Questions tagged [ardl]

ARDL stands for "Autoregressive-Distributed Lag". In its basic form, an ARDL regression model looks like this: $$ y_t = \beta_0 + \beta_1 y_{t-1} + \dots + \beta_p y_{t-p} + \alpha_0 x_t + \alpha_1 x_{t-1} + \dots + \alpha_q x_{t-q} + \varepsilon_t $$ where $\varepsilon_t$ is a random "disturbance" term.

The model is "autoregressive", in the sense that $y_t$ is "explained (in part) by lagged values of itself. It also has a "distributed lag" component, in the form of successive lags of the $x$ explanatory variable. Sometimes, the current value of $x_t$ itself is excluded from the distributed lag part of the model's structure.

ARDL models have come to play an important role recently in the modelling of non-stationary time-series data. In particular, they are used to implement the so-called "Bounds Tests" (Pesaran & Shin, 1999; and Pesaran et al., 2001), to see if long-run relationships are present when we have a group of time-series, some of which may be stationary, while others are not.

Based on Dave Giles' blog posts "ARDL Models - Part I" and "ARDL Models - Part II - Bounds Tests".

_{Pesaran, M. H. and Y. Shin, 1999. An autoregressive distributed lag modelling approach to cointegration analysis. Chapter 11 in S. Strom (ed.), Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symposium. Cambridge University Press, Cambridge.}

_{Pesaran, M. H., Shin, Y. and Smith, R. J., 2001. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16, 289–326.}