Functional-coefficient models for nonstationary time series data

This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean squared error. When the coefficient function is a function of a nonstationary variable, the new findings are that the asymptotic bias of its nonparametric estimator is the same as the stationary covariate case but convergence rate differs, and further, the asymptotic distribution is a mixed normal, associated with the local time of a standard Brownian motion. The asymptotic behavior at boundaries is also investigated.     

Forecasting unstable and nonstationary time series

Many time series are asymptotically unstable and intrinsically nonstationary, i.e. satisfy difference equations with roots greater than one (in modulus) and with time-varying parameters. Models developed by Box–Jenkins solve these problems by imposing on data two transformations: differencing (unit-roots) and exponential (Box–Cox). Owing to the Jensen inequality, these techniques are not optimal for forecasting and sometimes may be arbitrary. This paper develops a method for modeling time series with unstable roots and changing parameters. In particular, the effectiveness of recursive estimators in tracking time-varying unstable parameters is shown with applications to data-sets of Box–Jenkins. The method is useful for forecasting time series with trends and cycles whose pattern changes over time.     

Convergence in international output

This paper proposes and tests new definitions of convergence and common trends for per capita output. We define convergence for a group of countries to mean that each country has identical long-run trends, either stochastic or deterministic, while common trends allow for proportionality of the stochastic elements. These definitions lead naturally to the use of cointegration techniques in testing. Using century-long time series for 15 OECD economies, we reject convergence but find substantial evidence for common trends. Smaller samples of European countries also reject convergence but are driven by a lower number of common stochastic trends.     

Forecasting economic time series with unconditional time-varying variance

The classical forecasting theory of stationary time series exploits the second-order structure (variance, autocovariance, and spectral density) of an observed process in order to construct some prediction intervals. However, some economic time series show a time-varying unconditional second-order structure. This article focuses on a simple and meaningful model allowing this nonstationary behaviour. We show that this model satisfactorily explains the nonstationary behaviour of several economic data sets, among which are the U.S. stock returns and exchange rates. The question of how to forecast these processes is addressed and evaluated on the data sets.     

Finding common seasonal patterns among time series: An MDS approach

This paper provides an approach to the analysis of time series seasonal pattern similarities based on a special MDS approach — the non-metric SSA-I (Smallest Space Analysis) technique. Indices of dissimilarity for time series are defined generally while special cases drawn from the economic problems are treated by means of examples. The basic contributions of the paper are two-fold: First we extend the use of SSA-I to time series analysis by transforming the mutual relationship between (as well as within) the time series in a symmetric matrix. As a result, the tool of SSA-I developed by L. Guttman may easily be used. Second, by an introduction of non-metric techniques such as SSA-I in time series analysis we increase our capacity to deal with problems hitherto unsolved. In particular, ordinal data as well as behavioral data for which model processes are not defined and seasonal patterns similarities may be studied by our technique.     

Optimal estimation under nonstandard conditions

We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek–Le Cam optimality theory is adapted to cover this situation. We show that the expectation of certain monotone “bowl-shaped” functions of the squared estimation error are minimized by the ML estimator in locally asymptotically quadratic situations, which often occur in nonstationary time series analysis when the LAN property fails. Moreover, we demonstrate a direct connection between the (Bayesian property of) asymptotic normality of the posterior and the classical optimality properties of ML estimators.     

IN PRAISE OF IDEOLOGICAL OPENNESS

One's ideological views – that is, the pattern of positions one tends to take on important public‐policy issues – run deep and change little. Inevitably they involve commitments and judgments about the most important things. Just as we value disclosure of vested interests, we value disclosure of one's ideological tendencies. This article elaborates some virtues of ideological openness.     

Discrete choice modeling with nonstationary panels applied to exchange rate regime choice

