VARMA versus VAR for Macroeconomic Forecasting George - - PowerPoint PPT Presentation

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

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

VARMA versus VAR for Macroeconomic Forecasting Introduction 3

VAR models dominate Why VARMA?

More parsimonious representation Closed with respect to linear transformations

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

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 y2,t

• =

φ11 φ12 φ21 φ22 y1,t−1 y2,t−1

• +

ε1,t ε2,t

• −

θ11 θ12 θ21 θ22 ε1,t−1 ε2,t−1

• y2,t = ε2,t ⇒ y2,t−1 = ε2,t−1 ⇒ (φ12, θ12)
• SCM framework: Tiao & Tsay (1989) completed by Athanasopoulos &

Vahid (2006)

• Echelon form: Hannan & Kavalieris (1984); Poskitt (1992); L¨

utkepohl & Poskitt (1996), Athanasopoulos, Poskitt & Vahid (2007)

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

y2,t

• =
• φ11

φ12 y1,t−1 y2,t−1

• +
• ε1,t

ε2,t

• −
• θ11

θ12 ε1,t−1 ε2,t−1

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

y2,t

• =
• φ11

φ12 y1,t−1 y2,t−1

• +
• ε1,t

ε2,t

• −
• θ11

θ12 ε1,t−1 ε2,t−1

• y2,t = ε2,t ⇒ y2,t−1 = ε2,t−1

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

y2,t

• =
• φ11

φ12 y1,t−1 y2,t−1

• +
• ε1,t

ε2,t

• −
• θ11

θ12 ε1,t−1 ε2,t−1

• y2,t = ε2,t ⇒ y2,t−1 = ε2,t−1 ⇒ (φ12, θ12)

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

y2,t

• =
• φ11

φ12 y1,t−1 y2,t−1

• +
• ε1,t

ε2,t

• −
• θ11

θ12 ε1,t−1 ε2,t−1

• y2,t = ε2,t ⇒ y2,t−1 = ε2,t−1 ⇒ (φ12, θ12)
• SCM framework: Tiao & Tsay (1989) completed by Athanasopoulos &

Vahid (2006)

• Echelon form: Hannan & Kavalieris (1984); Poskitt (1992); L¨

utkepohl & Poskitt (1996), Athanasopoulos, Poskitt & Vahid (2007)

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

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6

Definition of a SCM: For a given K-dimensional VARMA(p, q) yt = Φ1yt−1 + . . . + Φpyt−p + ηt − Θ1ηt−1 − . . . − Θqηt−q (1)

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6

Definition of a SCM: For a given K-dimensional VARMA(p, q) yt = Φ1yt−1 + . . . + Φpyt−p + ηt − Θ1ηt−1 − . . . − Θqηt−q (1) zr,t = αr

′yt ∼ SCM(pr, qr)

if αr satisfies αr ′Φpr = 0T where 0 ≤ pr ≤ p αr ′Φl = 0T for l = pr + 1, ..., p αr ′Θqr = 0T where 0 ≤ qr ≤ q αr ′Θl = 0T for l = qr + 1, ..., q

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6

Definition of a SCM: For a given K-dimensional VARMA(p, q) yt = Φ1yt−1 + . . . + Φpyt−p + ηt − Θ1ηt−1 − . . . − Θqηt−q (1) zr,t = αr

′yt ∼ SCM(pr, qr)

if αr satisfies αr ′Φpr = 0T where 0 ≤ pr ≤ p αr ′Φl = 0T for l = pr + 1, ..., p αr ′Θqr = 0T where 0 ≤ qr ≤ q αr ′Θl = 0T for l = qr + 1, ..., q SCM Methodology: Find K-linearly independent vectors A = (α1, . . . , αK)′ which transform (1) into Ayt = Φ∗

1yt−1 + . . . + Φ∗ pyt−p + εt − Θ∗ 1εt−1 − . . . − Θ∗ qεt−q

(2) where Φ∗

i = AΦi, εt = Aηt and Θ∗ i = AΘiA−1

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 6

Definition of a SCM: For a given K-dimensional VARMA(p, q) yt = Φ1yt−1 + . . . + Φpyt−p + ηt − Θ1ηt−1 − . . . − Θqηt−q (1) zr,t = αr

′yt ∼ SCM(pr, qr)

if αr satisfies αr ′Φpr = 0T where 0 ≤ pr ≤ p αr ′Φl = 0T for l = pr + 1, ..., p αr ′Θqr = 0T where 0 ≤ qr ≤ q αr ′Θl = 0T for l = qr + 1, ..., q SCM Methodology: Find K-linearly independent vectors A = (α1, . . . , αK)′ which transform (1) into Ayt = Φ∗

1yt−1 + . . . + Φ∗ pyt−p + εt − Θ∗ 1εt−1 − . . . − Θ∗ qεt−q

(2) where Φ∗

i = AΦi, εt = Aηt and Θ∗ i = AΘiA−1

Series of C/C tests: E y1,t−1 y2,t−1 y1,t y2,t

• [α1] = 0

α′

1yt ∼ SCM(0, 0)

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 7

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 7

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  α11 α12 α13 α21 α22 α23 α31 α32 α33   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Reduce parameters of A to produce a Canonical SCM   1 α21 1 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−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?

