Life behavior of [delta]-shock model

Two traditional assumptions in shock models are that the failure of a system is related either to the cumulative effect of a large number of shocks or to the maximum magnitude of shocks ever occur. The present paper provide another type (only concentrating on inter-arrivals) of shock model (called [delta]-shock model). For the case with underlying homogeneous Poisson process, some results are given, such as, analytic survival function, moment of any order, class properties and asymptotic behavior of the normalized lifetime TM/E[TM] of a system as [delta]-->0. For another case with underlying non-homogeneous Poisson process with periodic intensity [lambda](t), analytic survival function is given as well. Moreover, under practical conditions, moment of any order is proved to be finite, and asymptotic behavior of T0/E[T0] is obtained as [delta]-->0. This [delta] shock model has diverse range of applications.[delta] shock model Life distribution Poisson process Exponential distribution NWU NBU Asymptotic behavior

Projected estimation for large-dimensional matrix factor models

10.1016/j.jeconom.2021.04.001Journal of Econometric

Stochastic regression and its application to hedging in finance

In this paper we investigate how to employ stochastic regression to hedge risks in finance, where the risk of a security is measured by its quadratic variation process. Mykland and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another security. In this paper, we investigate how to further reduce the remaining unhedgable risk by adding more hedging securities. Some practical guidelines on how to choose those hedging securities in practice is also given

Large-Dimensional Factor Analysis Without Moment Constraints

10.1080/07350015.2020.1811101JOURNAL OF BUSINESS & ECONOMIC STATISTIC

One-way or two-way factor model for matrix sequences?

This paper investigates the issue of determining the dimensions of row and column factor spaces in matrix-valued data. Exploiting the eigen-gap in the spectrum of sample second moment matrices of the data, we propose a family of randomised tests to check whether a one-way or two-way factor structure exists or not. Our tests do not require any arbitrary thresholding on the eigenvalues, and can be applied with (virtually) no restrictions on the relative rate of divergence of the cross-sections to the sample sizes as they pass to infinity. Although tests are based on a randomisation which does not vanish asymptotically, we propose a de-randomised, “strong” (based on the Law of the Iterated Logarithm) decision rule to choose in favour or against the presence of common factors. We use the proposed tests and decision rule in two ways. We further cast our individual tests in a sequential procedure whose output is an estimate of the number of common factors. Our tests are built on two variants of the sample second moment matrix of the data: one based on a row (or column) “flattened” version of the matrix-valued sequence, and one based on a projection-based method. Our simulations show that both procedures work well in large samples and, in small samples, the one based on the projection method delivers a superior performance compared to existing methods in virtually all cases considered.</p

Online Change-point Detection for Matrix-valued Time Series with Latent Two-way Factor Structure

This paper proposes a novel methodology for the online detectionof changepoints in the factor structure of large matrix time series. Ourapproach is based on the well-known fact that, in the presence of achangepoint, the number of spiked eigenvalues in the second momentmatrix of the data increases (e.g., in the presence of a change in theloadings, or if a new factor emerges). Based on this, we propose twofamilies of procedures - one based on the fluctuations of partial sums,and one based on extreme value theory - to monitor whether the firstnon-spiked eigenvalue diverges after a point in time in the monitoringhorizon, thereby indicating the presence of a changepoint. Our proce-dure is based only on rates; at each point in time, we randomise theestimated eigenvalue, thus obtaining a normally distributed sequencewhich isi.i.d.with mean zero under the null of no break, whereasit diverges to positive infinity in the presence of a changepoint. Webase our monitoring procedures on such sequence. Extensive simula-tion studies and empirical analysis justify the theory. An R packageimplementing the procedure is available on CRAN.</p

Factor and Idiosyncratic Empirical Processes

<p>The distributions of the common and idiosyncratic components for an individual variable are important in forecasting and applications. However, they are not identified with low-dimensional observations. Using the recently developed theory for large dimensional approximate factor model for large panel data, the common and idiosyncratic components can be estimated consistently. Based on the estimated common and idiosyncratic components, we construct the empirical processes for estimation of the distribution functions of the common and idiosyncratic components. We prove that the two empirical processes are oracle efficient when <i>T</i> = <i>o</i>(<i>p</i>) where <i>p</i> and <i>T</i> are the dimension and sample size, respectively. This demonstrates that the factor and idiosyncratic empirical processes behave as well as the empirical processes pretending that the common and idiosyncratic components for an individual variable are directly observable. Based on this oracle property, we construct simultaneous confidence bands (SCBs) for the distributions of the common and idiosyncratic components. For the first-order consistency of the estimated distribution functions, <math><mrow><msqrt><mi>T</mi></msqrt><mo>=</mo><mi>o</mi><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow></math> suffices. Extensive simulation studies check that the estimated bands have good coverage frequencies. Our real data analysis shows that the common-component distribution has a structural change during the crisis in 2008, while the idiosyncratic-component distribution does not change much. Supplementary materials for this article are available online.</p