Fractional differencing in stock market price and online presence of global tourist corporations

Abstract

Purpose This work aims to explore the behavior of stock market prices according to the autoregressive fractional differencing integrated moving average model. This behavior will be compared with a measure of online presence, search engine results as measured by Google Trends. Design/methodology/approach The study sample is comprised by the companies listed at the STOXX® Global 3000 Travel and Leisure. Google Finance and Yahoo Finance, along with Google Trends, were used, respectively, to obtain the data of stock prices and search results, for a period of five years (October 2012 to October 2017). To guarantee certain comparability between the two data sets, weekly observations were collected, with a total figure of 118 firms, two time series each (price and search results), around 61,000 observations. Findings Relationships between the two data sets are explored, with theoretical implications for the fields of economics, finance and management. Tourist corporations were analyzed owing to their growing economic impact. The estimations are initially consistent with long memory; so, they suggest that both stock market prices and online search trends deserve further exploration for modeling and forecasting. Significant differences owing to country and sector effects are also shown. Originality/value This research contributes in two different ways: it demonstrate the potential of a new tool for the analysis of relevant time series to monitor the behavior of firms and markets, and it suggests several theoretical pathways for further research in the specific topics of asymmetry of information and corporate transparency, proposing pertinent bridges between the two fields.

A note on time series differencing

“…The proposed differencing method allows to achieve accuracy level comparable to the third-order Runge-Kutta scheme yet significantly more efficiently. More recently, fractional differencing was applied to study stock market behavior and compared to online presence [6]. The authors find that both stock market prices and online search trends require further exploration for modeling and forecasting.…”

Corporate impact of carbon disclosures: a nonlinear empirical approach

“…Such a nonlinear approach has been widely applied in financial studies (Panas, 2001;Mynhardt et al, 2014;Ikeda, 2017;Ftiti et al, 2019;Arbi Madani and Ftiti, 2020), but a research gap still exists in the environmental and carbon disclosure context. Second, we draw on the contribution of Flores-Muñoz et al (2019b) to introduce a new proxy of "online popularity", i.e. Google Trends series, to enrich the empirical evidences on stakeholders' reactions to carbon disclosure practices.…”

“…Following Flores-Muñoz et al's (2019a, 2019b reasoning, Mandelbrot's (1983) dimension could be connected with time series analysis by means of the so-called "long-range dependence systems" or "long memory processes". Specifically, the autoregressive fractionally integrated moving average (ARFIMA) estimation model, originally proposed by Granger and Joyeux (1980), is an useful technique to analyse the fractal dimension in time series (Appendix 2 and related references for technical details).…”

“…Glen (2005) also identifies the chaos theory as an alternative instrument to understand markets behaviour going beyond the EMH. The ARFIMA technique is applied in some previous empirical studies, as shown in our previous literature review in Section 3 (Panas, 2001;Flores-Muñoz et al, 2019b;Arbi Madani and Ftiti, 2020). Hence, our attempt is to apply such nonlinear approach within a new Corporate impact of carbon disclosures context, i.e.…”

Analysing the linkage between total factor productivity and tourism growth in Latin American countries

“…The importance of tourism growth (TOUR) in the generation of economic growth has been extensively recognized by academics and policymakers base the increase in their macroeconomic data on the expansion and development of these findings (Manrai et al, 2018;Flores-Muñoz et al, 2019;Nguyen et al, 2020;Polemis et al, 2021). Since the work by Balaguer and Cantavella-Jorda (2002), was the first one to formally refer to the tourism-led growth hypothesis (TLGH), a plethora of authors has investigated that discipline [1].…”