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  1 α12 α13 α21 1 α23 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Normalise diagonally (test for improper normalisations)

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  1 α12 α13 α21 1 α23 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  1 α12 α13 α21 1 α23 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  1 α12 α13 α21 1 α23 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM

  1 α21 1 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1 + εt −   θ(1)

11

θ(1)

12

  εt−1

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  1 α12 α13 α21 1 α23 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM

  1 α21 1 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1 + εt −   θ(1)

11

θ(1)

12

  εt−1

Empirical Results:

VARMA versus VAR for Macroeconomic Forecasting Canonical SCM 8

Example:

K = 3 α′

1yt ∼ SCM(1, 1)

α′

2yt ∼ SCM(1, 0)

α′

3yt ∼ SCM(0, 0)

  1 α12 α13 α21 1 α23 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1+εt−   θ(1)

11

θ(1)

12

  εt−1

Normalise diagonally (test for improper normalisations) Reduce parameters of A to produce a Canonical SCM

  1 α21 1 α31 α32 1   yt =    φ(1)

11

φ(1)

12

φ(1)

13

φ(1)

21

φ(1)

22

φ(1)

23

   yt−1 + εt −   θ(1)

11

θ(1)

12

  εt−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

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

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)

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

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: N1 = 300 Estimated canonical SCM VARMA Unrestricted VAR(AIC) and VAR(BIC) Restricted VAR(AIC) and VAR(BIC)

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: N1 = 300 Estimated canonical SCM VARMA Unrestricted VAR(AIC) and VAR(BIC) Restricted VAR(AIC) and VAR(BIC) Hold-out sample: N2 = 180 Produced N2 − h + 1 out-of-sample forecasts for each h=1 to 15 Forecast error measures: |MSFE| and tr(MSFE) Percentage Better: PBh Relative Ratios: RRdMSFE h =

1 50

50

i=1 |MSFE VAR

i

| |MSFE VARMA

i

|

VARMA versus VAR for Macroeconomic Forecasting Forecast performance 11

Relative Ratios

Forecast horizon (h) % 2 4 6 8 10 12 14 1.05 1.10 1.15 1.20

VAR(AIC) VAR(BIC)

PANEL A RdMSFE for Unrestricted VAR Forecast horizon (h) % 2 4 6 8 10 12 14 1.05 1.10 1.15 1.20

VAR(AIC) VAR(BIC)

PANEL B RdMSFE for Restricted VAR

VARMA versus VAR for Macroeconomic Forecasting Forecast performance 12

Percentage Better: Unrestricted VAR

Forecast horizon (h) % 2 4 6 8 10 12 14 20 30 40 50 60 70 80

VARMA VAR(AIC)

PANEL A PB counts for tr(MSFE) for VARMA versus Unrestricted VAR Forecast horizon (h) % 2 4 6 8 10 12 14 20 30 40 50 60 70 80

• VARMA

VAR(BIC)

VARMA versus VAR for Macroeconomic Forecasting Forecast performance 13

Percentage Better: Restricted VAR

Forecast horizon (h) % 2 4 6 8 10 12 14 20 30 40 50 60 70 80

VARMA VAR(AIC)

PANEL B PB counts for tr(MSFE) for VARMA versus Restricted VAR Forecast horizon (h) % 2 4 6 8 10 12 14 20 30 40 50 60 70 80

• VARMA

VAR(BIC)

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) 1 4 8 12 15 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

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) 1 4 8 12 15 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:

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) 1 4 8 12 15 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

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) 1 4 8 12 15 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

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) 1 4 8 12 15 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

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) 1 4 8 12 15 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

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

VARMA versus VAR for Macroeconomic Forecasting Example 17

Example:

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

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

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

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)

    1 1 1 ∗ ∗ ∗ 1     yt =     ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗     yt−1 +     ∗ ∗ ∗ ∗     yt−2 −     ∗ ∗ ∗     et−1 + et

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)

    1 1 1 ∗ ∗ ∗ 1     yt =     ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗     yt−1 +     ∗ ∗ ∗ ∗     yt−2 −     ∗ ∗ ∗     et−1 + et 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 |MSFEVARMA| as a base Repeat by changing specific features and compare with the benchmark

VARMA versus VAR for Macroeconomic Forecasting Simulation 20

Why do VARMA forecast better:

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP1: Estimated model

VAR(AIC) VAR(BIC)

VARMA versus VAR for Macroeconomic Forecasting Simulation 21

Why do VARMA forecast better:

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP1: Estimated model

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP2: No MA

VAR(AIC) VAR(BIC)

VARMA versus VAR for Macroeconomic Forecasting Simulation 22

Why do VARMA forecast better:

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP1: Estimated model

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP3: 2 strong MAs

VAR(AIC) VAR(BIC)

VARMA versus VAR for Macroeconomic Forecasting Simulation 23

Why do VARMA forecast better:

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP1: Estimated model

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP5: 3 strong MAs

VAR(AIC) VAR(BIC)

VARMA versus VAR for Macroeconomic Forecasting Simulation 24

Why do VARMA forecast better:

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP1: Estimated model

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP6: 3 weak MAs

VAR(AIC) VAR(BIC)

VARMA versus VAR for Macroeconomic Forecasting Simulation 25

Why do VARMA forecast better:

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP1: Estimated model

% 2 4 6 8 10 12 10 20 30 40 50 60

• DGP7: Weak AR

VAR(AIC) VAR(BIC)

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

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

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

• f models to VARs only

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

• f models to VARs only

3

The existence of VMA components cannot be well-approximated by finite order VARs

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

• f 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

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

• f 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

VARMA versus VAR for Macroeconomic Forecasting Summary of findings and future research 28

Thank you!!!!!