服务业外商直接投资与经济增长关系的实证分析——以江苏省为视角

在述评相关领域已有成果的基础上,以江苏省1992年到2007年的数据为样本,运用时间序列分析和滞后变量模型对服务业外商直接投资和江苏省经济增长的关系进行了实证研究。结果表明:江苏省GDP和SFDI均为非稳定的时间序列数据,但两者之间存在协整关系和正相关关系。     

Fitting dynamic factor models to non-stationary time series

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time by proposing a deterministic time variation of its loadings. In this respect we generalize the existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as a time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a “double-asymptotic” framework of both cross-section and time dimension tending to infinity. The performance of the estimators is illustrated by a simulation study and an application to a macroeconomic data set.     

Coherent forecasting for count time series using Box–Jenkins's AR(p) model

During the last three decades, integer‐valued autoregressive process of order p [or INAR(p)] based on different operators have been proposed as a natural, intuitive and maybe efficient model for integer‐valued time‐series data. However, this literature is surprisingly mute on the usefulness of the standard AR(p) process, which is otherwise meant for continuous‐valued time‐series data. In this paper, we attempt to explore the usefulness of the standard AR(p) model for obtaining coherent forecasting from integer‐valued time series. First, some advantages of this standard Box–Jenkins's type AR(p) process are discussed. We then carry out our some simulation experiments, which show the adequacy of the proposed method over the available alternatives. Our simulation results indicate that even when samples are generated from INAR(p) process, Box–Jenkins's model performs as good as the INAR(p) processes especially with respect to mean forecast. Two real data sets have been employed to study the expediency of the standard AR(p) model for integer‐valued time‐series data.     

Toward regional economic planning: The New England case

As a result of the current change in economic thinking toward planning, this article, using New England as a case, after some preliminary data analysis on the continuity of the two sets of time series data, and the rejection of a hypothesis on the similarity between the regional and national economic structures, proposes first to estimate and then to project the regional economic structure and its possible shift in terms of industrial shares of their 10 component industries. Possible contributions of this kind of study toward regional economic planning then conclude the article.     

Dynamics of the federal funds target rate: a nonstationary discrete choice approach

We apply a discrete choice approach to model the empirical behaviour of the Federal Reserve in changing the federal funds target rate, the benchmark of short‐term market interest rates in the US. Our methods allow the explanatory variables to be nonstationary as well as stationary. This feature is particularly useful in the present application as many economic fundamentals that are monitored by the Fed and are believed to affect decisions to adjust interest rate targets display some nonstationarity over time. The chosen model successfully predicts the majority of the target rate changes during the time period considered (1994–2001) and helps to explain strings of similar intervention decisions by the Fed. Based on the model‐implied optimal interest rate, our findings suggest that there is a lag in the Fed's reaction to economic shocks during this period. Copyright © 2004 John Wiley & Sons, Ltd.     

Bayes model averaging of cyclical decompositions in economic time series

A flexible decomposition of a time series into stochastic cycles under possible non‐stationarity is specified, providing both a useful data analysis tool and a very wide model class. A Bayes procedure using Markov Chain Monte Carlo (MCMC) is introduced with a model averaging approach which explicitly deals with the uncertainty on the appropriate number of cycles. The convergence of the MCMC method is substantially accelerated through a convenient reparametrization based on a hierarchical structure of variances in a state space model. The model and corresponding inferential procedure are applied to simulated data and to cyclical economic time series like US industrial production and unemployment. We derive the implied posterior distributions of model parameters and some relevant functions thereof, shedding light on several key features of economic time series. Copyright © 2006 John Wiley & Sons, Ltd.     

Local block bootstrap inference for trending time series

Resampling for stationary sequences has been well studied in the last couple of decades. In the paper at hand, we focus on nonstationary time series data where the nonstationarity is due to a slowly-changing deterministic trend. We show that the local block bootstrap methodology is appropriate for inference under this locally stationary setting without the need of detrending the data. We prove the asymptotic consistency of the local block bootstrap in the smooth trend model, and complement the theoretical results by a finite-sample simulation.     

基于ARMA模型的我国第三产业总产值时间序列分析

大多数经济时间序列存在着惯性,或者说具有迟缓性。通过对这种惯性分析,可以由时间序列的当前值对其未来值进行估计。本文从我国历年(1953-2004)的第三产业总产值数据出发,将这些数据平稳化,建立自回归移动平均模型(ARAM),从中找出我国第三产业发展的内在规律性。     

Dynamic Structure of Disequilibrium Models

This paper investigates the dynamic structure of a standard disequilibrium model. By assuming that the model variables are non-stationary time series with respect to ample empirical evidence, we find the following: 1) It is the exogenous variables rather than the price adjustment process that form the real adjustment force of the model; 2) Quantity disequilibrium and price disequilibrium are isomeric in the model, and follow a weakly stationary process when all the variables areI (1) nonstationary; 3) The disequilibrium process has a none-zero mean when the weakly exogenous variables of the demand equation do not cointegrate with those of the supply equation, corresponding to certain 'chronic disequilibrium' phenomena; 4) The isomerism between quantity disequilibrium and price changes makes it unnecessary to lean on the 'min condition' to characterise disequilibrium.     

