(a) Sketch four time series exhibiting each of the characteristics listed below in i-iv. Make a note alongside each of your four sketches which indicate how you have shown the key characteristic in that individual sketch.

(i) Time varying mean

(ii) Time varying variance

(iii) Time varying covariance

(iv) Stationarity

(b) What is the difference between a cointegrated and spurious relationship between a pair of time series? 

(c) How might you spot a spurious regression from a set of regression outputs?