259 research outputs found
Modelling multiple time series via common factors
We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable (nonstationary) factors are identified via expanding the white noise space step by step; therefore solving a high-dimensional optimization problem by several low-dimensional subproblems. Asymptotic properties of the estimation were investigated. The proposed methodology was illustrated with both simulated and real data sets
Factor modeling for high-dimensional time series: Inference for the number of factors
This paper deals with the factor modeling for high-dimensional time series
based on a dimension-reduction viewpoint. Under stationary settings, the
inference is simple in the sense that both the number of factors and the factor
loadings are estimated in terms of an eigenanalysis for a nonnegative definite
matrix, and is therefore applicable when the dimension of time series is on the
order of a few thousands. Asymptotic properties of the proposed method are
investigated under two settings: (i) the sample size goes to infinity while the
dimension of time series is fixed; and (ii) both the sample size and the
dimension of time series go to infinity together. In particular, our estimators
for zero-eigenvalues enjoy faster convergence (or slower divergence) rates,
hence making the estimation for the number of factors easier. In particular,
when the sample size and the dimension of time series go to infinity together,
the estimators for the eigenvalues are no longer consistent. However, our
estimator for the number of the factors, which is based on the ratios of the
estimated eigenvalues, still works fine. Furthermore, this estimation shows the
so-called "blessing of dimensionality" property in the sense that the
performance of the estimation may improve when the dimension of time series
increases. A two-step procedure is investigated when the factors are of
different degrees of strength. Numerical illustration with both simulated and
real data is also reported.Comment: Published in at http://dx.doi.org/10.1214/12-AOS970 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A bootstrap detection for operational determinism.
We propose a bootstrap detection for operationally deterministic versus stochastic nonlinear modelling and illustrate the method with both simulated and real data sets.
Inference in components of variance models with low replication.
In components of variance models the data are viewed as arising through a sum of two random variables, representing between- and within-group variation, respectively. The former is generally interpreted as a group effect, and the latter as error. It is assumed that these variables are stochastically independent and that the distributions of the group effect and the error do not vary from one instance to another. If each group effect can be replicated a large number of times, then standard methods can be used to estimate the distributions of both the group effect and the error. This cannot be achieved without replication, however. How feasible is distribution estimation if it is not possible to replicate prolifically? Can the distributions of random effects and errors be estimated consistently from a small number of replications of each of a large number of noisy group effects, for example, in a nonparametric setting? Often extensive replication is practically infeasible, in particular, if inherently small numbers of individuals exhibit any given group effect. Yet it is quite unclear how to conduct inference in this case. We show that inference is possible, even if the number of replications is as small as 2. Two methods are proposed, both based on Fourier inversion. One, which is substantially more computer intensive than the other, exhibits better performance in numerical experiments.
Principal component analysis for second-order stationary vector time series
We extend the principal component analysis (PCA) to second-order stationary
vector time series in the sense that we seek for a contemporaneous linear
transformation for a -variate time series such that the transformed series
is segmented into several lower-dimensional subseries, and those subseries are
uncorrelated with each other both contemporaneously and serially. Therefore
those lower-dimensional series can be analysed separately as far as the linear
dynamic structure is concerned. Technically it boils down to an eigenanalysis
for a positive definite matrix. When is large, an additional step is
required to perform a permutation in terms of either maximum cross-correlations
or FDR based on multiple tests. The asymptotic theory is established for both
fixed and diverging when the sample size tends to infinity.
Numerical experiments with both simulated and real data sets indicate that the
proposed method is an effective initial step in analysing multiple time series
data, which leads to substantial dimension reduction in modelling and
forecasting high-dimensional linear dynamical structures. Unlike PCA for
independent data, there is no guarantee that the required linear transformation
exists. When it does not, the proposed method provides an approximate
segmentation which leads to the advantages in, for example, forecasting for
future values. The method can also be adapted to segment multiple volatility
processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple
Time Series by Contemporaneous Linear Transformation: PCA for Time Series
High dimensional stochastic regression with latent factors, endogeneity and nonlinearity
We consider a multivariate time series model which represents a high
dimensional vector process as a sum of three terms: a linear regression of some
observed regressors, a linear combination of some latent and serially
correlated factors, and a vector white noise. We investigate the inference
without imposing stationary conditions on the target multivariate time series,
the regressors and the underlying factors. Furthermore we deal with the
endogeneity that there exist correlations between the observed regressors and
the unobserved factors. We also consider the model with nonlinear regression
term which can be approximated by a linear regression function with a large
number of regressors. The convergence rates for the estimators of regression
coefficients, the number of factors, factor loading space and factors are
established under the settings when the dimension of time series and the number
of regressors may both tend to infinity together with the sample size. The
proposed method is illustrated with both simulated and real data examples
Counterparty credit risk management: estimating extreme quantiles for a bank
Counterparty credit risk (CCR) is a complex risk to assess and banks lacked scientifically robust methods for calculating their level of potential exposure. Qiwei Yao, together with his collaborators, developed an innovative methodology for estimating counterparty credit risk, which can help banks meet regulatory requirements and calculate appropriate capital reserves
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