This paper analyses seasonality and persistence in the number of UK overseas visitors applying a fractional integration framework to (monthly and quarterly) data from 1986 to 2017. The results indicate that long memory is present in the series and the degree of persistence is higher for seasonally adjusted data, with shocks having transitory but long-lasting effects.Ministerio de Economía y Competitivida

Caporale, GM

Gil-Alana, L

Tourism Economics

Brunel University Research Archive

Research NoteUK overseas visitors: Seasonalityand persistenceGuglielmo Maria CaporaleBrunel University London, UKLuis Alberiko Gil-AlanaUniversity of Navarra, SpainAbstractThis article analyses seasonality and persistence in the number of UK overseas visitors applying afractional integration framework to (monthly and quarterly) data from 1986 to 2017. The resultsindicate that long memory is present in the series and the degree of persistence is higher forseasonally adjusted data, with shocks having transitory but long-lasting effects.Keywordslong memory, persistence, seasonality, UK overseas visitorsIntroductionThis article analyses seasonality and persistence in the number of UK overseas visitors applying afractional integration framework to (monthly and quarterly) data from 1986 to 2017. These twofeatures are very common in tourism-related series, and despite the existence of numerous studiesanalysing them, there is still no consensus on the most appropriate empirical framework to apply.Seasonality can be modelled either deterministically (using seasonal dummy variables) or sto-chastically; in the latter case, either stationary Auto Regressive Moving Average (ARMA) sea-sonal models or seasonal unit roots (as in Dickey et al., 1984 or Hylleberg et al., 1990) can be used.Examples of tourism studies using these techniques are Kim and Moosa (2001), Alleyne (2006),Shen et al. (2009), Lean and Smyth (2008) and so on. As for persistence, unit root methods (e.g.Dickey and Fuller, 1979; Phillips and Perron, 1988; Elliot et al., 1996; etc.) have been widely usedto assess whether the effects of shocks are transitory or permanent and the dynamic adjustmentprocess (Narayan, 2003; Perles-Ribes et al., 2016).Corresponding author:Guglielmo Maria Caporale, Department of Economics and Finance, Brunel University London, London UB8 3PH, UK.Email: guglielmo-maria.caporale@brunel.ac.ukTourism Economics1–5ª The Author(s) 2018Article reuse guidelines:sagepub.com/journals-permissionsDOI: 10.1177/1354816618817884journals.sagepub.com/home/teuThe fractional integration model estimated in the present note is more general than others onlyallowing for integer degrees of integration, namely either 0 (in the case of stationary series) or 1 (inthe case of nonstationary unit root processes). Fractional integration methods have already beenapplied to analyse tourism data in a few other studies such as Cunado et al. (2004), Nowman andVan Dellen (2012) and Gil-Alana et al. (2015). Using this approach, we show that the degree ofpersistence of the series changes when applying standard seasonal adjustment procedures. This isthe key finding of our note, namely the degree of persistence of the series, measured by the dif-ferencing parameter, changes when seasonal adjustment is carried out. The remainder of the articleis structured as follows: “Methodology” section outlines the methodology; “Data and empiricalresults” section describes the data and presents the main empirical results, while “Conclusions”section offers some concluding remarks.MethodologyLet fyt, t ¼ 1, 2, . . . , Tg denote the time series of interest. Then consider the following modelyt ¼ b0 þ b1t þ xt; ð1 LÞdxt ¼ ut; t ¼ 1; 2; . . . ð1Þwhere b0 and b1 are unknown and stand respectively for the intercept and the coefficient on a lineartime trend, and xt is assumed to be I(d), where d can be any real value, thus also allowing forfractional degrees of integration. In this context, ut is by definition I(0) and is assumed to follow aseasonal AR process of the