VARMA versus VAR for Macroeconomic Forecasting
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1 VARMA versus VAR for Macroeconomic Forecasting 1 VARMA versus VAR for Macroeconomic Forecasting George Athanasopoulos Department of Econometrics and Business Statistics Monash University Farshid Vahid School of Economics Australian National University
2 VARMA versus VAR for Macroeconomic Forecasting Introduction 2 Outline 1 Introduction 2 Canonical SCM 3 Forecast performance 4 Example 5 Simulation 6 Summary of findings and future research
3 VARMA versus VAR for Macroeconomic Forecasting Introduction 3 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations
4 VARMA versus VAR for Macroeconomic Forecasting Introduction 3 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations Difficult to Identify If univariate ARIMA modelling is difficult then VARMA modelling is even more difficult - some might say impossible! - Chatfield
5 VARMA versus VAR for Macroeconomic Forecasting Introduction 3 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations Difficult to Identify If univariate ARIMA modelling is difficult then VARMA modelling is even more difficult - some might say impossible! - Chatfield Identification Problem [ y1,t ] = y 2,t [ ] [ ] φ11 φ 12 y1,t 1 + φ 21 φ 22 y 2,t 1 [ ε1,t y 2,t = ε 2,t y 2,t 1 = ε 2,t 1 (φ 12, θ 12 ) ε 2,t ] [ θ11 θ 12 ] [ ] ε1,t 1 θ 21 θ 22 ε 2,t 1 - SCM framework: Tiao & Tsay (1989) completed by Athanasopoulos & Vahid (2006) - Echelon form: Hannan & Kavalieris (1984); Poskitt (1992); Lütkepohl & Poskitt (1996), Athanasopoulos, Poskitt & Vahid (2007)
6 VARMA versus VAR for Macroeconomic Forecasting Introduction 4 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations Difficult to Identify If univariate ARIMA modelling is difficult then VARMA modelling is even more difficult - some might say impossible! - Chatfield Identification Problem [ y1,t ] = y 2,t [ φ11 φ ] [ ] y1,t 1 + y 2,t 1 [ ε1,t ] [ θ11 θ 12 ε 2,t 0 0 ] [ ] ε1,t 1 ε 2,t 1
7 VARMA versus VAR for Macroeconomic Forecasting Introduction 4 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations Difficult to Identify If univariate ARIMA modelling is difficult then VARMA modelling is even more difficult - some might say impossible! - Chatfield Identification Problem [ y1,t ] = y 2,t [ φ11 φ ] [ ] y1,t 1 + y 2,t 1 [ ε1,t ] [ θ11 θ 12 ε 2,t 0 0 ] [ ] ε1,t 1 ε 2,t 1 y 2,t = ε 2,t y 2,t 1 = ε 2,t 1
8 VARMA versus VAR for Macroeconomic Forecasting Introduction 4 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations Difficult to Identify If univariate ARIMA modelling is difficult then VARMA modelling is even more difficult - some might say impossible! - Chatfield Identification Problem [ y1,t ] = y 2,t [ φ11 φ ] [ ] y1,t 1 + y 2,t 1 [ ε1,t y 2,t = ε 2,t y 2,t 1 = ε 2,t 1 (φ 12, θ 12 ) ] [ θ11 θ 12 ε 2,t 0 0 ] [ ] ε1,t 1 ε 2,t 1
9 VARMA versus VAR for Macroeconomic Forecasting Introduction 4 VAR models dominate Why VARMA? More parsimonious representation Closed with respect to linear transformations Difficult to Identify If univariate ARIMA modelling is difficult then VARMA modelling is even more difficult - some might say impossible! - Chatfield Identification Problem [ y1,t ] = y 2,t [ φ11 φ ] [ ] y1,t 1 + y 2,t 1 [ ε1,t y 2,t = ε 2,t y 2,t 1 = ε 2,t 1 (φ 12, θ 12 ) ] [ θ11 θ 12 ε 2,t 0 0 ] [ ] ε1,t 1 ε 2,t 1 - SCM framework: Tiao & Tsay (1989) completed by Athanasopoulos & Vahid (2006) - Echelon form: Hannan & Kavalieris (1984); Poskitt (1992); Lütkepohl & Poskitt (1996), Athanasopoulos, Poskitt & Vahid (2007)
10 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 5 Outline 1 Introduction 2 Canonical SCM 3 Forecast performance 4 Example 5 Simulation 6 Summary of findings and future research