Change-point analysis through integer-valued autoregressive process with application to some COVID-19 data

In this article, we consider the problem of change-point analysis for the count time series data through an integer-valued autoregressive process of order 1 (INAR(1)) with time-varying covariates. These types of features we observe in many real-life scenarios especially in the COVID-19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time-varying smoothing covariate. By using such model, we can model both the components in the active cases at time-point t namely, (i) number of nonrecovery cases from the previous time-point and (ii) number of new cases at time-point t. We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID-19 data sets and compare our proposed model with another PINAR(1) process which has time-varying covariate but no change-point, to demonstrate the overall performance of our proposed model.     

Forecasting compositional time series

Compositional data sets occur in many disciplines and give rise to some interesting statistical considerations. In recent years, the modelling and forecasting of compositional time series has seen some important developments, although this approach does not seem to be widely known. This paper represents a modest step towards rectifying this. After briefly setting out the basic structure of compositional data sets and outlining the implications for forecasting compositional time series, it illustrates the techniques using three examples: modelling and forecasting expenditure shares in the U.K. economy; forecasting trends in obesity in England; and examining shifts in the proportions of English first class cricketers born during particular quarters of the year.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Mining the past to determine the future: Comments

In forecasting, data mining is frequently perceived as a distinct technological discipline without immediate relevance to the challenges of time series prediction. However, Hand (2009) postulates that when the large cross-sectional datasets of data mining and the high-frequency time series of forecasting converge, common problems and opportunities are created for the two disciplines. This commentary attempts to establish the relationship between data mining and forecasting via the dataset properties of aggregate and disaggregate modelling, in order to identify areas where research in data mining may contribute to current forecasting challenges, and vice versa. To forecasting, data mining offers insights on how to handle large, sparse datasets with many binary variables, in feature and instance selection. Furthermore data mining and related disciplines may stimulate research into how to overcome selectivity bias using reject inference on observational datasets and, through the use of experimental time series data, how to extend the utility and costs of errors beyond measuring performance, and how to find suitable time series benchmarks to evaluate computer intensive algorithms. Equally, data mining can profit from forecasting’s expertise in handling nonstationary data to counter the out-of-date-data problem, and how to develop empirical evidence beyond the fine tuning of algorithms, leading to a number of potential synergies and stimulating research in both data mining and forecasting.     

Recent Theoretical Results for Time Series Models with GARCH Errors

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA–GARCH are summarized. Various new ARCH–type models, including double threshold ARCH and GARCH, ARFIMA–GARCH, CHARMA and vector ARMA–GARCH, are also reviewed.     

Testing for convergence in left-right ideological positions

This paper investigates convergence in left-right ideological positions in The Netherlands using cointegration techniques. Our sample consists of 765 weekly observations on those positions as well as on the corresponding political party preference. The time series data display nonstationary patterns in the sense that their means are not constant over time. Therefore, we rely on recently developed techniques in the analysis of multivariate nonstationary time series to study convergence. One of our results is that the ideological positions, when considered relative to a benchmark, can be described by trend-stationary processes. This means that we cannot reject the presence of convergence. Implications of this result are discussed.     

On modeling panels of time series*

This paper reviews research issues in modeling panels of time series. Examples of this type of data are annually observed macroeconomic indicators for all countries in the world, daily returns on the individual stocks listed in the S&P500, and the sales records of all items in a retail store. A panel of time series concerns the case where the cross‐sectional dimension and the time dimension are large. Often, there is no a priori reason to select a few series or to aggregate the series over the cross‐sectional dimension. The use of, for example, a vector autoregression or other types of multivariate models then becomes cumbersome. Panel models and associated estimation techniques are more useful. Due to the large time dimension, one should however incorporate the time‐series features. And, the models should not have too many parameters to facilitate interpretation. This paper discusses representation, estimation and inference of relevant models and discusses recently proposed modeling approaches that explicitly aim to meet these requirements. The paper concludes with some reflections on the usefulness of large data sets. These concern sample selection issues and the notion that more detail also requires more complex models.     