This paper develops a regression limit theory for discrete choice nonstationary panels with large cross section (N) and time series (T) dimensions. Some results emerging from this theory are directly applicable in the wider context of M-estimation. This includes an extension of work by Wooldridge [Wooldridge, J.M., 1994. Estimation and Inference for Dependent Processes. In: Engle, R.F., McFadden, D.L. (Eds.). Handbook of Econometrics, vol. 4, North-Holland, Amsterdam] on the limit theory of local extremum estimators to multi-indexed processes in nonlinear nonstationary panel data models.It is shown that the maximum likelihood (ML) estimator is consistent without an incidental parameters problem and has a limit theory with a fast rate of convergence N^1/2T^3/4 (in the stationary case, the rate is N^1/2T^1/2) for the regression coefficients and thresholds, and a normal limit distribution. In contrast, the limit distribution is known to be mixed normal in time series modeling, as shown in [Park, J.Y., Phillips, P.C.B., 2000, Nonstationary binary choice. Econometrica, 68, 1249–1280] (hereafter PP), and [Phillips, P.C.B., Jin, S., Hu, L., 2007. Nonstationary discrete choice: A corrigendum and addendum. Journal of Econometrics 141(2), 1115–1130] (hereafter, PJH).The approach is applied to exchange rate regime choice by monetary authorities, and we provide an analysis of the empirical phenomenon known as “fear of floating”.     

Towards a New Methodology of Estimating Party Policy Positions

In the last twenty years, an international group of political scientists has coded nearly 2000 party manifestos with the help of one single coding scheme based on 56 categories which covers all main topics of these documents. However, there is a growing awareness of the shortcomings of the underlying coding scheme, such as overlapping and missing categories, which cannot be repaired without coding all manifestos all over again. Some have presented an alternative for manifesto-research by means of expert opinions on party policy positions, but these are unable to provide reliable time series for subsequent election years. The unborn solution to some of the problems with the coding scheme would be the computerised content analysis on digitalised party manifestos. This would open up a new universe of infinite possibilities for recodings and reanalyses. The extended consequences from full computerisation of textual analysis are mind boggling. But at the present, these possibilities are merely potentials as the computerised techniques are still underdeveloped. This article explores the possibilities for computerised content analysis in such a way that all postwar manifestos in established democracies can be compared with each other with the help of flexible coding schemes.     

Nonstationary nonlinear heteroskedasticity

In this paper, we consider time series with the conditional heteroskedasticities that are given by nonlinear functions of integrated processes. Such time series are said to have nonlinear nonstationary heteroskedasticity (NNH), and the functions generating conditional heterogeneity are called heterogeneity generating functions (HGF's). Various statistical properties of time series with NNH are investigated for a wide class of HGF's. For NNH models with a variety of HGF's, volatility clustering and leptokurtosis, which are common features of ARCH type models, are manifest. In particular, it is shown that the sample autocorrelations of their squared processes vanish only very slowly, or do not even vanish at all, in the limit. Volatility clustering is therefore well expected. The NNH models with certain types of HGF's indeed have sample characteristics that are very similar to those of ARCH type models. Moreover, the sample kurtosis of the NNH model either diverges or has a stable limiting distribution with support truncated on the left by the kurtosis of the innovations. This would well explain the presence of leptokurtosis in many observed time series data. To illustrate the empirical relevancy of our model, we analyze the spreads between the forward and spot rates of USD/DM exchange rates. It is found that the conditional variances of the spreads can be well modelled as a nonlinear function of the levels of the spot rates.     

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。     

Advances in the Analysis of Non-stationary Time Series: An Illustration of Cointegration and Error Correction Methods in Research on Crime and Immigration

Time series data of interest to social scientists often have the property of random walks in which the statistical properties of the series including means and variances vary over time. Such non-stationary series are by definition unpredictable. Failure to meet the assumption of stationarity in the process of analyzing time series variables may result in spurious and unreliable statistical inferences. This paper outlines the problems of using non-stationary data in regression analysis and identifies innovative solutions developed recently in econometrics. Cointegration and error-correction models have recently received positive attention as remedies to the problems of ``spurious regression' arising from non-stationary series. In this paper, we illustrate the relevant statistical concepts concerning these methods by referring to similar concepts used in cross-sectional analysis. An historical example is used to demonstrate how such techniques are applied. It illustrates that ``foreign' immigrants to Canada (1896–1940) experienced elevated levels of social control in areas of high police discretion. ``Foreign' immigration was unrelated to trends in serious crimes but closely related to vagrancy and drunkenness. The merits of cointegration are compared to traditional approaches to the regression analysis of time series.     

DeepAR: Probabilistic forecasting with autoregressive recurrent networks

Probabilistic forecasting, i.e., estimating a time series’ future probability distribution given its past, is a key enabler for optimizing business processes. In retail businesses, for example, probabilistic demand forecasts are crucial for having the right inventory available at the right time and in the right place. This paper proposes DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an autoregressive recurrent neural network model on a large number of related time series. We demonstrate how the application of deep learning techniques to forecasting can overcome many of the challenges that are faced by widely-used classical approaches to the problem. By means of extensive empirical evaluations on several real-world forecasting datasets, we show that our methodology produces more accurate forecasts than other state-of-the-art methods, while requiring minimal manual work.     

