Functional Causality between Oil Prices and GDP Based on Big Data

This paper examines the causal relationship between oil prices and the Gross Domestic Product (GDP) in the Kingdom of Saudi Arabia. The study is carried out by a data set collected quarterly, by Saudi Arabian Monetary Authority, over a period from 1974 to 2016. We seek how a change in real crude oil price affects the GDP of KSA. Based on a new technique, we treat this data in its continuous path. Precisely, we analyze the causality between these two variables, i.e., oil prices and GDP, by using their yearly curves observed in the four quarters of each year. We discuss the causality in the sense of Granger, which requires the stationarity of the data. Thus, in the first Step, we test the stationarity by using the Monte Carlo test of a functional time series stationarity. Our main goal is treated in the second step, where we use the functional causality idea to model the co-variability between these variables. We show that the two series are not integrated; there is one causality between these two variables. All the statistical analyzes were performed using R software.     

土性剖面随机场模型的平稳性和各态历经性验证

本文根据平稳的和各态历经的随机过程的基本概念及大量钻孔资料，提出了静力触探数据空间分布的平稳性和各态历经性检验的必要性及检验方法；讨论了相关函数形式的选择；通过大量计算比较了求解相关距离的各种方法；分析了相关距离这个概念的工程应用。     

Combining Cumulative Sum Change‐Point Detection Tests for Assessing the Stationarity of Univariate Time Series

We derive tests of stationarity for univariate time series by combining change‐point tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. The proposed approach relies on a general procedure for combining dependent tests based on resampling. After proving the asymptotic validity of the combining procedure under the conjunction of null hypotheses and investigating its consistency, we study rank‐based tests of stationarity by combining cumulative sum change‐point tests based on the contemporary empirical distribution function and on the empirical autocopula at a given lag. Extensions based on tests solely focusing on second‐order characteristics are proposed next. The finite‐sample behaviors of all the derived statistical procedures for assessing stationarity are investigated in large‐scale Monte Carlo experiments, and illustrations on two real datasets are provided. Extensions to multi‐variate time series are briefly discussed as well.     

光纤陀螺随机漂移的建模与滤波研究

时间序列模型是对光纤陀螺(FOG)随机漂移进行建模的一种重要方法.传统的时间序列建模方法难以应用于实时建模,且模型精度较低.因此,提出了适用于高精度FOG随机漂移的改进自回归整合移动平均模型(ARIMA),并基于该模型建立了FOG随机漂移的实时Kalman滤波器.实验结果表明,该改进ARIMA模型能较准确地描述FOG的随机漂移;Allan方差分析结果表明,与基于传统自回归移动平均模型(ARMA)的Kalman滤波结果相比,基于该模型的Kalman滤波对减小光纤陀螺的5项主要随机误差更有效.     

Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes

Abstract.  This article establishes the strong consistency and asymptotic normality (CAN) of the quasi-maximum likelihood estimator (QMLE) for generalized autoregressive conditionally heteroscedastic (GARCH) and autoregressive moving-average (ARMA)-GARCH processes with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution of the periodic GARCH (PGARCH) equation. As a result, it is shown that the moment of some positive order of the PGARCH solution is finite, under which we prove the strong consistency and asymptotic normality of the QMLE for a PGARCH process without any condition on its moments and for a periodic ARMA-GARCH (PARMA-PGARCH) under mild conditions.     

Effect of temporal aggregation on multiple time series in the frequency domain

The effect of temporal aggregation on bivariate spectral measures is investigated. First, the low‐frequency regression coefficient turns out to be invariant under aggregation irrespective of differencing, with the exception of when the aggregation of flow and stock variables is combined. Second, the long‐run squared coherency is invariant with respect to aggregation irrespective of differencing. Third, for frequencies different from zero, limiting results for a growing aggregation level m are obtained equal to those at frequency 0 of the underlying basic series. Hence, all frequency domain information is distorted by aggregation apart from the long‐run one. This also holds true for the phase angle that always approaches zero with growing aggregation level m. The sole exception to these findings is the case of the skip sampling stationary series. Moreover, for finite aggregation level, one may exactly quantify the aggregational effect on each cycle of interest. Numerical examples illustrate our results.     

ON THE EXISTENCE OF A GENERAL MULTIPLE BILINEAR TIME SERIES

Abstract. A sufficient condition is derived for the existence of a strictly stationary solution of the general multiple bilinear time series equations (without assuming subdiagonality). The condition is shown to reduce to the condition of Stensholt and Tjostheim in the special case which they consider. Under this condition a solution is constructed which is shown to be casual in the sense we define, strictly stationary and ergodic. It is moreover the unique causal solution and the unique stationary solution of the defining equations. In the special case when the defining equations contain no non-linear terms, i.e. the multiple autoregressive moving-average (ARMA) model. the condition given here reduces to the well-known sufficient condition for the existence of a casual stationary solution.     

An evolutionary spectrum approach to modeling non‐stationary fading channels

To evaluate mobile communication systems, it is important to develop accurate and concise fading channel models. However, fading encountered in mobile communication is usually non‐stationary, and the existing methods can only model quasi‐stationary or piecewise‐stationary fading instead of general non‐stationary fading. To address this, this paper proposes an evolutionary spectrum (ES)‐based approach to modeling non‐stationary fading channels. Our ES approach is more general than the existing piecewise‐stationary models and is capable of characterizing a general non‐stationary fading channel that has an arbitrary ES (or time‐varying power spectral density); our ES approach is parsimonious and is also able to generate stationary fading processes. As an example, we show how to apply our ES approach to generating stationary and non‐stationary correlated Nakagami‐m fading channel processes. Simulation results show that the ES of the channel gain process produced by our ES‐based channel model agrees well with the user‐specified ES, indicating the accuracy of our ES‐based channel model. Copyright © 2011 John Wiley & Sons, Ltd.     

Testing Composite Hypotheses for Locally Stationary Processes

For a class of locally stationary processes introduced by Dahlhaus, this paper discusses the problem of testing composite hypotheses. First, for the Gaussian likelihood ratio test (GLR), Wald test (W) and Lagrange multiplier test (LM), we derive the limiting distribution under a composite hypothesis in parametric form. It is shown that the distribution of GLR, W and LM tends to a χ² distribution under the hypothesis. We also evaluate their local powers under a sequence of local alternatives, and discuss their asymptotic optimality. The results can be applied to testing for stationarity. Some examples are given. They illuminate the local power property via simulation. On the other hand, we provide a nonparametric LAN theorem. Based on this result, we obtain the limiting distribution of the GLR under both null and alternative hypotheses described in nonparametric form. Finally, the numerical studies are given.     

Statistical analysis of a spatio‐temporal model with location‐dependent parameters and a test for spatial stationarity

Abstract. In this article, we define a spatio‐temporal model with location‐dependent parameters to describe temporal variation and spatial nonstationarity. We consider the prediction of observations at unknown locations using known neighbouring observations. Further, we propose a local least squares‐based method to estimate the parameters at unobserved locations. The sampling properties of these estimators are investigated. We also develop a statistical test for spatial stationarity. To derive the asymptotic results, we show that the spatially nonstationary process can be locally approximated by a spatially stationary process. We illustrate the methods of estimation with some simulations.