11 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6 Definition of a SCM: For a given K-dimensional VARMA(p, q) y t = Φ 1 y t Φ p y t p + η t Θ 1 η t 1... Θ q η t q (1)
12 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6 Definition of a SCM: For a given K-dimensional VARMA(p, q) y t = Φ 1 y t Φ p y t p + η t Θ 1 η t 1... Θ q η t q (1) z r,t = α r y t SCM(p r, q r ) if α r satisfies α r Φ pr 0 T where 0 p r p α r Φ l = 0 T for l = p r + 1,..., p α r Θ qr 0 T where 0 q r q α r Θ l = 0 T for l = q r + 1,..., q
13 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6 Definition of a SCM: For a given K-dimensional VARMA(p, q) y t = Φ 1 y t Φ p y t p + η t Θ 1 η t 1... Θ q η t q (1) z r,t = α r y t SCM(p r, q r ) if α r satisfies α r Φ pr 0 T where 0 p r p α r Φ l = 0 T for l = p r + 1,..., p α r Θ qr 0 T where 0 q r q α r Θ l = 0 T for l = q r + 1,..., q SCM Methodology: Find K-linearly independent vectors A = (α 1,..., α K ) which transform (1) into Ay t = Φ 1y t Φ py t p + ε t Θ 1ε t 1... Θ qε t q (2) where Φ i = AΦ i, ε t = Aη t and Θ i = AΘ i A 1
14 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6 Definition of a SCM: For a given K-dimensional VARMA(p, q) y t = Φ 1 y t Φ p y t p + η t Θ 1 η t 1... Θ q η t q (1) z r,t = α r y t SCM(p r, q r ) if α r satisfies α r Φ pr 0 T where 0 p r p α r Φ l = 0 T for l = p r + 1,..., p α r Θ qr 0 T where 0 q r q α r Θ l = 0 T for l = q r + 1,..., q SCM Methodology: Find K-linearly independent vectors A = (α 1,..., α K ) which transform (1) into Ay t = Φ 1y t Φ py t p + ε t Θ 1ε t 1... Θ qε t q (2) where Φ i = AΦ i, ε [ t = Aη t and ] Θ i = AΘ i A 1 y1,t 1 [ ] Series of C/C tests: E y1,t y y 2,t [α1 ] = 0 2,t 1 α 1 y t SCM(0, 0)
15 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 7 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0)
16 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 7 Example: K = 3 α 1 α 11 α 12 α 13 α 21 α 22 α 23 α 31 α 32 α 33 y t = yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 Reduce parameters of A to produce a Canonical SCM α α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 y t 1 +ε t θ(1) 11 θ (1) Empirical Results: 1. Average performance across many trivariate systems 2. A four variable example 3. Simulation: Why do VARMA models do better than VARs? ε t ε t 1
17 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) 1 α 12 α 13 α 21 1 α 23 α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 ε t 1 Normalise diagonally (test for improper normalisations)
18 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) 1 α 12 α 13 α 21 1 α 23 α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 ε t 1 Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM
19 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) 1 α 12 α 13 α 21 1 α 23 α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 ε t 1 Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM
20 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) 1 α 12 α 13 α 21 1 α 23 α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 ε t 1 Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM φ (1) α φ (1) 12 φ (1) 13 y t = φ (1) 21 φ (1) 22 φ (1) y t 1 + ε t θ(1) 11 θ (1) 12 0 ε t 1 23 α 31 α 32 1
21 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) 1 α 12 α 13 α 21 1 α 23 α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 ε t 1 Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM φ (1) α φ (1) 12 φ (1) 13 y t = φ (1) 21 φ (1) 22 φ (1) y t 1 + ε t θ(1) 11 θ (1) α 31 α 32 1 Empirical Results: ε t 1
22 VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8 Example: K = 3 α 1 yt SCM(1, 1) α 2yt SCM(1, 0) α 3yt SCM(0, 0) 1 α 12 α 13 α 21 1 α 23 α 31 α 32 1 y t = φ (1) 11 φ (1) 12 φ (1) 13 φ (1) 21 φ (1) 22 φ (1) 23 y t 1 +ε t θ(1) 11 θ (1) 12 0 ε t 1 Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM φ (1) α φ (1) 12 φ (1) 13 y t = φ (1) 21 φ (1) 22 φ (1) y t 1 + ε t θ(1) 11 θ (1) α 31 α 32 1 Empirical Results: 1. Average performance across many trivariate systems 2. A four variable example 3. Simulation: Why do VARMA models do better than VARs ε t 1