Asymptotic theory for heterogeneous dynamic pseudo-panels

Dynamic pseudo-panel models with inter-cohort parameter heterogeneity are studied. The population is divided into cohorts and the cohort sample means are used as a heterogeneous panel. Least squares and instrumental variables estimators are considered. Multidimensional limits are analyzed as the cross-sectional and temporal dimensions of the data pass to infinity, allowing for both stationary and nonstationary cases. Monte-Carlo simulations on the finite-sample performance of the estimators in these two dimensions are conducted and these, in conjunction with the asymptotic results, are used to make recommendations for practical implementation of the techniques. An empirical illustration finds heterogeneity in consumption growth rates among Taiwanese birth cohorts.     

Solvability of perturbation solutions in DSGE models

We prove that the undetermined Taylor series coefficients of local approximations to the policy function of arbitrary order in a wide class of discrete time dynamic stochastic general equilibrium (DSGE) models are solvable by standard DSGE perturbation methods under regularity and saddle point stability assumptions on first order approximations. Extending the approach to nonstationary models, we provide necessary and sufficient conditions for solvability, as well as an example in the neoclassical growth model where solvability fails. Finally, we eliminate the assumption of solvability needed for the local existence theorem of perturbation solutions, complete the proof that the policy function is invariant to first order changes in risk, and attribute the loss of numerical accuracy in progressively higher order terms to the compounding of errors from the first order transition matrix.     

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.     

Mispricing and trader positions in the S&P 500 index futures market

This study examines the effect of traders’ net positions on mispricing in the S&P 500 index futures market. We find that while positive mispricing is associated with hedgers’ net short and speculators’ net long positions, negative mispricing is related to hedgers’ net long and speculators’ net short positions. This relationship is stable for speculators across the pre- and post-2004 periods; however, it is dominant for hedgers particularly during the pre-2004 period. Contrary to the popular belief, our analysis finds no evidence that speculators are responsible for irrational movements in futures prices by enlarging the size of mispricing. Furthermore, a high magnitude of hedgers’ net positions signals the convergence of mispricing. We also found that according to a recent new disaggregation for trader positions, asset managers tend to delay the convergence of mispricing and hedge funds help shrink the size of mispricing. However, these relationships are not stronger than those implies by the hedger/speculator classification. These findings support the view that speculators’ positions are informative about the direction of index futures mispricing, while hedgers’ positions determine the convergence of mispricing.     

Extreme-quantile tracking for financial time series

Time series of financial asset values exhibit well-known statistical features such as heavy tails and volatility clustering. We propose a nonparametric extension of the classical Peaks-Over-Threshold method from extreme value theory to fit the time varying volatility in situations where the stationarity assumption may be violated by erratic changes of regime, say. As a result, we provide a method for estimating conditional risk measures applicable to both stationary and nonstationary series. A backtesting study for the UBS share price over the subprime crisis exemplifies our approach.     

A drunk and her dog: a spurious relation? Cointegration tests as instruments to detect spurious correlations between integrated time series

A significant correlation between integrated time series does not necessarily imply a meaningful relation. The relation can also be meaningless, i.e. spurious. Cointegration is sometimes illustrated by the metaphor of ‘a drunk and her dog’. The relation between integrated processes is meaningful, if they are cointegrated. To prevent spurious correlations, integrated series are usually transformed. This implies a loss of information. In case of cointegration, these transformations are no longer necessary. Moreover, it can be shown that cointegration tests are instruments to detect spurious correlations between integrated time series. This paper compares the Dickey–Fuller and the Johansen cointegration test. By means of Monte Carlo simulations, we found that these cointegration tests are a much more accurate alternative for the identification of spurious relations compared to the rather imprecise method of utilizing the R ²-and DW-statistics recommended by some authors. Furthermore, we demonstrate that cointegration techniques are precise methods of distinguishing between spurious and meaningful relations even if the dependency between the processes is very low. Using these tests, the researcher is not in danger of either neglecting a small but meaningful relation or regarding a relation as meaningful which is actually spurious.