Regional Inequalities in Consumption Patterns: A Multilevel Approach to the Case of Italy

The main aim of this paper is to evaluate the disparities in the Italian regions on the demand side. In more detail, an attempt will be made to find if the consumption behaviour of Italian households is different in the regions. With this in mind, Istat's 2000 Italian Family Budget data set was analysed. The data in question, which were collected through a two‐stage sample over Italy's 20 regions, contains information regarding the expenses of approximately 23,000 households. In this analysis, both households and regions are considered as units: households are nested in the regions so that the basic data structure is hierarchical. In order to take this hierarchical structure into account, a multilevel model was used, making it possible for parameters to vary randomly from region to region. The model in question also made it possible to consider heterogeneity across different groups (regions), such as stochastic variation. First, regional inequalities were tested using a simple model in which households constituted the first level of analysis and were grouped according to their region (the second level). As a second step, and in order to investigate the interaction between geographical context and income distribution, another model was used. This was cross‐classified by income and regions. The most relevant results showed that there is wide fragmentation of consumption behaviour and, at the same time, various differentiated types of behaviour in the regions under analysis. These territorial differentials become clear from income class and items of consumption.     

Estimation of Markov regime-switching regression models with endogenous switching

Following Hamilton [1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384], estimation of Markov regime-switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous. We relax this assumption and develop a parsimonious model of endogenous Markov regime-switching. Inference via maximum likelihood estimation is possible with relatively minor modifications to existing recursive filters. The model nests the exogenous switching model, yielding straightforward tests for endogeneity. In Monte Carlo experiments, maximum likelihood estimates of the endogenous switching model parameters were quite accurate, even in the presence of certain model misspecifications. As an application, we extend the volatility feedback model of equity returns given in Turner et al. [1989. A Markov model of heteroskedasticity, risk, and learning in the stock market. Journal of Financial Economics 25, 3–22] to allow for endogenous switching.     

To criticize the critics: An objective bayesian analysis of stochastic trends

In two recent articles, Sims (1988) and Sims and Uhlig (1988/1991) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as ‘sterile ideas’, the application of nonstationary limit theory as ‘wrongheaded and unenlightening’, and the use of classical methods of inference as ‘unreasonable’ and ‘logically unsound’. They advocate in place of classical methods an explicit Bayesian approach to inference that utilizes a flat prior on the autoregressive coefficient. DeJong and Whiteman adopt a related Bayesian approach in a group of papers (1989a,b,c) that seek to re-evaluate the empirical evidence from historical economic time series. Their results appear to be conclusive in turning around the earlier, influential conclusions of Nelson and Plosser (1982) that most aggregate economic time series have stochastic trends. So far these criticisms of unit root econometrics have gone unanswered; the assertions about the impropriety of classical methods and the superiority of flat prior Bayesian methods have been unchallenged; and the empirical re-evaluation of evidence in support of stochastic trends has been left without comment. This paper breaks that silence and offers a new perspective. We challenge the methods, the assertions, and the conclusions of these articles on the Bayesian analysis of unit roots. Our approach is also Bayesian but we employ what are known in the statistical literature as objective ignorance priors in our analysis. These are developed in the paper to accommodate explicitly time series models in which no stationarity assumption is made. Ignorance priors are intended to represent a state of ignorance about the value of a parameter and in many models are very different from flat priors. We demonstrate that in time series models flat priors do not represent ignorance but are actually informative (sic) precisely because they neglect generically available information about how autoregressive coefficients influence observed time series characteristics. Contrary to their apparent intent, flat priors unwittingly bias inferences towards stationary and i.i.d. alternatives where they do represent ignorance, as in the linear regression model. This bias helps to explain the outcome of the simulation experiments in Sims and Uhlig and some of the empirical results of DeJong and Whiteman. Under both flat priors and ignorance priors this paper derives posterior distributions for the parameters in autoregressive models with a deterministic trend and an arbitrary number of lags. Marginal posterior distributions are obtained by using the Laplace approximation for multivariate integrals along the lines suggested by the author (Phillips, 1983) in some earlier work. The bias towards stationary models that arises from the use of flat priors is shown in our simulations to be substantial; and we conclude that it is unacceptably large in models with a fitted deterministic trend, for which the expected posterior probability of a stochastic trend is found to be negligible even though the true data generating mechanism has a unit root. Under ignorance priors, Bayesian inference is shown to accord more closely with the results of classical methods. An interesting outcome of our simulations and our empirical work is the bimodal Bayesian posterior, which demonstrates that Bayesian confidence sets can be disjoint, just like classical confidence intervals that are based on asymptotic theory. The paper concludes with an empirical application of our Bayesian methodology to the Nelson-Plosser series. Seven of the 14 series show evidence of stochastic trends under ignorance priors, whereas under flat priors on the coefficients all but three of the series appear trend stationary. The latter result corresponds closely with the conclusion reached by DeJong and Whiteman (1989b) (based on truncated flat priors). We argue that the DeJong-Whiteman inferences are biased towards trend stationarity through the use of flat priors on the autoregressive coefficients, and that their inferences for some of the series (especially stock prices) are fragile (i.e. not robust) not only to the prior but also to the lag length chosen in the time series specification.