23 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 9 Outline 1 Introduction 2 Canonical SCM 3 Forecast performance 4 Example 5 Simulation 6 Summary of findings and future research
24 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 10 Forecasting: 40 monthly macroeconomic variables from 8 general categories of economic activity, 1959:1-1998:12 (N=480)
25 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 10 Forecasting: 40 monthly macroeconomic variables from 8 general categories of economic activity, 1959:1-1998:12 (N=480) 50 3 variable systems
26 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 10 Forecasting: 40 monthly macroeconomic variables from 8 general categories of economic activity, 1959:1-1998:12 (N=480) 50 3 variable systems Test sample: N 1 = 300 Estimated canonical SCM VARMA Unrestricted VAR(AIC) and VAR(BIC) Restricted VAR(AIC) and VAR(BIC)
27 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 10 Forecasting: 40 monthly macroeconomic variables from 8 general categories of economic activity, 1959:1-1998:12 (N=480) 50 3 variable systems Test sample: N 1 = 300 Estimated canonical SCM VARMA Unrestricted VAR(AIC) and VAR(BIC) Restricted VAR(AIC) and VAR(BIC) Hold-out sample: N 2 = 180 Produced N 2 h + 1 out-of-sample forecasts for each h=1 to 15 Forecast error measures: MSFE and tr(msfe) Percentage Better: PB h Relative Ratios: RRdMSFE h = 1 50 MSFE VAR i 50 i=1 MSFEi VARMA
28 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 11 Relative Ratios PANEL A PANEL B 1.20 RdMSFE for Unrestricted VAR VAR(AIC) VAR(BIC) 1.20 RdMSFE for Restricted VAR VAR(AIC) VAR(BIC) % % Forecast horizon (h) Forecast horizon (h)
29 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 12 Percentage Better: Unrestricted VAR PANEL A PB counts for tr(msfe) for VARMA versus Unrestricted VAR 80 VARMA VAR(AIC) 80 VARMA VAR(BIC) % 50 % Forecast horizon (h) Forecast horizon (h)
30 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 13 Percentage Better: Restricted VAR PANEL B PB counts for tr(msfe) for VARMA versus Restricted VAR 80 VARMA VAR(AIC) 80 VARMA VAR(BIC) % 50 % Forecast horizon (h) Forecast horizon (h)
31 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 14 Diebold-Mariano test for tr(msfe): VARMA sign better (5%, 25%, 25%,5%) VARMA sign worst Forecast horizon (h) VAR(AIC) - Unrest 24,46,20,14 16,38,10,0 14,32,6,4 10,22,10,0 10,22,8,0 VAR(BIC) - Unrest 24,50,22,12 10,38,18,10 12,26,22,8 12,18,16,4 12,18,16,2 VAR(AIC) - Rest 34,54,26,12 14,36,16,0 14,26,8,2 12,22,10,0 10,24,10,0 VAR(BIC) - Rest 32,54,22,14 10,38,18,8 12,26,22,6 10,20,20,6 10,16,14,2
32 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 14 Diebold-Mariano test for tr(msfe): VARMA sign better (5%, 25%, 25%,5%) VARMA sign worst Forecast horizon (h) VAR(AIC) - Unrest 24,46,20,14 16,38,10,0 14,32,6,4 10,22,10,0 10,22,8,0 VAR(BIC) - Unrest 24,50,22,12 10,38,18,10 12,26,22,8 12,18,16,4 12,18,16,2 VAR(AIC) - Rest 34,54,26,12 14,36,16,0 14,26,8,2 12,22,10,0 10,24,10,0 VAR(BIC) - Rest 32,54,22,14 10,38,18,8 12,26,22,6 10,20,20,6 10,16,14,2 Messages:
33 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 14 Diebold-Mariano test for tr(msfe): VARMA sign better (5%, 25%, 25%,5%) VARMA sign worst Forecast horizon (h) VAR(AIC) - Unrest 24,46,20,14 16,38,10,0 14,32,6,4 10,22,10,0 10,22,8,0 VAR(BIC) - Unrest 24,50,22,12 10,38,18,10 12,26,22,8 12,18,16,4 12,18,16,2 VAR(AIC) - Rest 34,54,26,12 14,36,16,0 14,26,8,2 12,22,10,0 10,24,10,0 VAR(BIC) - Rest 32,54,22,14 10,38,18,8 12,26,22,6 10,20,20,6 10,16,14,2 Messages: 1 There are cases where VARMA significantly outperform VAR and vice versa
