_{\mathrm{S}}^{\mathrm{D}}{\mathrm{H}}_{\mathrm{t}}={\mathrm{\theta }}_{\mathrm{q}}\left(\mathrm{B}\right){\mathrm{\Theta }}_{\mathrm{Q}}\left(\mathrm{B}\right){\mathrm{e}}_{\mathrm{t},}$$E1

where

p is the order of the non-seasonal autoregressive part,

d is the order of integration, which is a whole number for discrete time series,

P is the order of the seasonal autoregressive seasonal part,

D is the seasonal differencing,

S is the maximum number of seasons (S can be 4 for quarterly data or 12 for monthly data),

Q represents the order of the non-seasonal moving average part,

Q represents the order of the seasonal moving average part,

${\mathrm{\Delta }}^{\mathrm{d}}$ represent a non-seasonal difference with ${\mathrm{\Delta }}^{\mathrm{d}}={\left(1-\mathrm{B}\right)}^{\mathrm{d}}$,

${\mathrm{\Delta }}_{\mathrm{S}}^{\mathrm{D}}$ represent the seasonal difference with ${\mathrm{\Delta }}_{\mathrm{S}}^{\mathrm{D}}={\left(1-{\mathrm{B}}^{\mathrm{S}}\right)}^{\mathrm{D}}$.

3.2 Model adequacy

The Box-Jenkins methodology employs three main steps to model building which are model identification, model estimation and model diagnostic checking (model adequacy checking). Model adequacy checking play a crucial role in determining model accuracy as well as model’s forecasting power. Model diagnostic checking involves an examination of the model specified and estimated’s residuals in addressing to the assumptions of constant variance (homoscedasticity), linearity, autocorrelation, normality. On model specification, one need to consider the area the data is coming from as well as data stationarity as this influence fulfilment of constant variance, autocorrelation and normality assumptions. The Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Mean Absolute Scaled Error (MASE) are measures primarily adopted for the model’s goodness of fit. In this study, the MAPE and the RMSE are to be used to evaluate the forecasting accuracy of the model developed. The model to be considered is the one with the least value of BIC.

3.3 Box-Ljung test

The Box-Ljung test is a diagnostic tool used in checking the fitted model’s residuals for serial dependence. Its test statistic is denoted by

$${\chi }^2=n\left(n+2\right)\sum _{k=1}^h\frac{{\widehat{\rho }}_k^2}{n-k},$$E2

where n is the sample size, ${\widehat{\rho }}_k$is the estimate of the sample autocorrelation at lag k, and h is the number of lags being tested.

3.4 Bayesian information criterion (BIC)

The BIC is used for model selection, when the model with a lower BIC is considered the better model from a set of finite models. Mathematically, it can be represented as:

$$\mathit{BIC}=\mathit{ln}\left(n\right)k-2\mathit{ln}\left(\widehat{L}\right),$$E3

where $\left(\widehat{L}\right)$ is the maximum value of the likelihood function, n is the number of data points and k, being the number of free parameters to be estimated.

3.5 Data analysis

Monthly total tourist arrivals data to SA were obtained from http://www.statssa.gov.za/publications/P0351 of the Statistics South Africa’s (Stats SA) through the Tourism and Migration P0531 reports for the January 2009 to December 2023 period. Monthly data from January 2009 to February 2019 were used as the train data for developing a forecasting model, and this is also data from the pre-COVID-19 era; data from March 2019 to December 2023 was used as the test data set. The period from March 2019 to February 2020 is considered the validation period as it helps highlight model adequacy through a comparison of actual and forecasted values and data for validation still from the pre-COVID-19 era. The test data from March 2020 to the end of April 2023 is considered the COVID-19 era, and data from May 2023 to December 2023 still from test data is considered the post-COVID-19 era. The pre-COVID-19 era, validation period, COVID-19 era and post-COVID-19 era will help give a visual view of tourist arrivals dynamics for the SA case as well as the effect of a rare event COVID-19 era on tourist arrivals. The R software package was used in data analysis.

4. Data analysis on total tourist arrivals in South Africa

4.1 Model development and analysis

Model development and analysis, started with an analysis of the descriptive statistics. The descriptive statistics were obtained using data from January 2009 to December 2023.

