Midterm_Review (1)

One for example starting at artwo0 at for time zero

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: of one period. one For example, starting at ARTWO(0) at For time zero, ARTWO(2) = b2 ARTWO(0) , time ignoring the white noise shocks, and ARTWO(4) = b2 ARTWO(2) = ARTWO(4) b 2 ARTWO(0) and for stability -1<b <1 9 Triangle of Stable Parameter Triangle Space Space 1 b2 b1 = 0 ­1 10 10 Triangle of Stable Parameter Triangle Space: Boundary points 1 b2 ­1 b1 = 0 b2 = 1 – b1 If b1 = 0, b2 = 1, If b1 = 1, b2 =0, If b2 = ­1, b1 =2 +1 ­1 Draw a horizontal line through (0, ­1) for (b1, b2) 11 11 Triangle of Stable Parameter Triangle Space: (0, 1) b2 (­1, 0) (1, 0) b1 = 0 (0, ­1) Draw a line from the vertex, for (b1=0, b2=1), though the end points for b1, i.e. through (b1=1, b2= 0) and (b1=­1, b2=0), 12 12 Triangle of Stable Parameter Triangle Space: (0,1) b2 = 1 ­ b1 b2 (­1, 0) (1, 0) b1 = 0 ­1 (2, ­1) Note: along the boundary, when b1 = 0, b2 = 1, when b1 = 1, b2 = 0, and when b2 = ­1, b2 = 2. 13 13 Triangle of Stable Parameter Triangle Space: (0, 1) b2 (­1, 0) b1<0 b2>0 b1<0 b2<0 b1>0 b2>0 b1 = 0 (1, 0) b1>0 b2<0 (0, ­1) 14 14 Is the behavior different in each Is Quadrant? (0, 1) II (­1, 0) b1<0 b2>0 b1<0 b2<0 III b2 b1>0 b2>0 I b1 = 0 (0, ­1) (1, 0) b1>0 b2<0 IV 15 15 We could study with simulation 16 16 Is the behavior different in each Is Quadrant? (0, 1) II (­1, 0) b1= ­0.3 b2= 0.3 b1= ­0.3 b2= ­0.3 III b2 b1= 0.3 I b2= 0.3 b1 = 0 (0, ­1) (1, 0) b1= 0.3 b2= ­0.3 IV 17 17 Simulation Sample 1 1000 Sample 1 1000 Genr wn=nrnd Sample 1 2 Genr artwo =wn Sample 3 1000 Genr artwo = 0.3*artwo(-1)+0.3*artwo(-2) + Genr wn wn Sample 1 1000 18 18 II. Augmented Dickey-Fuller Tests 19 19 Part II: Unit Roots First First Order Autoregressive or RandomWalk? RandomWalk? y(t) = b*y(t-1) + wn(t) y(t) = y(t-1) + wn(t) 20 20 Unit Roots y(t) = b*y(t-1) + wn(t) we could test the null: b=1 against b<1 instead, subtract y(t-1) from both sides: y(t) - y(t-1)...
View Full Document

This document was uploaded on 01/15/2014.

Ask a homework question - tutors are online