Finite-sample properties of estimators for first and second order autoregressive processes

The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like . A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying -package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

The CUSUM statistic of change point under NA sequences

In this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes. Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

A Performance Comparison of Various Bootstrap Methods for Diffusion Processes

In this paper, we compare the finite sample performances of various bootstrap methods for diffusion processes. Though diffusion processes are widely used to analyze stocks, bonds, and many other financial derivatives, they are known to heavily suffer from size distortions of hypothesis tests. While there are many bootstrap methods applicable to diffusion models to reduce such size distortions, their finite sample performances are yet to be investigated. We perform a Monte Carlo simulation comparing the finite sample properties, and our results show that the strong Taylor approximation method produces the best performance, followed by the Hermite expansion method.

Finite Sample Properties for Closed Loop System Identification

In this paper, after closed loop system identification is reviewed, asymptotic analysis and finite sample analysis for closed loop system identification are studied respectively, corresponding to the infinite data and finite data. More specifically, within the framework of infinite data, the cost function is modified to its simplified form, and one optimal feedback controller is obtained based on our own derivations. The simplified cost function and optimal feedback controller are benefit for practical application. Furthermore, the asymptotic variance of that optimal feedback controller is also yielded from the point of asymptotic analysis. In the case of finite data, finite sample properties are constructed for closed loop system identification, then one difference between the sampled identification criterion and its corresponding expected criterion is derived as an explicit form, which can bound one guaranteed interval for the sampled identification criterion. Finally, one simulation example is used to prove the efficiency of our proposed theories.

Two-sample Tests for Functional Data Using Characteristic Functions

In this paper, we consider the two-sample problem for univariate and multivariate functional data. To solve this problem, we use tool of characteristic function and a basis function representation of functional data. We construct test statistics for conformity of distributions based on a weighted distance between characteristic functions of random vectors obtained in basis representation. Different weight functions result in different test statistics, whose distributions are approximated by permutation method. Testing procedures are implemented in the R program and the code is available. Simulation study shows good finite sample properties of proposed methods, while real data example illustrates the application of them.

Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.

Adversarial Inference Is Efficient

We study properties of the adversarial framework, introduced in Kaji, Manresa and Pouliot (2020). We show that the adversarial inference with an oracle classifier is statistically efficient. In addition, we study the finite sample properties of the adversarial estimation framework for the autoregressive parameter of a linear dynamic fixed effects panel data model with Gaussian errors. Unlike maximum likelihood, but similarly as other minimum distance estimators, the adversarial estimators do not suffer from the incidental parameter bias. In our simulations, using a one-hidden-layer neural network as discriminator delivers the estimates with smallest root mean squared error.

Dynamic Factor Copula Models with Estimated Cluster Assignments

This paper proposes a dynamic multi-factor copula for use in high dimensional time series applications. A novel feature of our model is that the assignment of individual variables to groups is estimated from the data, rather than being pre-assigned using SIC industry codes, market capitalization ranks, or other ad hoc methods. We adapt the k-means clustering algorithm for use in our application and show that it has excellent finite-sample properties. Applying the new model to returns on 110 US equities, we find around 20 clusters to be optimal. In out-of-sample forecasts, we find that a model with as few as five estimated clusters significantly outperforms an otherwise identical model with 21 clusters formed using two-digit SIC codes.