Time Series Literature Research Articles

The periodogram at the Fourier frequencies

In the time series literature one can often find the claim that the periodogram ordinates of an iid sequence at the Fourier frequencies behave like an iid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes, point processes, the empirical distribution function and the empirical process. We show when the analogy with an iid exponential sequence is valid and study situations when it fails. Periodogram ordinates of an infinite variance iid sequence are also considered.

Testing for Structural Breaks in the Evaluation of Programs

A youth homicide reduction initiative in Boston in the mid- 1990s poses particular difficulties for program evaluation because it did not have a control group and the exact implementation date is unknown. A standard methodology in program evaluation is to use time series variation to compare pre- and postprogram outcomes. Such an approach is not valid, however, when the timing of program implementation or effect is unknown. To evaluate the Boston initiative, we adapt from the time series literature an unknown-breakpoint test to test for a change in regime. Tests for parameter instability provide a flexible framework for testing a range of hypotheses commonly posed in program evaluation. These tests both pinpoint the timing of maximal break and provide a valid test of statistical significance. We evaluate the results of the estimation using the asymptotic results in the literature and with our own Monte Carlo analyses. We conclude there was a statistically significant discontinuity in youth homicide incide...

Aggregation and Disaggregation of Structural Time Series Models

The aggregation/disaggregation problem has been widely studied in the time series literature. Some main issues related to this problem are modelling, prediction and robustness to outliers. In this paper we look at the modelling problem with particular interest in the local level and local trend structural time series models together with their corresponding ARIMA(0, 1, 1) and ARIMA(0, 2, 2) representations. Given an observed time series that can be expressed by a structural or autoregressive integrated moving‐average (ARIMA) model, we derive the necessary and sufficient conditions under which the aggregate and/or disaggregate series can be expressed by the same class of model. Harvey's cycle and seasonal components models (Harvey, Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press, 1989) are also briefly discussed. Systematic sampling of structural and ARIMA models is also discussed.

Nonparametric and Non-Linear Models and Data Mining in time Series: A Case-Study on the Canadian Lynx Data

SUMMARY Nonparametric regression methods are used as exploratory tools for formulating, identifying and estimating non-linear models for the Canadian lynx data, which have attained bench-mark status in the time series literature since the work of Moran in 1953. To avoid the curse of dimensionality in the nonparametric analysis of this short series with 114 observations, we confine attention to the restricted class of additive and projection pursuit regression (PPR) models and rely on the estimated prediction error variance to compare the predictive performance of various (non-)linear models. A PPR model is found to have the smallest (in-sample) estimated prediction error variance of all the models fitted to these data in the literature. We use a data perturbation procedure to assess and adjust for the effect of data mining on the estimated prediction error variances; this renders most models fitted to the lynx data comparable and nearly equivalent. However, on the basis of the mean-squared error of out-of-sample prediction error, the semiparametric model Xt=1.08+1.37Xt−1+f(Xt−2)+et and Tong’s self-exciting threshold autoregression model perform much better than the PPR and other models known for the lynx data.

Optimal Prediction Under Asymmetric Loss

Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric loss is not well developed. We study the optimal prediction problem under general loss structures and characterize the optimal predictor. We compute the optimal predictor analytically in two leading tractable cases and show how to compute it numerically in less tractable cases. A key theme is that the conditionally optimal forecast is biased under asymmetric loss and that the conditionally optimal amount of bias is time varying in general and depends on higher order conditional moments. Thus, for example, volatility dynamics (e.g., GARCH effects) are relevant for optimal point prediction under asymmetric loss. More generally, even for models with linear conditionalmean structure, the optimal point predictor is in general nonlinear under asymmetric loss, which provides a link with the broader nonlinear time series literature.

On a structural time series method for estimating stock biomass and recruitment from catch and effort data

Structural time series or state-space methods are well suited to stock assessment, where catch and effort are readily available observations, and population size is an unobserved component that one would like to describe. We discuss the use of such a model in estimating absolute abundance and recruitment from catch data and an index of abundance. We discuss the model in the context of the time series literature and the earlier fisheries models for such data. Model fitting is via maximum likelihood and the Kaiman Filter; the approach has advantages over traditional models in that it allows for both stochastic population dynamics and sampling error in index measurement. Further, it makes no assumptions about density-dependent growth or any functional relationship between recruitment and spawning stock size. We illustrate the method with an investigation of performance using simulated data and two sets of data pertaining to cod ( Gadus morhua) in the North Sea. In the real examples the age-composition of the catch is available for part of the duration of the series. Virtual population analysis can therefore also be used; the results are found to be compatible with those from a time series approach.

