Lectures on by SÃ¸ren Johansen Department of Economics ...

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3 Inference is asymptotically normal: If x t is stationary Law of Large Numbers : M zz P ! > 0 Central Limit Theorem : T 1 M z" d ! Npp (0; ) T 1=2 ( ^B B) = T 1=2 M 1 zz M z" w ! N(0; 1 ) ^ = T 1 (M xx M xz M 1 zz M zx ) = T 1 (M "" M "z M 1 zz M z" ) P ! f = #(B) 2 log LR(B = h()) = 2 log max B=h() L(B) max B L(B) #() w ! 2 (f)
29 DLEVEL 15 10 Actual and Fitted 1.00 0.75 0.50 Autocorrelations 5 0.25 0 0.00 0.25 5 0.50 10 0.75 15 1883 1890 1897 1904 1911 1918 1925 1932 1939 1946 1953 1960 1967 1974 1981 1988 1995 2002 1.00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Lag 3 2 Standardized Residuals 0.45 0.40 0.35 Histogram SB D H : C hiSqr(2) = 0.07 [0.96] K S = 0.95 [5% C .V. = 0.08] JB: ChiSqr(2) = 0.29 [0.86] 1 0.30 0 0.25 0.20 1 0.15 2 0.10 0.05 3 1883 1890 1897 1904 1911 1918 1925 1932 1939 1946 1953 1960 1967 1974 1981 1988 1995 2002 0.00 3.2 1.6 0.0 1.6 3.2 1.Residual analysis.
Page 1 and 2: 1 Lectures on THE
Page 3 and 4: LECTURE 2 THE STATISTICAL ANALYSIS
Page 5: 2 2. ESTIMATION OF THE UNRESTRICTED
Page 9 and 10: 31 Roots of the Companion Matrix 1.
Page 11 and 12: 6 4. REDUCED RANK REGRESSION Consid
Page 13 and 14: 8 5. ANALYSIS OF THE I(1) COINTEGRA
Page 15 and 16: 8. DETERMINATION OF COINTEGRATION R
Page 17 and 18: 33 0.6 Temperature versus Sea Level
Page 19 and 20: 38 0.4 Temperature against Temperat
Page 21 and 22: 13 6. ESTIMATION IN THE I(1) MODEL
Page 23 and 24: 15 9. CONCLUSION We have shown that
Page 25 and 26: 17 THE DATA The data 1948:1 to 2002
Page 27 and 28: 19 STATISTICAL ASSUMPTIONS AND ANAL
Page 29 and 30: The model considered by Ireland add
Page 31 and 32: 24 Hypotheses of interest: two scen
Page 33 and 34: 36 0.05 khat 0.10 0.15 0.05
Page 35 and 36: 26 We take the models for period I
Page 38: 28 11. CONCLUSION 2 When taking a m

Lectures on by SÃ¸ren Johansen Department of Economics ...

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