34 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 14 Diebold-Mariano test for tr(msfe): VARMA sign better (5%, 25%, 25%,5%) VARMA sign worst Forecast horizon (h) VAR(AIC) - Unrest 24,46,20,14 16,38,10,0 14,32,6,4 10,22,10,0 10,22,8,0 VAR(BIC) - Unrest 24,50,22,12 10,38,18,10 12,26,22,8 12,18,16,4 12,18,16,2 VAR(AIC) - Rest 34,54,26,12 14,36,16,0 14,26,8,2 12,22,10,0 10,24,10,0 VAR(BIC) - Rest 32,54,22,14 10,38,18,8 12,26,22,6 10,20,20,6 10,16,14,2 Messages: 1 There are cases where VARMA significantly outperform VAR and vice versa 2 VARMA models significantly outperform VAR more than the reverse
35 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 14 Diebold-Mariano test for tr(msfe): VARMA sign better (5%, 25%, 25%,5%) VARMA sign worst Forecast horizon (h) VAR(AIC) - Unrest 24,46,20,14 16,38,10,0 14,32,6,4 10,22,10,0 10,22,8,0 VAR(BIC) - Unrest 24,50,22,12 10,38,18,10 12,26,22,8 12,18,16,4 12,18,16,2 VAR(AIC) - Rest 34,54,26,12 14,36,16,0 14,26,8,2 12,22,10,0 10,24,10,0 VAR(BIC) - Rest 32,54,22,14 10,38,18,8 12,26,22,6 10,20,20,6 10,16,14,2 Messages: 1 There are cases where VARMA significantly outperform VAR and vice versa 2 VARMA models significantly outperform VAR more than the reverse 3 As h increases the number significant differences decreases dummy space
36 VARMA versus VAR for Macroeconomic Forecasting Forecast performance 15 Diebold-Mariano test for tr(msfe): VARMA sign better (5%, 25%, 25%,5%) VARMA sign worst Forecast horizon (h) VAR(AIC) - Unrest 24,46,20,14 16,38,10,0 14,32,6,4 10,22,10,0 10,22,8,0 VAR(BIC) - Unrest 24,50,22,12 10,38,18,10 12,26,22,8 12,18,16,4 12,18,16,2 VAR(AIC) - Rest 34,54,26,12 14,36,16,0 14,26,8,2 12,22,10,0 10,24,10,0 VAR(BIC) - Rest 32,54,22,14 10,38,18,8 12,26,22,6 10,20,20,6 10,16,14,2 Messages: 1 There are cases where VARMA significantly outperform VAR and vice versa 2 VARMA models significantly outperform VAR more than the reverse 3 As h increases the number significant differences decreases 4 Restrictions do not improve VAR performance when significant differences
37 VARMA versus VAR for Macroeconomic Forecasting Example 16 Outline 1 Introduction 2 Canonical SCM 3 Forecast performance 4 Example 5 Simulation 6 Summary of findings and future research
38 VARMA versus VAR for Macroeconomic Forecasting Example 17 Example:
39 VARMA versus VAR for Macroeconomic Forecasting Example 17 Example: Four variables (also six variables): GDP growth rate inflation rate spread (10 yr gvt bill yield) (3-month treasury bill rate) 3-month treasury bill rate - in line with term structure literature: Ang, Piazzesi, Wei (2006) - variations in New Keynesian DSGE - contributions in Taylor (1999) Quarterly data
40 VARMA versus VAR for Macroeconomic Forecasting Example 17 Example: Four variables (also six variables): GDP growth rate inflation rate spread (10 yr gvt bill yield) (3-month treasury bill rate) 3-month treasury bill rate - in line with term structure literature: Ang, Piazzesi, Wei (2006) - variations in New Keynesian DSGE - contributions in Taylor (1999) Quarterly data Message: We should start considering VARMA
41 VARMA versus VAR for Macroeconomic Forecasting Simulation 18 Outline 1 Introduction 2 Canonical SCM 3 Forecast performance 4 Example 5 Simulation 6 Summary of findings and future research
42 VARMA versus VAR for Macroeconomic Forecasting Simulation 19 Why do VARMA forecast better? Estimated a VARMA(2,1): - SCM(2,0) - SCM(1,1) - SCM(1,0) - SCM(0,0) yt = y t e t 1 + e t y t 2