Political Parties and the Variable Duration of Business Cycles

A number of recent studies explore how political factors influence real economic activity. With electoral models, economic performance peaks near the election, as in the retrospective model of Nordhaus [30]. Electoral cycles also emerge (at least in fiscal policy) in the rational-expectations model of Rogoff and Sibert [34] and Rogoff [33]. With partisan models, economic activity differs systematically by party, as in both the ideological model of Hibbs [26] and the rationalexpectations model of Alesina [1]. Economic activity surges after election of Democratic presidents and recedes after election of Republican presidents. Although recent tests of the electoral approach are supportive [21; 22; 24; 25], the partisan approach enjoys the more compelling support [2; 3; 9; 10; 23; 26; 27]. The electoral and partisan views are not mutually exclusive, as the possibility of conflict between ideology and the desire to be reelected as the election approaches is well recognized. Indeed, our evidence here is consistent with a combined electoralpartisan model.' The macroeconomic literature at large, however, has been slow to absorb accumulating evidence that the party affiliation of the incumbent president, together with the timing of the electoral period, are linked to real economic activity. In this study, we gauge the significance of these links for the United States and relate them to two important strands of the macroeconomic literature. One strand, the time-series literature, investigates the statistical properties of measures of real economic activity, finding that these measures often exhibit nonconstant means and heteroscedastic variances. In autoregressive, integrated, moving-average (ARIMA) models, the conditional mean is a function of past innovations, while the conditional variance is constant. Applications of ARIMA and related models, beginning with Nelson and Plosser [29], suggest that real economic activity for the United States exhibits near random-walk behavior. In autoregressive, conditional heteroscedastic (ARCH) models, the conditional variance is a function of past (squared) innovations, while the conditional mean is constant. Applications of ARCH and related models, beginning with Engle [17], suggest that real activity exhibits heteroscedastic variances.

Efficient instrumental variables estimation of nonlinear dependent processes

The efficient instruments for Method of Moments estimation of nonlinear models are often of unknown or intractable functional form. Existing semiparametric results on this are geared to situations either of random sampling or limited forms of time dependence. This paper considers a popular empirical example from the econometrics time series literature to illustrate that a substantial efficiency gain is possible using a semiparametric approach.

List of references on spectral line analysis

The spectral line analysis (SLA), also called line spectrum analysis, deals with the problem of extracting information on sinusoidal signals from noise-corrupted measurements. It has numerous applications in sonar, radar, underwater surveillance, communications, geophysical exploration, speech analysis, nuclear physics and other fields. The sinusoids-in-noise model, called the hidden periodicity model in the time series literature, also has a significant theoretical relevance as a typical example of a composite spectrum consisting of both continuous and discrete (or line) components, and it is frequently used in theoretical and empirical performance studies of spectral estimation methods. Owing to its practical and theoretical interest, the SLA is a ubiquituous topic in the signal processing literature. When seen from outside by a newcomer, the SLA may appear as a rather narrow field of research. Actually, it contains a myriad of techniques and analysis methods, many of them borrowed from other fields, such as time-series analysis, system identification, matrix algebra, multivariate statistical analysis, complexity theory and others. In the following, we provide a comprehensive list of basic and recent references on SLA. While this list is not, and cannot be, exhaustive, it is believed that it includes most of the key references. The list should be useful to all those interested in the SLA problem, particularly to the newcomers but also to the researchers trying to find the roots of a specific result or recent references for a particular topic. The field of SLA has many ramifications in other fields of signal processing. Many SLA methods can, for example, be used to estimate the parameters of a transient signal, such as a damped sine wave, or the direction-of-arrival of the plane waves impinging on an array of sensors. In general, references on the methods used to solve signal processing problems related to SLA are not provided, unless those methods are strictly relevant to the SLA problem.

Stock prices, efficiency and cointegration: The case of the UK

In this paper a high quality disaggregate data base consisting of the stock prices of 40 companies quoted on the UK stock exchange is analyzed using recently developed techniques from the time series literature. In particular, unit root and cointegration techniques are used to test the concept of static efficiency for individual share prices. Amongst the results reported in the paper is the finding that disaggregate stock prices are cointegrated which is interpreted as a violation of static efficiency.

ROBUST METHODS FOR DEPENDENT CELL PEDIGREE DATA

Summary This paper studies a robust approach to the analysis of cell pedigree data, building on the work of Huggins & Marschner (1991) which discussed M-estimation for the so-called bifurcating autoregressive process. The study allows for incomplete observation of the pedigree, and incorporates the possibility of additive effects outliers, as discussed in the time series literature. Some properties of the proposed estimation procedure are studied, including a Monte Carlo investigation of robustness in the presence of contamination.

Variance formulae for feedback stochastic control systems

Abstract An approach to evaluating the performance of a feedback stochastic controller is presented. The controller is evaluated by the values of the autocovariances of the feedback output and input variable time series. To calculate the autocovariances, the feedback output and input variable time series are identified first, then using time series literature, the formula for the autocovariances is derived. The approach can be used for both univariable or multivariable systems and delayed or non-delayed processes.

