2,006 research outputs found
A generalization of periodic autoregressive models for seasonal time series
Many nonstationary time series exhibit changes in the trend and seasonality structure, that may be modeled by splitting the time axis into different regimes. We propose multi-regime models where, inside each regime, the trend is linear and seasonality is explained by a Periodic Autoregressive model. In addition, for achieving parsimony, we allow season grouping, i.e. seasons may consists of one, two, or more consecutive observations. Since the set of possible solutions is very large, the choice of number of regimes, change times and order and structure of the Autoregressive models is obtained by means of a Genetic Algorithm, and the evaluation of each possible solution is left to an identication criterion such as AIC, BIC or MDL. The comparison and performance of the proposed method are illustrated by a real data analysis. The results suggest that the proposed procedure is useful for analyzing complex phenomena with structural breaks, changes in trend and evolving seasonality
Selected Challenges From Spatial Statistics For Spatial Econometricians
Griffith and Paelinck (2011) present selected non-standard spatial statistics and spatial econometrics topics that address issues associated with spatial econometric methodology. This paper addresses the following challenges posed by spatial autocorrelation alluded to and/or derived from the spatial statistics topics of this book: the Gaussian random variable Jacobian term for massive datasets; topological features of georeferenced data; eigenvector spatial filtering-based georeferenced data generating mechanisms; and, interpreting random effects.Artykuł prezentuje wybrane, niestandardowe statystyki przestrzenne oraz zagadnienia ekonometrii przestrzennej. Rozważania teoretyczne koncentrują się na wyzwaniach wynikających z autokorelacji przestrzennej, nawiązując do pojęć Gaussowskiej zmiennej losowej, topologicznych cech danych georeferencyjnych, wektorów własnych, filtrów przestrzennych, georeferencyjnych mechanizmów generowania danych oraz interpretacji efektów losowych
Independent subspace analysis can cope with the 'curse of dimensionality'
We search for hidden independent components, in particular we consider the independent subspace analysis (ISA) task. Earlier ISA procedures assume that the dimensions of the components are known. Here we show a method that enables the non-combinatorial estimation of the components. We make use of a decomposition principle called the ISA separation theorem. According to this separation theorem the ISA task can be reduced to the independent component analysis (ICA) task that assumes one-dimensional components and then to a grouping procedure that collects the respective non-independent elements into independent groups. We show that non-combinatorial grouping is feasible by means of the non-linear f-correlation matrices between the estimated components
Noise-Robust End-to-End Quantum Control using Deep Autoregressive Policy Networks
Variational quantum eigensolvers have recently received increased attention,
as they enable the use of quantum computing devices to find solutions to
complex problems, such as the ground energy and ground state of
strongly-correlated quantum many-body systems. In many applications, it is the
optimization of both continuous and discrete parameters that poses a formidable
challenge. Using reinforcement learning (RL), we present a hybrid policy
gradient algorithm capable of simultaneously optimizing continuous and discrete
degrees of freedom in an uncertainty-resilient way. The hybrid policy is
modeled by a deep autoregressive neural network to capture causality. We employ
the algorithm to prepare the ground state of the nonintegrable quantum Ising
model in a unitary process, parametrized by a generalized quantum approximate
optimization ansatz: the RL agent solves the discrete combinatorial problem of
constructing the optimal sequences of unitaries out of a predefined set and, at
the same time, it optimizes the continuous durations for which these unitaries
are applied. We demonstrate the noise-robust features of the agent by
considering three sources of uncertainty: classical and quantum measurement
noise, and errors in the control unitary durations. Our work exhibits the
beneficial synergy between reinforcement learning and quantum control
Surrogate time series
Before we apply nonlinear techniques, for example those inspired by chaos
theory, to dynamical phenomena occurring in nature, it is necessary to first
ask if the use of such advanced techniques is justified "by the data". While
many processes in nature seem very unlikely a priori to be linear, the possible
nonlinear nature might not be evident in specific aspects of their dynamics.
The method of surrogate data has become a very popular tool to address such a
question. However, while it was meant to provide a statistically rigorous,
foolproof framework, some limitations and caveats have shown up in its
practical use. In this paper, recent efforts to understand the caveats, avoid
the pitfalls, and to overcome some of the limitations, are reviewed and
augmented by new material. In particular, we will discuss specific as well as
more general approaches to constrained randomisation, providing a full range of
examples. New algorithms will be introduced for unevenly sampled and
multivariate data and for surrogate spike trains. The main limitation, which
lies in the interpretability of the test results, will be illustrated through
instructive case studies. We will also discuss some implementational aspects of
the realisation of these methods in the TISEAN
(http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at
http://www.mpipks-dresden.mpg.de/~tisea
Causal inference for social network data
We describe semiparametric estimation and inference for causal effects using
observational data from a single social network. Our asymptotic result is the
first to allow for dependence of each observation on a growing number of other
units as sample size increases. While previous methods have generally
implicitly focused on one of two possible sources of dependence among social
network observations, we allow for both dependence due to transmission of
information across network ties, and for dependence due to latent similarities
among nodes sharing ties. We describe estimation and inference for new causal
effects that are specifically of interest in social network settings, such as
interventions on network ties and network structure. Using our methods to
reanalyze the Framingham Heart Study data used in one of the most influential
and controversial causal analyses of social network data, we find that after
accounting for network structure there is no evidence for the causal effects
claimed in the original paper
- …