Autoregressive distributed lag ARDL(1,1) Represents an infinite distributed lag with weights: ARDL(p,q) Approximates an infinite lag of any shape when p and q are large.
Stationarity The usual properties of the least squares estimator in a regression using time series data depend on the assumption that the variables involved are stationary stochastic processes. A series is stationary if its mean and variance are constant over time, and the covariance between two values depends only on the length of time separating the two values
AR(1) Random walk Random walk with drift Deterministic trend Summary of time series processes
Trends Stochastic trend –Random walk –Series has a unit root –Series is integrated I(1) –Can be made stationary only by first differencing Deterministic trend –Series can be made stationary either by first differencing or by subtracting a deterministic trend.
Cointegration In general non-stationary variables should not be used in regression. In general a linear combination of I(1) series, eg: is I(1). If e t is I(0) x t and y t are cointegrated and the regression is not spurious e t can be interpreted as the error in a long- run equilibrium.
Example of a cointegration test Model1%5%10% 3.90 3.34 3.04