The minimum number of tourists per month is 29,341, with 1,103,940 as its corresponding maximum value, as shown in Table 1 for the period under consideration. The values of this dataset are too far apart, as evidenced by its range; hence, data from the COVID-19 period will be excluded in model development as we try to highlight the effects of COVID-19 on time series model forecasts.

Mean	First Qu.	Min.	Max.	Median	Third Qu.
674,244	614,740	29,341	1,103,940	726,628	823,353

Table 1.

Descriptive statistics of SA tourists.

The plot of all tourists to SA in Figure 1 indicates that the data follow a steady and fluctuating increasing pattern with seasonality from January 2009 to February 2020, a massive drop from March 2020, and a sluggish increase as COVID-19 restrictions were continuously being reviewed. The peak values are recorded in December each year, typically because of the festive season. The lowest values were recorded in February, May and June for each year. A time plot of the train data is done, as shown in Figure 2.

Figure 1.

Time series plot on total tourist arrivals to SA.

Figure 2.

Time plot of total tourist arrivals from January 2009 to February 2019.

Figure 2 show that total tourist arrivals to SA depict an increasing fluctuating pattern. Decomposition of time series data of total tourist arrivals is performed to gain a deeper understanding of the various components of a time series present in the total tourist arrivals data, as shown in Figure 3.

Figure 3.

Decomposition of the additive time series model on tourist arrivals to SA.

Observing the four graphs in Figure 3 on the decomposition of monthly total arrivals data, one can see the need to deal with the increasing pattern. The total tourist arrivals data set shows seasonality as evidenced by regular fluctuating patterns, hence the need for non-seasonal and seasonal differences. The Box-Cox transformation is employed on the data before the non-seasonal and seasonal difference as this serves as a diagnostic tool to identify potential data transformations necessary in attaining normality, as shown in Figure 4.

Figure 4.

Box-Cox plot of total tourist arrivals.

The Box-Cox transform in Figure 4 shows a lambda = 0.5, thus indicating the need for a square-root transformation of the total number of tourist arrivals. The square-root transformed data is deseasonalised and detrended through a first and seasonal differenced tourism data and checked for stationarity using the Augmented Dickey-Fuller (ADF) test showing a p-value of 0.01 confirming stationarity. The Kwiatkowski–Phillips Schmidt–Shin (KPSS) test for stationarity is done on the square root, transformed data that is deseasonalised and detrended through a first and seasonal differenced and a p-value of 0.01 is obtained, indicating the data is now stationary and ready for use. Graphs of the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots of square-root, first and seasonal differenced tourism data are in Figure 5.

Figure 5.

ACF and PACF plot of square-root, first and seasonal differenced tourism data.

The ACF plot shows that the model cuts off at lag 1, with a seasonal spike at lag 12. The PACF plot is cutting off at lag 2, suggesting a SARIMA(0,1,1)(1,1,2)₁₂ as the initial model. The extended autocorrelation function (EACF) is shown in Table 2 to confirm the tentative model further.

AR/MA
	0	1	2	3	4	5	6	7	8	9	10	11	12	13
0	x	o	o	o	o	o	o	o	o	o	x	x	o	o
1	x	x	x	o	o	o	o	o	o	o	o	x	x	x
2	x	o	o	o	o	o	o	o	o	o	o	x	o	o
3	o	o	o	o	o	o	o	o	o	o	o	x	o	o
4	x	x	o	o	o	o	o	o	o	o	o	x	o	o
5	x	x	o	o	o	o	o	o	o	o	o	x	x	o
6	x	x	o	o	o	o	o	o	o	o	o	x	o	o
7	x	x	o	o	o	o	o	o	o	o	o	x	o	o

Table 2.

The EACF plot of the square-root, first and seasonal differenced tourism data.

The EACF plot in Table 3 of the square root, first and seasonal differenced tourism data suggests the existence of models such as ARIMA (0,1,1)(0,1,2)₁₂, ARIMA (0,1,1)(1,1,3)₁₂, ARIMA (0,1,1)(0,1,2)₁₂, and ARIMA (2,1,1)(0,1,1)₁₂ as examples. The tentative models and other potential models are considered, with their results tabulated in Table 3 taking into consideration the model adequacy measure, BIC.