following formðLsÞut ¼ et; t ¼ 1; 2; . . . ð2Þwhere Ls is the seasonal lag operator (Lsut ¼ uts) and et is a white noise process. The chosen spe-cification includes stochastic seasonality because we find no evidence of deterministic seasonalitywhen estimating simple models with seasonal (quarterly and monthly) dummy variables, all theircoefficients not being statistically significant (these results are not reported for brevity’s sake).When the data are seasonally adjusted (SA), instead of (2) we assume that ut is autocorrelated asin the exponential spectral model of Bloomfield (1973), which is a non-parametric approach ofapproximating ARMA models with a small number of parameters. The estimation is carried outusing the Whittle function in the frequency domain (Dahlhaus, 1989; Robinson, 1994) and theFortran programme codes of are available from the authors upon request.Data and empirical resultsThe series analysed are the number of UK overseas visitors (All visits, thousands), quarterly andmonthly, non-seasonally adjusted (NSA) and SA, for the time period 1986 (m1/q1)  2017(m12/q4). The data were obtained from the Office for National Statistics (Overseas travel andtourism time series (OTT)).Figure 1 displays the series of interest. These appear to be highly persistent, and seasonalpatterns are very noticeable in the case of the seasonally unadjusted data. Tables 1 and 2 report theresults for the monthly and quarterly data, respectively. In all cases, we estimate the model givenby equation (1); as already mentioned, the error term is assumed to follow a seasonal auto-regressive process in the case of the raw data, and Bloomfield’s (1973) autocorrelation model inthe case of the SA ones. Both tables show the estimated values of d along with the 95% confidenceintervals for the three standard cases of (i) no deterministic terms (i.e. b0 ¼ b1 ¼ 0 a priori in (1)),2 Tourism Economics XX(X)01000(a) (b)(c) (d)20003000400050002017q41986m11986q1 2017q41986q1010002000300040002017m122017m12 1986m1020004000600080001000012000020004000600080001000012000Figure 1. Time series plots. (a) Non-seasonal monthly data, (b) seasonally adjusted monthly data, (c) non-seasonal quarterly data and (d) seasonally adjusted quarterly data.Table 1. Estimated coefficients for the monthly data.Monthly data No terms An intercept A linear time trendNSA 0.36 (0.29, 0.48) 0.49 (0.46, 0.54) 0.36 (0.29, 0.43)rs¼12 ¼ 0.906 rs¼12 ¼ 0.892 rs¼12 ¼ 0.906SA (no autocorrelation) 0.63 (0.57, 0.69) 0.57 (0.54, 0.61) 0.50 (0.46, 0.56)SA (autocorrelated) 0.82 (0.73, 0.94) 0.73 (0.65, 0.84) 0.70 (0.62, 0.83)Note: NSA: non-seasonally adjusted; SA: seasonally adjusted.Table 2. Estimated coefficients for the quarterly data.Quarterly No terms An intercept A linear time trendNSA 0.35 (0.28, 0.46) 0.60 (0.53, 0.70) 0.44 (0.30, 0.60)rs¼12 ¼ 0.950 rs¼12 ¼ 0.965 rs¼12 ¼ 0.962SA (no autocorrelation) 0.87 (0.77, 1.00) 0.86 (0.76, 1.02) 0.85 (0.73, 1.01)SA (autocorrelated) 0.87 (0.68, 1.06) 0.74 (0.61, 0.98) 0.73 (0.50, 1.00)Note: NSA: non-seasonally adjusted; SA: seasonally adjusted.Caporale and Gil-Alana 3(ii) with an intercept only (b0 unknown and b1 ¼ 0), and with an intercept and a linear trend (bothb0 and b1 estimated from the data), with the significant coefficients (on the basis of the t-statistics)in bold. A time trend appears to be required in all cases.Table 1 shows that for the raw monthly data, the estimated value of d is equal to 0.36, and theconfidence interval is above 0 and below 0.5, which implies stationarity and long-memorybehaviour; further, the seasonal AR coefficient is extremely high (0.906). When the data areSA, the estimated value of d increases sharply, being equal to 0.50 with uncorrelated errors, and0.70 under Bloomfield autocorrelation. In both cases, the confidence intervals only include valuesbelow 1, which implies mean-reverting behaviour.Table 2 reports the estimates for the quarterly data; these are slightly higher than in the monthlycase, but the general pattern is the same: for the raw data, the