ARDL

ARDL stands for autoregressive distributed lag model. It is a class of econometric models used to examine dynamic relationships between a dependent variable and one or more regressors in time-series data. A key feature is that the regressors can be a mix of I(0) and I(1) variables, and, under standard conditions, none of the variables should be I(2). This flexibility makes ARDL suitable for small-sample studies and when the integration order of variables is uncertain.

The general ARDL(p, q1, q2, ..., qk) model regresses the dependent variable on its own lagged values and on current and lagged values of the regressors. The long-run equilibrium relationship, if present, can be derived from the model and expressed in terms of the long-run coefficients. An alternative representation is the ARDL error correction model (ARDL-ECM), which separates short-run dynamics from the long-run relationship.

A common method to test for a long-run relationship is the bounds testing approach proposed by Pesaran, Shin, and Smith (2001). This procedure assesses whether a long-run link exists irrespective of whether the regressors are I(0) or I(1), provided none is I(2). If cointegration is indicated, one can estimate the long-run coefficients and/or the error-correction representation.

Advantages of ARDL include suitability for small samples, flexibility with mixed integration orders, and straightforward estimation via ordinary least squares. Limitations include sensitivity to lag selection, potential bias from omitted variables or structural breaks, and the requirement that no variable be integrated of order two.

Applications span macroeconomic dynamics, energy demand, trade balances, and financial time series. The concept originated with the work of Pesaran, Shin, and Smith in 2001.