Macroeconomics

h = 1
h = 4
h = 8
2.5
Normal: AR(1)
2.5
Normal: AR(1)-B
2.5
Student-t: AR(1)
2.5
Student-t: AR(1)-B
2
2
2
2
1.5
1.5
1.5
1.5
1
1
1
1
0.5
0.5
0.5
0.5
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
3
3
3
3
2
2
2
2
1
1
1
1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
29
3
3
3
3
2
2
2
2
1
1
1
1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
0
0 0.2 0.4 0.6 0.8 1
Figure 4: Probability density function of the PITs (normalized) for various AR(1) specifications of the model for one quarter (upper panels),
one year (middle panel) and two years (lower panel) ahead forecasts. The dashed lines denote the 95% confidence interval constructed using a
Normal approximation to a binomial distribution, as in Diebold et al. (1998).