Estimation and testing in models containing both jumps and conditional heteroskedasticity

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Abstract

In this paper we develop tests for the hypothesis that a series (observed in discrete time) is generated by a diffusion process and discuss the results of these tests for several exchange rates and stock market indices. The tests of this hypothesis that have been proposed up to now in literature are all based on arbitrary and non-testable assumptions on the conditional distribution of the smooth component of the series. Instead, our tests are based on the weaker assumption that the series is weak GARCH; this hypothesis can easily be tested. To investigate the presence of jumps, we propose a test that is based on an overidentifying relation between variance and kurtosis parameters at an arbitrary frequency, which holds for GARCH diffusions. Monte Carlo evidence suggests that this test is slightly conservative, but nevertheless it has good power properties. The empirical results clearly indicate the presence of jumps in dollar exchange rates. For stock market indices the results are mixed. The finding of jumps has important consequences for derivative pricing as well as for modeling the distribution of future spot prices. In order to assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroskedasticity.
Original languageEnglish
PublisherUnknown Publisher
Number of pages20
Volume1994-105
Publication statusPublished - 1994

Publication series

NameCentER Discussion Paper
Volume1994-105

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Conditional heteroskedasticity
Testing
Jump
Generalized autoregressive conditional heteroscedasticity
Stock market index
Exchange rates
Empirical results
Spot price
Kurtosis
Conditional distribution
Derivative pricing
Diffusion process
Modeling
Discrete-time

Keywords

  • GARCH Models
  • econometrics

Cite this

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title = "Estimation and testing in models containing both jumps and conditional heteroskedasticity",
abstract = "In this paper we develop tests for the hypothesis that a series (observed in discrete time) is generated by a diffusion process and discuss the results of these tests for several exchange rates and stock market indices. The tests of this hypothesis that have been proposed up to now in literature are all based on arbitrary and non-testable assumptions on the conditional distribution of the smooth component of the series. Instead, our tests are based on the weaker assumption that the series is weak GARCH; this hypothesis can easily be tested. To investigate the presence of jumps, we propose a test that is based on an overidentifying relation between variance and kurtosis parameters at an arbitrary frequency, which holds for GARCH diffusions. Monte Carlo evidence suggests that this test is slightly conservative, but nevertheless it has good power properties. The empirical results clearly indicate the presence of jumps in dollar exchange rates. For stock market indices the results are mixed. The finding of jumps has important consequences for derivative pricing as well as for modeling the distribution of future spot prices. In order to assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroskedasticity.",
keywords = "GARCH Models, econometrics",
author = "F.C. Drost and T.E. Nijman and B.J.M. Werker",
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year = "1994",
language = "English",
volume = "1994-105",
series = "CentER Discussion Paper",
publisher = "Unknown Publisher",
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}

Estimation and testing in models containing both jumps and conditional heteroskedasticity. / Drost, F.C.; Nijman, T.E.; Werker, B.J.M.

Unknown Publisher, 1994. (CentER Discussion Paper; Vol. 1994-105).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Estimation and testing in models containing both jumps and conditional heteroskedasticity

AU - Drost, F.C.

AU - Nijman, T.E.

AU - Werker, B.J.M.

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PY - 1994

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N2 - In this paper we develop tests for the hypothesis that a series (observed in discrete time) is generated by a diffusion process and discuss the results of these tests for several exchange rates and stock market indices. The tests of this hypothesis that have been proposed up to now in literature are all based on arbitrary and non-testable assumptions on the conditional distribution of the smooth component of the series. Instead, our tests are based on the weaker assumption that the series is weak GARCH; this hypothesis can easily be tested. To investigate the presence of jumps, we propose a test that is based on an overidentifying relation between variance and kurtosis parameters at an arbitrary frequency, which holds for GARCH diffusions. Monte Carlo evidence suggests that this test is slightly conservative, but nevertheless it has good power properties. The empirical results clearly indicate the presence of jumps in dollar exchange rates. For stock market indices the results are mixed. The finding of jumps has important consequences for derivative pricing as well as for modeling the distribution of future spot prices. In order to assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroskedasticity.

AB - In this paper we develop tests for the hypothesis that a series (observed in discrete time) is generated by a diffusion process and discuss the results of these tests for several exchange rates and stock market indices. The tests of this hypothesis that have been proposed up to now in literature are all based on arbitrary and non-testable assumptions on the conditional distribution of the smooth component of the series. Instead, our tests are based on the weaker assumption that the series is weak GARCH; this hypothesis can easily be tested. To investigate the presence of jumps, we propose a test that is based on an overidentifying relation between variance and kurtosis parameters at an arbitrary frequency, which holds for GARCH diffusions. Monte Carlo evidence suggests that this test is slightly conservative, but nevertheless it has good power properties. The empirical results clearly indicate the presence of jumps in dollar exchange rates. For stock market indices the results are mixed. The finding of jumps has important consequences for derivative pricing as well as for modeling the distribution of future spot prices. In order to assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroskedasticity.

KW - GARCH Models

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M3 - Discussion paper

VL - 1994-105

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BT - Estimation and testing in models containing both jumps and conditional heteroskedasticity

PB - Unknown Publisher

ER -