7 Autoregressive distributed lag ARDL(1,1)ARDL(p,q)Represents an infinite distributed lag with weights:Approximates an infinite lag of any shape when p and q are large.
8 StationarityThe 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
12 Summary of time series processes Random walkRandom walk with driftDeterministic trend
13 Trends Stochastic trend Deterministic trend Random walk Series has a unit rootSeries is integrated I(1)Can be made stationary only by first differencingDeterministic trendSeries can be made stationary either by first differencing or by subtracting a deterministic trend.
22 CointegrationIn general non-stationary variables should not be used in regression.In general a linear combination of I(1) series, eg: is I(1).If et is I(0) xt and yt are cointegrated and the regression is not spuriouset can be interpreted as the error in a long-run equilibrium.
23 Example of a cointegration test Model1%5%10%3.903.343.04