Book Review: New Introduction to Multiple Time Series Analysis

ABSTRACT

This paper proposes a test for the null hypothesis of periodic stationarity against the alternative hypothesis of periodic integration. We derive the limiting distribution of the test statistic and its characteristic function, which are the same as those of the test developed in Kwiatkowski, Phillips, Schmidt and Shin.[15] Kwiatkowski, D., Phillips, P.C. B., Schmidt, P. and Shin, Y. 1992. Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root.. Journal of Econometrics, 54: 159–178. [Crossref], [Web of Science ®] , [Google Scholar] We find that some parameters, which we must assume under the alternative, have an important effect on the limiting power, so we should choose such parameters carefully. A Monte Carlo simulation reveals that the test has reasonable power but may be affected by the lag truncation parameter that is used for the correction of nuisance parameters.     

时间序列分析中的异方差性

文章阐述异方差性在时间序列分析中的影响及识别方法 ,并比较各方法的应用特点。以双能 X线骨密度仪基线漂移数据为例 ,说明异方差性的一种检验手段。能够识别出序列中的方差变化区域及显著变化区域。对时间序列中的异方差性 ,建议使用假设检验方法予以判别     

时间序列分析在经济预测中的应用

社会消费品零售总额是一项重要、敏感的政府统计。定期发布的消费品零售统计资料,常常引起国内外的强烈关注,间或还会引发一些疑义和争议。文章拟通过运用EXCEL及SAS软件建立季节分解模型和季节哑变量、ARIMA模型,对我国的社会消费零售总额的情况进行预测分析,从初步确定几个不同的模型中,把拟合效果最好的模型保留,并对模型的实用性进行了探讨。     

Time Series Classification Based on Spectral Analysis

For time series data with obvious periodicity (e.g., electric motor systems and cardiac monitor) or vague periodicity (e.g., earthquake and explosion, speech, and stock data), frequency-based techniques using the spectral analysis can usually capture the features of the series. By this approach, we are able not only to reduce the data dimensions into frequency domain but also utilize these frequencies by general classification methods such as linear discriminant analysis (LDA) and k-nearest-neighbor (KNN) to classify the time series. This is a combination of two classical approaches. However, there is a difficulty in using LDA and KNN in frequency domain due to excessive dimensions of data. We overcome the obstacle by using Singular Value Decomposition to select essential frequencies. Two data sets are used to illustrate our approach. The classification error rates of our simple approach are comparable to those of several more complicated methods.     

The Multiple Outlier Problem in Time Series Analysis

In this paper we consider the multiple outlier problem in time series analysis. The underlying undisturbed time series is assumed to be an autoregressive process. The location of the suspicious values is supposed to be known. We introduce conditional least squares estimators for the parameters. The estimates are shown to be strongly consistent. Using similar arguments as in the theory of linear models, we get a test statistic for the general linear hypothesis. Its asymptotic distribution is derived.     

Econometric Time Series Analysis Software: A Review

This article assesses the impact that the late W. Edwards Deming had on statistical practice in general and industrial statistics in particular. It provides a direct-from-the-trenches comparison of Deming's goals with their realizations and a commentary on the relevance and challenges of Deming's concepts to today's industrial environment.     

A Benchmarking Approach to Temporal Disaggregation of Economic Time Series by Related Series

Several methods have been devised to deal with the problem of temporal disaggregation of economic time series (a) either when related series are available or (b) when only aggregate figures exist. In this article, we propose a statistical model-based approach to temporal disaggregation of economic time series by related series. The proposed approach is performed in two stages. In the first stage, we evaluate a preliminary estimate of the disaggregated series using a regression model for the disaggregated series and related series observed in the same frequency. The preliminary estimate of disaggregated series obtained in the first step is not consistent with aggregate figures. To ensure consistency we propose in the second stage, the use of a modified benchmarking approach based on signal extraction (Hillmer and Trabelsi, 1987 Hillmer , S. C. , Trabelsi , A. ( 1987 ). Benchmarking of economic time series . J. Amer. Statist. Assoc. 82 ( 400 ): 1064 – 1071 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Trabelsi and Hillmer, 1990 Trabelsi , A. , Hillmer , S. C. ( 1990 ). Benchmarking time series with reliable benchmarks . Appl. Statist. 39 ( 3 ): 367 – 379 .[Crossref], [Web of Science ®] , [Google Scholar]) to adjust the preliminary estimate of disaggregate series. The approach developed here is used for Seasonally Adjusted (SA) and Not Seasonally Adjusted (NSA) data. A comparison with previous temporal disaggregation methods has been done.     

中国GDP数据周期性的时间序列分析——基于制度及其变迁的一个解释

文章利用时间序列模型等计量方法,对中国GDP总量序列进行了时间趋势分解并结合实证结果对中国经济的发展周期进行了重新的划分.同时以此为视角,进一步提出了我国经济周期波动的特点;中国经济周期的超制度特征以及转轨期经济波动的新规律.     

Periodogram Analysis of Censored Time Series from a Designed Experiment

Growth hormone plasma concentrations vary rhythmically between high and low values. Radioimmunoassay measurements of low values are often indistinguishable from low controls, and are reported as a censored value, the 'minimum detectable dose'. This paper reports such a dataset from a designed experiment with about 60% of the values censored but large distinct signals for the remainder of the data. The ordinates of the average periodogram for each treatment group are independently gamma distributed, with distribution depending on the underlying spectrum and the replication for that group. This situation can lead to an analysis for common spectral shape using a gamma generalized linear model with log link, and the hypothesis of common spectral shape is rejected here. Since such a level of censoring reduces the variance of each profile, the periodogram, which is a partition of the variance, is also reduced in overall magnitude. A simulation study shows that this reduction is not necessarily uniform over the frequency domain, but may be more pronounced at lower or higher ordinates depending on the underlying model. Therefore it is possible that the rejection of common spectral shape is an artefact of the censoring.     

Time Series Modeling of Degradation Due to Outdoor Weathering

Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure.     

An Introduction to Modern Matrix Methods and Statistics

In this article, using the representation that the Kalman filter recursions in state-space models can be expressed as a matrix-weighted average of prior and sample estimates, we supplement the usual filtering algorithm by an extreme bounds analysis. Specifically, as the covariance matrix of the state error is varied in the class of symmetric and positive-definite matrices, the filtering estimates are shown to be in an ellipsoid.