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Density Forecasting of the  Dow Jones Stock Index
Stockholm University, Faculty of Social Sciences, Department of Statistics.
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2010 (English)Report (Other academic)
Abstract [en]

The distribution of differences in logarithms of the Dow Jones stock index is compared to the Normal (N), Normal Mixture (NM) and a weighted sum of a normal and an asymmetric Laplace distribution (NAL). It is found that the NAL fits best. We came to this result by studying samples with high, medium and low volatility, thus circumventing strong heteroscedasticity in the entire series. The NAL distribution also fitted economic growth, thus revealing a new analogy between financial data and real growth.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University , 2010. , 21 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 1
Keyword [en]
Density forecasting, heteroscedasticity, mixed Normal - Asymmetric Laplace distribution, Method of Moments estimation, connection with economic growth
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-38647OAI: oai:DiVA.org:su-38647DiVA: diva2:311766
Available from: 2010-04-23 Created: 2010-04-23 Last updated: 2010-04-23Bibliographically approved
In thesis
1. Some Contributions to Filtering, Modeling and Forecasting of Heteroscedastic Time Series
Open this publication in new window or tab >>Some Contributions to Filtering, Modeling and Forecasting of Heteroscedastic Time Series
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Heteroscedasticity (or time-dependent volatility) in economic and financial time series has been recognized for decades. Still, heteroscedasticity is surprisingly often neglected by practitioners and researchers. This may lead to inefficient procedures. Much of the work in this thesis is about finding more effective ways to deal with heteroscedasticity in economic and financial data. Paper I suggest a filter that, unlike the Box-Cox transformation, does not assume that the heteroscedasticity is a power of the expected level of the series. This is achieved by dividing the time series by a moving average of its standard deviations smoothed by a Hodrick-Prescott filter. It is shown that the filter does not colour white noise.

An appropriate removal of heteroscedasticity allows more effective analyses of heteroscedastic time series. A few examples are presented in Paper II, III and IV of this thesis. Removing the heteroscedasticity using the proposed filter enables efficient estimation of the underlying probability distribution of economic growth. It is shown that the mixed Normal - Asymmetric Laplace (NAL) distributional fit is superior to the alternatives. This distribution represents a Schumpeterian model of growth, the driving mechanism of which is Poisson (Aghion and Howitt, 1992) distributed innovations. This distribution is flexible and has not been used before in this context. Another way of circumventing strong heteroscedasticity in the Dow Jones stock index is to divide the data into volatility groups using the procedure described in Paper III. For each such group, the most accurate probability distribution is searched for and is used in density forecasting. Interestingly, the NAL distribution fits best also here. This could hint at a new analogy between the financial sphere and the real economy, further investigated in Paper IV. These series are typically heteroscedastic, making standard detrending procedures, such as Hodrick-Prescott or Baxter-King, inadequate. Prior to this comovement study, the univariate and bivariate frequency domain results from these filters are compared to the filter proposed in Paper I. The effect of often neglected heteroscedasticity may thus be studied.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2010. 34 p.
Keyword
Heteroscedasticity, variance stabilizing filters, the mixed Normal - Asymmetric Laplace distribution, density forecasting, detrending filters, spectral analysis, the connection between financial data and economic growth
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-38627 (URN)978-91-7447-107-6 (ISBN)
Public defence
2010-06-04, hörsal 4, hus B, Universitetsvägen 10 B, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2010-05-11 Created: 2010-04-22 Last updated: 2010-06-16Bibliographically approved

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