Model	BIC	RMSE	MAPE
ARIMA $\left(0,1,1\right){\left(0,1,2\right)}_{12}$	1037.08	23.45012	1.922099
ARIMA $\left(0,1,2\right){\left(0,1,2\right)}_{12}$	1041.4	23.44053	1.922912
ARIMA $\left(1,1,1\right){\left(0,1,2\right)}_{12}$	1041.52	23.44254	1.919928
ARIMA$\left(\mathbf{0},\mathbf{1},\mathbf{1}\right){\left(\mathbf{0},\mathbf{1},\mathbf{1}\right)}_{\mathbf{12}}$	1034.81	23.68839	1.934579
ARIMA $\left(1,0,1\right){\left(0,1,2\right)}_{12}$	1051.01	23.50619	1.91125
ARIMA $\left(3,1,1\right){\left(1,1,1\right)}_{12}$	1044.31	23.28691	1.928692
ARIMA $\left(2,1,1\right){\left(0,1,1\right)}_{12}$	1041.53	23.4845	1.929295

Table 3.

Model adequacy checking.

Note: Better model is in bold.

The ARIMA $\left(0,1,1\right){\left(0,1,1\right)}_{12}$ was considered as the better model due to its low value of BIC, as presented in Table 3, despite its corresponding high values of RMSE and MAPE. The model has a MAPE value of 1.934579%, which is less than 10%, implying a high accuracy level in forecasting. A plot of the model residual is shown in Figure 6.

Figure 6.

Residual, ACF and histogram plots of residuals for the ARIMA (0,1,1)(0,1,1)₁₂.

The residuals obtained from the ARIMA (0,1,1)(0,1,1)₁₂ are plotted as shown in Figure 6, highlighting that the model chosen is a good fit for the total tourist arrivals data with residual behaving in a white noise fashion. The histogram of residuals does indicate that the normality of residuals is being reasonably fulfilled. The Box-Ljung test’s p-value of 0.5548 approves independence of residuals.

Model parameters of the ARIMA $\left(0,1,1\right){\left(0,1,1\right)}_{12}$ in Table 4 are all significant. The model has managed to capture the trend and seasonality with a monthly pattern present in the square-root transformed total tourist arrivals data. A plot of the train data, forecasts and test data before during and after the COVID-19 era is shown in Figure 7.

	MA1	SMA1	z value	Pr(> |z|)
Coefficients	−0.6100	−0,7185	−7.6737	1.671e-14
Standard error	0.079490	0.085817	−8.3721	2.2e-16

Table 4.

Model parameters of the ARIMA $\left(0,1,1\right){\left(0,1,1\right)}_{12}$.

Figure 7.

Plot of square root, detrended and seasonal differenced train data and test data on total tourist arrivals.

The 82 ahead forecasts of the ARIMA $\left(0,1,1\right){\left(0,1,1\right)}_{12}$ model forecasts are shown in Figure 7. The plot in Figure 7 is in four phases, which show the train data phase, the model validation phase, the COVID-19 pandemic phase and the post-COVID-19 pandemic phase. The validation phase between the two green lines, as shown in Figure 7, solidifies the model’s adequacy in forecasting total tourist arrivals in the SA pre-COVID-19 era. The close pattern between the forecasts and the validation data is evidence of a better model obtained, as the pattern between the forecasts and the validation data shows very little variability that can be of concern. The COVID-19 era and post-COVID-19 phase show how devastating the COVID-19 pandemic inflicted on the tourism and hospitality sector, as evidenced by a drastic decline in the number of total tourist arrivals from March 2020 due to travel bans imposed by governments in curbing the pandemic. This period is shown in Figure 7 as the period between the second green line and the purple line. The COVID-19 era in this study is the period when strict measures were taken to curb the virus and the period when COVID-19 was stated as no longer a public health emergency starting 5 May 2023, even though some strict COVID-19 measures had been loosened. The substantial increase in the number of total tourist arrivals after the strict lockdown had been lifted is evidence enough that the tourism sector in SA is a necessity in influencing people’s behaviours and spending as they try to deal with the aftershock of the COVID-19 pandemic. The period beyond the purple line shows that the total pattern is continuously increasing. Statistics SA (2023) reported that 1.4 million same-day visitors were recorded in 2022 considering the massive drop in tourist arrivals from February 2020, thus highlighting a massive tourism recovery.

