Sunday, Aug 6: 2:00 PM - 3:50 PM
Topic-Contributed Paper Session
Metro Toronto Convention Centre
Business and Economic Statistics Section
Section on Nonparametric Statistics
We review white noise tests in the context of functional time series, and compare many of them using the R package wwntests. The tests are categorized based on whether they are conducted in the time domain or spectral domain, and whether they are valid for i.i.d. or general uncorrelated noise. We also review and extend several residual-based goodness-of-fit tests of popular models used in functional data analysis.
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying structure of the covariance matrix. We discuss how results from Random Matrix Theory, can be used to study the behaviour of our test statistic in a moderate dimensional setting (i.e. the number of variables is comparable to the length of the data). In particular, we demonstrate that the test statistic converges point wise to a normal distribution under the null hypothesis. We evaluate the performance of the proposed approach on a range of simulated datasets and find that it outperforms a range of alternative recently proposed methods. Finally, we use our approach to study changes in covariance within business applications.
The focus is on on stationary vector count time series models defined via deterministic functions of a latent stationary vector Gaussian series. The construction is very general and ensures a pre-specified marginal distribution for the counts in each dimension, depending on unknown parameters that can be marginally estimated. The Gaussian vector series injects flexibility in the model's temporal and cross-sectional dependencies, perhaps through a parametric model akin to a vector autoregression. It is discussed how the latent Gaussian model can be estimated by relating the covariances of the observed counts and the latent Gaussian series. In a possibly high-dimensional setting, concentration bounds are established for the differences between the estimated and true latent Gaussian autocovariance for the observed count series and the estimated marginal parameters. The result is applied to the case when the latent Gaussian series follows a VAR model, and its parameters are estimated sparsely through a LASSO-type procedure.
In time series analysis, many data sets of practical interest contain abrupt changes in structure, such as the mean level or serial dependence. Nonparametric change point detection is a flexible approach which aims to find general distributional changes in the data. In this talk, we propose a methodology for nonparametric detection of multiple change points in multivariate time series. We define a notion of distributional change using a weighted integral of the joint characteristic function of the time series and its lagged values. This is used in combination with a moving sum-type procedure to identify multiple change points by finding local maximisers of a V-statistic calculated in a rolling fashion over the data. This enables the detection of changes in both the marginal and pairwise joint distributions of a serially dependent time series. We examine the theoretical properties of the procedure and illustrate the flexibility of the method by applying it to an economic data example.
Online change point detection consists of sequentially monitoring a time series and raising alarm if a shift in the data distribution is detected. Given data generated by a high-dimensional vector auto-regressive model, we propose an algorithm to detect changes in the model transition matrices in an online format. The algorithm consists of two main steps. First, estimation of transition matrices and variance of error terms are calculated by applying regularization methods on the training data. As new batches of data are observed, in the second step, a specific test statistic is calculated to check whether the transition matrices have changed. Asymptotic normality of the test statistic in the regime of no change points is established under mild conditions. Further, the relationship between the power of the test and jump size is established. Effectiveness of the algorithm is confirmed empirically through various simulation settings as well as an application to detect the timing of seizure in an EEG data.