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  • 1.
    Gustafsson, Oskar
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Stockhammar, Pär
    Stockholm University, Faculty of Social Sciences, Department of Statistics. National Institute of Economic Research (NIER), Sweden.
    Variance stabilizing filters2019In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed)
    Abstract [en]

    In this paper new filters for removing unspecified form of heteroscedasticity are proposed. The filters build on the assumption that the variance of a pre-whitened time series can be viewed as a latent stochastic process by its own. This makes the filters flexible and useful in many situations. A simulation study shows that removing heteroscedasticity before fitting a model leads to efficiency gains and bias reductions when estimating the parameters of ARMA models. A real data study shows that pre-filtering can increase the forecasting precision of quarterly US GDP growth.

  • 2.
    Stockhammar, Pär
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Comovements of the Dow Jones Stock Index and US GDP2010Report (Other academic)
    Abstract [en]

    This paper explores the connection between Dow Jones industrial average (DJIA) stock prices and the US GDP growth. Both series are heteroscedastic, making standard detrending procedures, such as Hodrick-Prescott or Baxter-King, inadequate. The results from these procedures are compared to the results from heteroscedasticity corrected data, thus the effect of the neglected heteroscedasticity is measured. The analysis is mainly done in the frequency domain but relevant time domain results are also reported.

  • 3.
    Stockhammar, Pär
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Some Contributions to Filtering, Modeling and Forecasting of Heteroscedastic Time Series2010Doctoral 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.

  • 4.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    A Simple Heteroscedasticity Removing filter2007Report (Other academic)
    Abstract [en]

    In this paper variance stabilizing filters are discussed. A new filter with nice properties is proposed which makes use of moving averages and moving standard deviations, the latter smoothed with the Hodrick-Prescott filter. This filter is compared to a GARCH-type filter. An ARIMA model is estimated for the filtered GDP series, and the parameter estimates are used in forecasting the unfiltered series. These forecasts compare well with those of ARIMA, ARFIMA and GARCH models based on the unfiltered data. The filter does not colour white noise.

  • 5.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    A Simple Heteroscedasticity Removing Filter2012In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 41, no 2, p. 281-299Article in journal (Refereed)
    Abstract [en]

    In this article, variance stabilizing filters are discussed. A new filter with nice properties is proposed which makes use of moving averages and moving standard deviations, the latter smoothed with the Hodrick-Prescott filter. This filter is compared to a GARCH-type filter. An ARIMA model is estimated for the filtered GDP series, and the parameter estimates are used in forecasting the unfiltered series. These forecasts compare well with those of ARIMA, ARFIMA, and GARCH models based on the unfiltered data. The filter does not color white noise.

  • 6.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Density Forecasting of the  Dow Jones Stock Index2010Report (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.

  • 7.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Economic Forecasting, by Nicolas Carnot, Vincent Koen and Bruno Tissot, Palgrave Macmillan 2005, ISBN 1-4039-3653-6 (hardback)2008In: International Journal of Forecasting, ISSN 0169-2070, E-ISSN 1872-8200, Vol. 24, no 1, p. 183-184p. 183-184Article, book review (Other academic)
  • 8.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    On the Probability Distribution  of Economic Growth2008Report (Other academic)
    Abstract [en]

    Normality is often mechanically and without sufficient reason assumed in econometric models. In this paper three important and significantly heteroscedastic GDP series are studied. Heteroscedasticity is removed and the distributions of the filtered series are then compared to Normal, Normal Mixture and Normal - Asymmetric Laplace (NAL) distributions. NAL represents a skewed and leptokurtic distribution, which is in line with the Aghion and Howitt (1992) model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL competes well with the alternatives.

  • 9.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    On the probability distribution of economic growth2011In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, no 9, p. 2023-2041Article in journal (Refereed)
    Abstract [en]

    Three important and significantly heteroscedastic gross domestic product series are studied. Omnipresent heteroscedasticity is removed and the distributions of the series are then compared to normal, normal mixture and normal-asymmetric Laplace (NAL) distributions. NAL represents a skewed and leptokurtic distribution, which is in line with the Aghion and Howitt [1] model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL fits the data better than the alternatives.

  • 10.
    Stockhammar, Pär
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Öller, Lars-Erik
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Vad driver den ekonomiska tillväxten?2011In: Ekonomiska samfundets tidskrift, ISSN 0013-3183, E-ISSN 2323-1378, no 2, p. 109-115Article in journal (Refereed)
    Abstract [sv]

    Schumpeter (1942) framkastade idén om att det är företagares innovationer som driver tillväxten. Aghion och Howitt (1992) specificerar en hypotes om kopplingarna innovationer → tillväxt → innovationer. Vi studerar tillväxtens frekvensfunktion för att ta reda på om den uppvisar likheter med Poissonfördelningen, den överföringsmekanism som antas i deras hypotes. Ett nytt filter introduceras för eliminering av heteroskedasticitet. Och visst, en blandning av en normal och Poisson- fördelningarna har den bästa tillpassningen till data! Vidare uppvisar aktiebörsindex samma sorts fördelning. Till slut redovisas några resultat om aktiebörsens roll i tillväxtprocessen.

  • 11.
    Ul Hassan, Mahmood
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Stockhammar, Pär
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Fitting probability distributions to economic growth: a maximum likelihood approach2016In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 43, no 9, p. 1583-1603Article in journal (Refereed)
    Abstract [en]

    The growth rate of the gross domestic product (GDP) usually carries heteroscedasticity, asymmetry and fat-tails. In this study three important and significantly heteroscedastic GDP series are examined. A Normal, normal-mixture, normal-asymmetric Laplace distribution and a Student's t-Asymmetric Laplace (TAL) distribution mixture are considered for distributional fit comparison of GDP growth series after removing heteroscedasticity. The parameters of the distributions have been estimated using maximum likelihood method. Based on the results of different accuracy measures, goodness-of-fit tests and plots, we find out that in the case of asymmetric, heteroscedastic and highly leptokurtic data the TAL-distribution fits better than the alternatives. In the case of asymmetric, heteroscedastic but less leptokurtic data the NM fit is superior. Furthermore, a simulation study has been carried out to obtain standard errors for the estimated parameters. The results of this study might be used in e.g. density forecasting of GDP growth series or to compare different economies.

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