The ARIMA $\left(0,1,1\right){\left(0,1,1\right)}_{12}$ can be expanded as follows:

$$H_t=H_{t-1}+H_{t-12}-H_{t-13}+e_t-{\theta }_1{e}_{t-1}-{\mathrm{\Theta }}_1{e}_{t-12}+{\theta }_1{\mathrm{\Theta }}_1{e}_{t-13}$$E4

where ${\Theta }_1$ and ${\theta }_1$ are the model coefficients and $e_t$ is a random error term. With the parameter estimates, the model becomes:

$$H_t=H_{t-1}+H_{t-12}-H_{t-13}+e_t+0.6100e_{t-1}+0.7185e_{t-12}+0.438285e_{t-13}$$E5

The coefficients of the estimated model are all significant as they are less than one in magnitude, and the model used to obtain forecasts from March 2019 to December 2025. Actual values from March 2019 to December 2023 were used to determine the accuracy of forecasts before, during and after the COVID-19 era.

5. Conclusions and recommendations

5.1 Conclusions

The main thrust of this chapter was to give an insight on trends in tourist arrivals before, during and after the COVID-19 pandemic, with SA considered as a case study using data of total tourist arrivals to SA from January 2009 to December 2023. Tourist arrivals are one key indicator used in determining the viability of the tourism sector in a host country as well as around the globe. Tourist arrivals are prejudiced by numerous push/pull factors, and these factors may lead to the extinction of tourism resources when not properly managed. Tourism has been considered a driver of the economy, be it developing or developed economies, SA included, as the sector has demonstrated continuous growth in employment creation, infrastructure development, cultural preservation and foreign currency earnings as examples. The industry is reported to have contributed to 5% of direct GDP globally and 235 million jobs as of 2018, according to [11]. In 2020, [12] highlighted that the Travel and Tourism sector contributed to the creation of 334 million jobs (direct, indirect and induced) and was responsible for 1 in every 4 of all new jobs generated from 2014 to 2019 and US$ 10.3 trillion of global GDP which translates to 10.4%. These statistics are, therefore, reason enough why the modelling of tourist arrivals needs to be prioritised for informative planning, decision making and policy formulation, considering the occurrence of rare events.

The data used exhibits a steadily increasing variance and seasonality. The square-root transformation was employed to tame the increasing variance. The transformed data was detrended and deseasonalised for model building. An ARIMA (0,1,1)(0,1,1)₁₂ model was fitted and considered due to its low BIC value. Ref. [1] highlighted that, as the COVID-19 pandemic is a random event, their consequences are therefore not subject to forecasting as rare events may come in a nature that destroys infrastructure and accessibility to a host country, thus making accessibility more difficult, which will in turn affect impact negatively on expected over actual results. However, rare events, such as COVID-19, do not invalidate the need for statistical modelling of tourist arrivals due to the many benefits of forecasting tourist arrivals. Forecasts help responsible authorities to come up with various models that will help in the optimal utilisation of resources for increased viability and sustainability of the tourism sector through full stakeholder engagement strategies that will minimise issues of bottlenecks during implementation.

5.2 Recommendations

With the SA tourism industry contributing immensely to the country’s GDP and employment creation, according to Ref. [68], good forecasts are therefore needed for informative planning, restructuring and growth as well as employment of aggressive marketing strategies. The SA tourism sector needs maximise on activities and products they can improve or develop such as twin packs of product coupling for use during its peak periods and maximum spending by tourists. Gender and age-sensitive tourism products also need to be considered. Social media platforms such as Facebook, TikTok, Instagram, twitter, and WhatsApp have been knowing of late to impact positively on information dissemination coupled with the use of prominent socialites in marketing. The tourism sector may therefore need to make use of socialites and social media platforms in marketing tourism products and dissemination of information.

According to Ref. [31], understanding the effects of seasonality and push/pull factors on tourist arrivals is crucial for destination managers, tourism operators and policymakers in developing effective strategies for rebuilding and resilience of the tourism sector. Ref. [69] also supports the contribution of seasonality on tourist arrivals to SA, pointing out that the country’s peak tourism season is typically during the summer months (November to March), when the weather is warm and sunny. This information helps in maximising products or services to be offered during the peak periods, diversification of tourism products or services, targeting new market segments, maximising new weather trends and their effect on the ecosystem and adapting to changing consumer preferences and travel patterns. Age and gender issues may also be considered in product development.

With artificial intelligence (AI) and machine learning (ML) taking a toll in almost every sector of the economy, the authors propose the adoption of AI-based algorithms in tourism modelling.