estimated value of d is 0.44 and theconfidence interval excludes the cases of d ¼ 0 and d ¼ 1; for the SA data, the estimates of d arehigher, namely 0.85 with white noise errors and 0.73 with autocorrelated errors (and closer to theunit root case).ConclusionsIn this short note, we have examined persistence and seasonality in the number of UK overseasvisitors using fractional integration techniques. The main findings can be summarized as follows:the estimates of d are in the interval (0, 1) in all cases, thus suggesting the presence of long memoryand fractionally integrated behaviour; higher values are obtained with the SA data and also for thequarterly rather than the monthly ones. This is an important result, which implies that a higherdegree of persistence is found when using SA data, that is, the effect of shocks are estimated to lastfor longer in this case. From the point of view of policymakers whose task is to design appropriatepolicy responses to exogenous shocks, it would therefore be advisable to use unadjusted data todetermine the degree of persistence and decide on how it should be handled using policy tools. Inthe case of UK overseas visitors, our results imply that shocks will have transitory but long-lastingeffects, and such evidence should inform tourism policies.AcknowledgementsComments from the Editor and an anonymous reviewer are gratefully acknowledged.Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/orpublication of this article.FundingThe author(s) disclosed receipt of the following financial support for the research, authorship, and/or publi-cation of this article: This work was financially supported by the Ministerio de Economı́a y Competitividad(ECO2017-85503-R) to LAG-A.ORCID iDGuglielmo Maria Caporale https://orcid.org/0000-0002-0144-4135ReferencesAlleyne D (2006) Can seasonal unit root testing improve the forecasting accuracy of tourist arrivals? TourismEconomics 12: 45–64.4 Tourism Economics XX(X)Bloomfield P (1973) An exponential model in the spectrum of a scalar time series. 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Current Issues in Tourism 2016; 19(12): 12101–1234.Phillips PCB and Perron P (1988) Testing for a unit root in time series regression. Biometrika 75: 335–346.Robinson PM (1994) Efficient tests of nonstationary hypotheses. Journal of the American Statistical Asso-ciation 89(428): 1420–1437.Shen S, Li G and Song H (2009) Effect of seasonality treatment on the forecasting performance of tourismdemand model. Tourism Economics 15(4): 693–708.Author biographiesGuglielmo Maria Caporale (Laurea, LUISS; MSc Econ, PhD Econ, LSE) is Professor of Economics andFinance and Director of the Centre for Empirical Finance at Brunel University London; also Visiting Pro-fessor at LSBU, Research Professor at DIW Berlin, CESifo Research Network Fellow and AssociateResearcher at ICEF, HSE, Moscow. Previously Research Officer at NIESR; Research Fellow and then SeniorResearch Fellow at LBS; Professor of Economics at UEL; Professor of Economics and Finance and Directorof the Centre for Monetary and Financial Economics at LSBU.Luis Alberiko Gil-Alana pursued BSc in Economics, University Basque Country, Bilbao, Spain. MSc inMonetary Economics, Center Monetary and Finance Studies, Bank of Spain, Madrid. MSc in Econometricsand PhD in Economics, London School of Economics. Research and Teaching Assistant, London School ofEconomics. Researcher, European University Institute, Florence, Italy. Research officer, London BusinessSchool. Visiting Researcher, Humboldt University, Berlin, Germany. Assistant Professor, Associate Profes-sor, Professor of Econometrics, University of Navarra, Pamplona, Spain. Presenter at conferences in the field.Scientific Committee Member, Advances in Tourism Economics, Lisbon, Portugal.Caporale and Gil-Alana 5

UK overseas visitors: seasonality and persistence

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UK overseas visitors: seasonality and persistence

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