Brazilian airline industry: Persistence and breaks

ABSTRACT

This article examines the degree of persistence and breaks in the Brazilian airline industry. For this purpose we use innovative fractional integration and autoregressive models, which are more flexible than the standard approaches employed in the literature. Our model focuses on three important series, namely revenue passenger kilometers (RPK), available seat kilometers (ASK), and load factor (LF = RPK/ASK), disaggregated into domestic and international series. We found first that all series are highly persistent with orders of integration above 0.5 in all cases, thus implying nonstationary behavior. However, for the domestic series mean reversion is also achieved, while orders of integration close to 1 or above 1 are obtained in the case of the international data. Moreover, a structural break is clearly identified in all the series. Policy implications are then derived.

KEYWORDS:

• Brazilian airlines
• fractional integration
• persistence and breaks

Notes

¹ Covariance stationarity means that the time series is relatively stable across time. Rigorously speaking it means that the mean and the variance do not depend on time, and the covariance between any two observations does not depend on the specific location of time but on the distance between them.

² The proper definition of I(0) behavior is presented later, in Section 4.

³ Fractional integration was theoretically justified in terms of aggregation by Robinson (1978) and Granger (1980). Similarly, Cioczek-Georges and Mandelbrot (1995), Taqqu, Willinger, and Sherman (1997), Chambers (1998), and Lippi and Zaffaroni (1999) also use aggregation to motivate long memory processes, while Parke (1999) uses a closely related discrete time error duration model.

⁴ See also Narayan and Poop (2013) for a recent survey of unit roots in the context of structural breaks.

⁵ An I(0) process is defined as a covariance stationary process satisfying that or alternatively, in the frequency domain, if 0 < f(λ) < ∞ for all λ.

⁶ See, e.g., Arteche and Robinson (1999) and Arteche (2002).

⁷ This method seems to be robust agaisnt heterocedastic errors.

⁸ It has been argued in recent years that fractional integration may be a spurious phenomenon caused by the presence of breaks in the data (see, e.g., Cheung, 1993; Diebold & Inoue, 2001; Giraitis et al., 2001; Mikosch & Starica, 2004; Granger & Hyung, 2004).

⁹ ANAC homepage: http://www.anac.gov.br/Conteudo.aspx?slCD_ORIGEM=26&ttCD_CHAVE=173.

¹⁰ Higher seasonal AR processes were also employed leading to essentially the same results as those reported here.