MGARCH An R Package for Fitting Multivariate GARCH Models Harald - - PowerPoint PPT Presentation

▶
mgarch
SMART_READER_LITE
LIVE PREVIEW

MGARCH An R Package for Fitting Multivariate GARCH Models Harald - - PowerPoint PPT Presentation

Mar 22, 2024 364 likes •523 views

MGARCH An R Package for Fitting Multivariate GARCH Models Harald Schmidbauer Bilgi University, Istanbul, Turkey FOM & SUFE, Taiyuan, China Vehbi Sinan Tunalo glu Bilgi University, Istanbul, Turkey Angi R osch FOM & SDAU,

slide-1
SLIDE 1

MGARCH

An R Package for Fitting Multivariate GARCH Models

Harald Schmidbauer Bilgi University, Istanbul, Turkey FOM & SUFE, Tai’yuan, China Vehbi Sinan Tunalıo˘ glu Bilgi University, Istanbul, Turkey Angi R¨

  • sch

FOM & SDAU, Tai’an, China FOM University of Applied Sciences, Munich, Germany Rennes, July 2009 c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
slide-2
SLIDE 2

Outline.

  • 1. Univariate GARCH
  • 2. Multivariate GARCH
  • 3. MGARCH Functionality
  • 4. Further Functionality
  • 5. mgarch in Progress

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch OPEC News Announcements and Oil Price Volatility 2/14
slide-3
SLIDE 3
  • 1. Univariate GARCH

Example: GARCH(1, 1).

  • Model equations:

rt = µt + ǫt, ǫt = νt ·

  • ht,

ht = α0 + α1ǫ2

t−1

ARCH term

+ β1ht−1

GARCH term

  • (νt): white noise with σ2

ν = var(νt) = 1.

  • Parameters α0, α1, β1 ≥ 0 such that α1 + β1 < 1.

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 3/14
slide-4
SLIDE 4
  • 1. Univariate GARCH

Example: The price of Brent crude oil (in USD).

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 4/14
slide-5
SLIDE 5
  • 1. Univariate GARCH

Example: The price of Brent crude oil (in USD).

Typical result: the series of conditional standard deviations.

conditional standard deviation 200 400 600 800 1000 1200 1400 2 3 4 5

(Obtained using garch from package tseries.)

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 5/14
slide-6
SLIDE 6
  • 2. Multivariate GARCH

Example: BEKK(1, 1).

  • Model equations:

rt = Mt + ǫt, ǫt = H1/2

t

· νt, Ht = C′C + A′ǫt−1ǫ′

t−1A

  • ARCH term

+ B′Ht−1B GARCH term

  • (νt): white noise with var(νt) = I.
  • Parameters matrices C, A, B.

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 6/14
slide-7
SLIDE 7
  • 2. Multivariate GARCH

Example: The price of gold (in USD).

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 7/14
slide-8
SLIDE 8
  • 2. Multivariate GARCH

Example: Daily returns on Brent crude oil and on gold.

Typical result: the series of conditional correlations.

conditional correlation 200 400 600 800 1000 1200 −0.2 0.0 0.2 0.4 0.6

(Obtained using mvBEKK.est from package mgarch.)

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 8/14
slide-9
SLIDE 9
  • 3. MGARCH Functionality

So far:

  • BEKK models:

– fitting, diagnostics, simulation – any size, any order

  • DCC models (Tse & Tsui):

– fitting (still slow) – bivariate

  • bivariate asymmetric quadratic GARCH:

– fitting, diagnostics

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 9/14
slide-10
SLIDE 10
  • 4. Further Functionality

Comparing returns.

brent gold first day 2004-01-02 2004-01-02 last day 2009-06-30 2009-03-02

  • bservations

1400 1297 NAs 33 50 mean 0.08899 0.07151 std error 0.07038 0.03752 var 6.25734 1.77969 std deviation 2.50147 1.33405 skewness 0.38444 −0.25295 std error 0.37698 0.20818 kurtosis 5.72231 3.35217 std error 1.98225 0.63969 min −15.49167 −7.66241 lower quartile −1.28346 −0.52890 median 0.08206 0.07101 upper quartile 1.41644 0.75006 max 19.87716 6.19755 day of min 2008-12-05 2008-10-13 day of max 2009-01-02 2008-11-24 c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch OPEC News Announcements and Oil Price Volatility 10/14
slide-11
SLIDE 11
  • 5. mgarch in Progress

How is mgarch being developed?

  • mgarch is a Free and Open Source Software.
  • Actively and collectively developed
  • Multisite: Turkey, Germany, China and Singapore
  • Hosted on Sourceforge.net (SF.net)

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch OPEC News Announcements and Oil Price Volatility 11/14
slide-12
SLIDE 12
  • 5. mgarch in Progress

How is mgarch being developed?

  • Wikipedia says about SF.net:

SourceForge offers free access to hosting and tools for developers of free/open source software. . .

  • Main mgarch webpage:

http://mgarch.sf.net

  • SF.net mgarch page:

https://sourceforge.net/projects/mgarch

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch OPEC News Announcements and Oil Price Volatility 12/14
slide-13
SLIDE 13
  • 5. mgarch in Progress

What and how can you contribute?

  • We design, code, test and document the mgarch package.
  • You can do this, too.
  • Become an mgarch contributor on SF.net:

– Create an account on SF.net – Let us know your SF.net username: Vehbi Sinan Tunalıo˘ glu < vst@vsthost.com > Harald Schmidbauer < harald@hs-stat.com > – Contribute!

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch OPEC News Announcements and Oil Price Volatility 13/14
slide-14
SLIDE 14
  • 5. mgarch in Progress

c 2009 H. Schmidbauer / V.S. Tunalıo˘ glu / A. R¨

  • sch
  • 4. GARCH Models 14/14