Detecting changes in functional linear models

We observe two sequences of curve which are connected via an integral operator. Our model includes linear models as well as autoregressive models in Hilbert spaces. We wish to test the null hypothesis that the operator did not change during the observation period. Our method is based on projecting the observations onto a suitably chosen finite dimensional space. The testing procedure is based on functionals of the weighted residuals of the projections. Since the quadratic form is based on estimating the long-term covariance matrix of the residuals, we also provide some results on Bartlett-type estimators

Near-integrated GARCH sequences

Motivated by regularities observed in time series of returns on speculative assets, we develop an asymptotic theory of GARCH(1,1) processes {y_k} defined by the equations y_k=\sigma_k\epsilon_k, \sigma_k^2=\omega +\alpha y_{k-1}^2+\beta \sigma_{k-1}^2 for which the sum \alpha +\beta approaches unity as the number of available observations tends to infinity. We call such sequences near-integrated. We show that the asymptotic behavior of near-integrated GARCH(1,1) processes critically depends on the sign of \gamma :=\alpha +\beta -1. We find assumptions under which the solutions exhibit increasing oscillations and show that these oscillations grow approximately like a power function if \gamma \leq 0 and exponentially if \gamma >0. We establish an additive representation for the near-integrated GARCH(1,1) processes which is more convenient to use than the traditional multiplicative Volterra series expansion.Comment: Published at http://dx.doi.org/10.1214/105051604000000783 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Functional generalized autoregressive conditional heteroskedasticity

Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the focus of research with attention given to methods seeking an efficient and economic estimation of a large number of model parameters. Due to the need for estimation of many parameters, however, these models may not be suitable for modeling now prevalent high-frequency volatility data. One potentially useful way to bypass these issues is to take a functional approach. In this paper, theory is developed for a new functional version of the generalized autoregressive conditionally heteroskedastic process, termed fGARCH. The main results are concerned with the structure of the fGARCH(1,1) process, providing criteria for the existence of a strictly stationary solutions both in the space of square-integrable and continuous functions. An estimation procedure is introduced and its consistency verified. A small empirical study highlights potential applications to intraday volatility estimation

Merits and drawbacks of variance targeting in GARCH models

Variance targeting estimation is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood (QML) estimation of GARCH models. It relies on a reparameterization of the model and a first-step estimation of the unconditional variance. The remaining parameters are estimated by QML in a second step. This paper establishes the asymptotic distribution of the estimators obtained by this method in univariate GARCH models. Comparisons with the standard QML are provided and the merits of the variance targeting method are discussed. In particular, it is shown that when the model is misspecified, the VTE can be superior to the QMLE for long-term prediction or Value-at-Risk calculation. An empirical application based on stock market indices is proposed.Consistency and Asymptotic Normality; GARCH; Heteroskedastic Time Series; Quasi Maximum Likelihood Estimation; Value-at-Risk; Variance Targeting Estimator.

THE MANIFESTATION OF HEALTH-CONSCIOUSNESS IN FOOD PREFERENCE AND CONSUMPTION AMONG YOUNG PEOPLE ACCORDING TO AN EMPIRIC STUDY

In our study we set out to find answers to the question of how today’s secondary schools students in Hungary assessed certain food products. We examined in the target group also the development of relationship between the preference of a certain product and its assessment from the health point of view. We assumed that both the preference and assessment of food for its effects on health were not only influenced by the gender of consumers but also by the type of the school attended and to a large extent by the development level of the region of domicile. In conclusion, young people had shown some signs of awareness of what is healthy eating and they had been able to differentiate between healthy and unhealthy foodstuffs, but their consumption was still significantly dominated by what they considered to be pleasant food. A possible consequence of this finding is that nearly a quarter of young people and a third of boys consider themselves suffering from overweight. XXXXXXXXXXXXXXXXXXXXXXXXXXXXX Kutatásunkban arra kerestük a választ, hogy a mai magyar középiskolások körében milyen a megítélése az egyes élelmiszeripari termékeknek. Vizsgáltuk, hogy az élelmiszerek kedveltsége és annak egészségesség megítélése között ho-gyan alakul a kapcsolat a vizsgált csoport esetében. Feltételezésünk volt, hogy mind a kedveltséget, mind a különbözÅ‘ élelmiszerek megítélését az egészségesség szempontjából nemcsak a fogyasztók neme, de az iskola típusa és a lakóhely sze-rinti régió gazdasági fejlettsége is nagy mértékben befolyásolja. Összességében megállapítást nyert, hogy bár a fiatalok mutattak olyan jeleket, hogy ismerik az egészséges táplálkozás alapjait, illetve hogy különbséget tudnak tenni egészséges és egészségtelen élelmiszerek között, mégis fogyasztásukat ma még sokkal inkább az élvezeti jellemzÅ‘k dominálják. Talán ennek is köszönhetÅ‘, hogy a fiatalok saját magukról kiállított bizonyítványa alapján közel egynegyedük küszködik súlyproblémával – a fiúknak pedig az egyharmada!questionnary, high schools, level of healthy consumption, kérdőíves felmérés, középiskolások, egészséges fogyasztás szintje, Food Consumption/Nutrition/Food Safety, Marketing,

Cosmology with Gamma-Ray Bursts Using k-correction

In the case of Gamma-Ray Bursts with measured redshift, we can calculate the k-correction to get the fluence and energy that were actually produced in the comoving system of the GRB. To achieve this we have to use well-fitted parameters of a GRB spectrum, available in the GCN database. The output of the calculations is the comoving isotropic energy E_iso, but this is not the endpoint: this data can be useful for estimating the {\Omega}M parameter of the Universe and for making a GRB Hubble diagram using Amati's relation.Comment: 4 pages, 6 figures. Presented as a talk on the conference '7th INTEGRAL/BART Workshop 14 -18 April 2010, Karlovy Vary, Czech Republic'. Published in Acta Polytechnic

Limit Laws in Transaction-Level Asset Price Models

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such e®ects as intraday seasonal patterns in volatility, and non-trading periods that may be di®erent for the two assets. Most assumptions are stated directly on the point process, though we provide su±cient conditions on the corresponding inter-trade durations for these assumptions to hold. We obtain the asymptotic distribution of the log-price process. We also obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrat- ing parameter based on data sampled from an equally-spaced discretization of calendar time, in the case of weak fractional cointegration. Finally, we obtain the limiting distribution of the ordinary least-squares estimator of the autoregressive parameter in a simpli¯ed transaction-level univariate model with a unit root.NYU, Stern, Center for Digital Economy Researc