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Browsing by Author "Kokoszka, Piotr S., advisor"

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    Inference for cumulative intraday return curves
    (Colorado State University. Libraries, 2018) Zheng, Ben, author; Kokoszka, Piotr S., advisor; Cooley, Dan, committee member; Miao, Hong, committee member; Zhou, Wen, committee member
    The central theme of this dissertation is inference for cumulative intraday return (CIDR) curves computed from high frequency data. Such curves describe how the return on an investment evolves with time over a relatively short period. We introduce a functional factor model to investigate the dependence of cumulative return curves of individual assets on the market and other factors. We propose a new statistical test to determine whether this dependence is the same in two sample periods. The statistical power of the new test is validated by asymptotic theory and a simulation study. We apply this test to study the impact on individual stocks and Sector Exchanged-Traded Funds (ETF) of the recent financial crisis and of trends in the oil price. Our analysis reveals that the functional approach has an information content different from that obtained from scalar factor models for point-to-point returns. Motivated by the risk inherent in intraday investing, we propose several ways of quantifying extremal behavior of a time series of curves. A curve can be extreme if it has shape and/or magnitude much different than the bulk of observed curves. Our approach is at the nexus of Functional Data Analysis and Extreme Value Theory. The risk measures we propose allow us to assess probabilities of observing extreme curves not seen in a historical record. These measures complement risk measures based on point-to-point returns, but have different interpretation and information content. Using our approach, we study how the financial crisis of 2008 impacted the extreme behavior of intraday cumulative return curves. We discover different impacts on shares in important sectors of the US economy. The information our analysis provides is in some cases different from the conclusions based on the extreme value analysis of daily closing price returns. In a different direction, we investigate a large-scale multiple testing problem motivated by a biological study. We introduce mixed models to fit the longitudinal data and incorporate a bootstrap method to construct a false discovery rate (FDR) controlling procedure. A simulation study is implemented to show its effectiveness.
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    Inference for functional time series with applications to yield curves and intraday cumulative returns
    (Colorado State University. Libraries, 2016) Young, Gabriel J., author; Kokoszka, Piotr S., advisor; Miao, Hong, committee member; Breidt, F. Jay, committee member; Zhou, Wen, committee member
    Econometric and financial data often take the form of a functional time series. Examples include yield curves, intraday price curves and term structure curves. Before an attempt is made to statistically model or predict such series, we must address whether or not such a series can be assumed stationary or trend stationary. We develop extensions of the KPSS stationarity test to functional time series. Motivated by the problem of a change in the mean structure of yield curves, we also introduce several change point methods applied to dynamic factor models. For all testing procedures, we include a complete asymptotic theory, a simulation study, illustrative data examples, as well as details of the numerical implementation of the testing procedures. The impact of scheduled macroeconomic announcements has been shown to account for sizable fractions of total annual realized stock returns. To assess this impact, we develop methods of derivative estimation which utilize a functional analogue of local-polynomial smoothing. The confidence bands are then used to find time intervals of statistically increasing cumulative returns.
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    Methods for extremes of functional data
    (Colorado State University. Libraries, 2018) Xiong, Qian, author; Kokoszka, Piotr S., advisor; Cooley, Daniel, committee member; Pinaud, Olivier, committee member; Wang, Haonan, committee member
    Motivated by the problem of extreme behavior of functional data, we develop statistical theory at the nexus of functional data analysis (FDA) and extreme value theory (EVT). A fundamental technique of functional data analysis is to replace infinite dimensional curves with finite dimensional representations in terms of functional principal components (FPCs). The coefficients of these projections, called the scores, encode the shapes of the curves. Therefore, the study of the extreme behavior of functional time series can be transformed to the study on functional principal component scores. We first derive two tests of significance of the slope function using functional principal components and their empirical counterparts (EFPC's). Applied to tropical storm data, these tests show a significant trend in the annual pattern of upper wind speed levels of hurricanes. Then we establish sufficient conditions under which the asymptotic extreme behavior of the multivariate estimated scores is the same as that of the population scores. We clarify these issues, including the rate of convergence, for Gaussian functions and for more general functional time series whose projections are in the Gumbel domain of attraction. Finally, we derive the asymptotic distribution of the sample covariance operator and of the sample functional principal components for functions which are regularly varying and whose fourth moment does not exist. The new theory is applied to establish the consistency of the regression operator in a functional linear model, with such errors.
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    Test of change point versus long-range dependence in functional time series
    (Colorado State University. Libraries, 2024) Meng, Xiangdong, author; Kokoszka, Piotr S., advisor; Cooley, Dan, committee member; Wang, Haonan, committee member; Miao, Hong, committee member
    In scalar time series analysis, a long-range dependent (LRD) series cannot be easily distinguished from certain non-stationary models, such as the change in mean model with short-range dependent (SRD) errors. To be specific, realizations of LRD series usually have a characteristic of changing local mean if the time span taken into account is long enough, which resembles the behavior of change in mean models. Test procedure for distinguishing between these two types of model has been investigated a lot in scalar case, see e.g. Berkes et al. (2006) and Baek and Pipiras (2012) and references therein. However, no analogous test for functional observations has been developed yet, partly because of omitted methods and theory for analyzing functional time series with long-range dependence. My dissertation establishes a procedure for testing change in mean models with SRD errors against LRD processes in functional case, which is an extension of the method of Baek and Pipiras (2012). The test builds on the local Whittle (LW) (or Gaussian semiparametric) estimation of the self-similarity parameter, which is based on the estimated level 1 scores of a suitable functional residual process. Remarkably, unlike other parametric methods such as Whittle estimation, whose asymptotic properties heavily depend on validity of the underlying spectral density on the full frequency range (−π, π], LW estimation imposes mild restrictions on the spectral density only near the origin and is thus more robust to model misspecification. We shall prove that the test statistic based on LW estimation is asymptotically normally distributed under the null hypothesis and it diverges to infinity under the LRD alternative.