43 VARMA versus VAR for Macroeconomic Forecasting Simulation 19 Why do VARMA forecast better? Estimated a VARMA(2,1): - SCM(2,0) - SCM(1,1) - SCM(1,0) - SCM(0,0) yt = y t e t 1 + e t y t 2 Simulate from the benchmark estimated model assuming e N(0, Σ) n = 164 estimate VARMA(2,1), VAR(AIC), VAR(BIC) nout = 42 compute 1 to 12-step ahead forecasts iterations = 100 calculate MSFE for all models Compare the percentage difference using MSFE VARMA as a base Repeat by changing specific features and compare with the benchmark
44 VARMA versus VAR for Macroeconomic Forecasting Simulation 20 Why do VARMA forecast better: DGP1: Estimated model % VAR(AIC) VAR(BIC)
45 VARMA versus VAR for Macroeconomic Forecasting Simulation 21 Why do VARMA forecast better: DGP1: Estimated model DGP2: No MA % % VAR(AIC) VAR(BIC)
46 VARMA versus VAR for Macroeconomic Forecasting Simulation 22 Why do VARMA forecast better: DGP1: Estimated model DGP3: 2 strong MAs % % VAR(AIC) VAR(BIC)
47 VARMA versus VAR for Macroeconomic Forecasting Simulation 23 Why do VARMA forecast better: DGP1: Estimated model DGP5: 3 strong MAs % % VAR(AIC) VAR(BIC)
48 VARMA versus VAR for Macroeconomic Forecasting Simulation 24 Why do VARMA forecast better: DGP1: Estimated model DGP6: 3 weak MAs % % VAR(AIC) VAR(BIC)
49 VARMA versus VAR for Macroeconomic Forecasting Simulation 25 Why do VARMA forecast better: DGP1: Estimated model DGP7: Weak AR % % VAR(AIC) VAR(BIC)
50 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 26 Outline 1 Introduction 2 Canonical SCM 3 Forecast performance 4 Example 5 Simulation 6 Summary of findings and future research
51 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 27 Summary of findings: 1 We can obtain better forecasts for macroeconomic variables by considering VARMA models
52 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 27 Summary of findings: 1 We can obtain better forecasts for macroeconomic variables by considering VARMA models 2 With the methodological developments and the improvement in computer power there is no compelling reason to restrict the class of models to VARs only
53 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 27 Summary of findings: 1 We can obtain better forecasts for macroeconomic variables by considering VARMA models 2 With the methodological developments and the improvement in computer power there is no compelling reason to restrict the class of models to VARs only 3 The existence of VMA components cannot be well-approximated by finite order VARs
54 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 27 Summary of findings: 1 We can obtain better forecasts for macroeconomic variables by considering VARMA models 2 With the methodological developments and the improvement in computer power there is no compelling reason to restrict the class of models to VARs only 3 The existence of VMA components cannot be well-approximated by finite order VARs 4 Are these favourable results specific the SCM methodology? No! Athanasopoulos, Poskitt and Vahid (2007) show that similar conclusions emerge when one uses the Echelon form approach
55 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 27 Summary of findings: 1 We can obtain better forecasts for macroeconomic variables by considering VARMA models 2 With the methodological developments and the improvement in computer power there is no compelling reason to restrict the class of models to VARs only 3 The existence of VMA components cannot be well-approximated by finite order VARs 4 Are these favourable results specific the SCM methodology? No! Athanasopoulos, Poskitt and Vahid (2007) show that similar conclusions emerge when one uses the Echelon form approach Future Research: 1 Developing a fully automated identification process 2 Developing an alternative estimation approach which avoids fitting a long VAR to estimate the lagged innovations 3 Move into the non-stationary world
56 VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 28 Thank you!!!!!
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