Negative cointegration I am new to the topic of cointegration and my question might be trivial.
Let's say $X_t$ is an increasing series and $Y_t$ is a decreasing series; is it possible that they will be cointegrated?
 A: Yes, it is possible. As long as $X_t$ and $Y_t$ are integrated series and their integration order is the same (e.g. I(1)), they may be cointegrated. 
$X_t$ and $Y_t$ may each contain a deterministic time trend. The deterministic time trend(s) should be accounted for when considering cointegration. There might be a need to include a deterministic time trend $\tau$ into the cointegration vector so that a linear combination of $X_t$, $Y_t$ and $\tau$ would be integrated to a lower order than $X_t$ and $Y_t$ are (e.g. $X_t$ and $Y_t$ are I(1) but a linear combination of $X_t$, $Y_t$ and $\tau$ is I(0)).
Example: suppose $Z_t$ is a random walk, $\varepsilon_{1,t}$ and $\varepsilon_{2,t}$ are stationary processes, and $c_1$ and $c_2$ are positive constants. Define 
$$X_t:=Z_t+c_1 t+\varepsilon_{1,t}$$
$$Y_t:=Z_t-c_2 t+\varepsilon_{2,t}$$ 
It can be seen that


*

*$X_t$ and $Y_t$ are integrated of order one (I(1));

*they have linear time trends with opposite signs ($X_t$ has a positive time trend, $Y_t$ has a negative time trend);

*$X_t$ and $Y_t$ are cointegrated since their linear combination (with a linear time trend included) $X_t-Y_t-(c_1-c_2)t=\varepsilon_{1,t}-\varepsilon_{2,t}$ is stationary.

