Essay in dividend modelling and forecasting: does nonlinearity help?

Abstract

This article develops a method of nonlinear modelling for the dividends of the Group of seven (G7) indexes using threshold techniques: Smooth Transition Autoregressive Models (STAR). First, smoothness and nonlinearity are justified by the presence of heterogeneous expectations and companies of different sizes. Then, we show that this methodology is adapted to reproduce persistence in the dividend adjustment dynamics. Finally, we highlight the superiority of STAR models compared to the linear process in modelling dividends and reducing measurement error while forecasting future dividends. STAR forecasting supplanted those of linear model in the short and medium terms.

Notes

¹ See Section II.

² λ is an adjustment term.

³ According to Timmermann (1994), stock prices reflect information asymmetry while exercising a feedback on dividends. Prices could induce persistence and nonlinearity in dividends.

⁴ ‘Normal’ dividends are defined as a weighted average of past dividends for which weighting coefficients decrease exponentially with remoteness in time.

⁵ d_t = log(D_t ).

⁶ Variable c is an arbitrary constant and λ is a positive root of the quadratic equation:

⁷ Culter, Poterba and Summers (1988) showed that the S&P dividend yield ratio (D_t /P_t ) has been on average around 4.8% since 1871, 4% in 1950 and 1.17% in 1999 indicating changes in dividend growth.

⁸ In the empirical literature, several studies focusing on exchange rate adjustment modelling used also STAR models such as Taylor et al. (2001). See also Taylor and Taylor (2004) for a recent survey of this literature.

⁹ For more details on STAR modelling steps, see Teräsvirta (1994) and Van Dijk et al. (2002).

¹⁰ See Van Dijk et al. (2002) for more details on these tests.

¹¹ Nevertheless, nonlinear forecasting models have been improved for other economic series such as the exchange rates (e.g. Kililan and Taylor, 2003; Boero and Maorrocu, 2004).

¹² Variable n is the number of predictions.