The market for second-hand ships: some results on efficiency using cointegration

This paper extends earlier investigations into the structure of shipping markets, and, in particular, examines the implicit assumption made in some applied studies that these markets are efficient. The idea of cointegration, recently developed in the time series literature, is used to analyse the world-wide markets for secondhand dry bulk carriers. The results raise serious doubts over the validity of efficient markets hypothesis in these cases.

Gibrat's Law and the Growth of Canadian Cities

This paper tests for the existence of diseconomies of size for Canadian cities using Gibrat's Law. If diseconomies of size are not present, then the growth rate of cities is shown to contain a unit root. Therefore, testing for Gibrat's Law is equivalent to testing for unit roots commonly found in the time series literature. Our tests indicate that Gibrat's Law cannot be rejected for the seven largest Canadian cities.

Time Series Generation and Transformation—The Role of Phase

Abstract Random signals with some desired power spectrum may be generated by a variety of methods, including summation of sinusoids, convolution of white noise with a kernel function or integration of a differential equation driven by white noise. These continuous models of the spectrum have discrete time equivalents, the moving average (MA) and autoregressive moving average (ARMA), respectively. This paper relates the various techniques and discusses a problem which appears in all of them. Each method involves an amplitude function, the square root of the desired power spectrum and some phase behavior which is unknown and must therefore be assumed. Results from the time series literature presented here provide a rational basis for the choice of phase. In the convolution method, the resulting kernel function is the shortest possible, consistent with the given spectrum and hence minimizes the computational cost of the subsequent signal generation. The corresponding differential equation is the simplest possible, consistent with the form of the amplitude curve. No properties of the time series are affected by the assumed phase spectrum, but phase is critical to the synthesis of correlated signals such as velocity at different points in a random wave field. The results are illustrated by a nondimensional fourth-order differential equation model of the Pierson-Moskowitz spectrum.

Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm

An algorithm is presented for the problem of maximum likelihood (ML) estimation of parameters of partially observed continuous time random processes. This algorithm is an extension of the EM algorithm [3] used in the time series literature, and preserves its main features. It is then applied to the problem of parameter estimation of continuous time, finite state or infinite state (diffusions) Markov processes observed via a noisy sensor. The algorithm in general involves iterations of non-linear smoothing with known parameters and then a non-stochastic maximization. For special cases, including linear models and AR/ARMA processes observed in white noise, each iteration is easily performed with finite dimensional filters. Finally, the algorithm is applied to parameter estimation of “randomly slowly varying” linear systems observed in white noise, and explicit results are derived.

Estimation of Aquifer Parameters Under Transient and Steady State Conditions: 1. Maximum Likelihood Method Incorporating Prior Information

In this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions. The parameters include values and directions of principal hydraulic conductivities (or transmissivities) in anisotropic media, specific storage (or storativity), interior and boundary recharge or leakage rates, coefficients of head‐dependent interior and boundary sources, and boundary heads. In transient situations, the initial head distribution can also be estimated if the system is originally at a steady state. Paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters. The inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters. Since not all the factors which contribute to the prior errors can be quantified statistically at the outset, the covariance matrices of these errors are expressed in terms of several parameters which, if unknown, can be estimated jointly with the hydraulic parameters by a stagewise optimization process. When transient head data are separated by a fixed time interval, the temporal structure of these data is approximated by a lag‐one autoregressive model with a correlation coefficient that can be treated as another unknown parameter. Estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace. Paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature, all of which are based on the maximum likelihood concept, might be useful for selecting the best groundwater model (or the best method of parameterizing a particular model) among a number of given alternatives.

Maximum-likelihood adjoint-state finite-element estimation of groundwater parameters under steady- and nonsteady-state conditions

A method is presented for estimating the hydraulic parameters of groundwater flow models under steady- and nonsteady-state conditions. The estimation problem is posed in the framework of maximum-likelihood theory by means of a log-likelihood criterion that includes prior estimates of the parameters. To allow for an incomplete knowledge of the covariances of the prior head and parameter errors, these covariances are expressed in terms of a few unknown statistical parameters that may be estimated jointly with the hydraulic parameters. Computational efficiency is achieved by evaluating the gradient of the estimation criterion with an adjoint-state finite-element scheme and using a combination of conjugate-gradient algorithms, coupled with Newton's method for determining the step size to be taken at each iteration. Model structure identification criteria developed in the time-series literature (all of which utilize the maximum-likelihood concept) are shown to be useful for selecting the best way to parametrize a groundwater flow region when a number of alternative schemes of parametrization are given. The paper also demonstrates the potential utility of the proposed estimation method for the optimum design of space-time measurement networks. A case study dealing with three-dimensional flow in a multiaquifer system is briefly discussed.

A survey of cross-sectional and time-series literature on factors affecting child welfare

This paper reviews the literature on the socio-economic determinants of child welfare. Cross-sectional evidence is first analysed. The relevant literature is subdivided into four groups of studies depending on the main factors influencing child welfare: demographic; related to family circumstances; related to health care and sanitation; and economic. The very few time-series studies on this subject are then examined. While the existing literature does not allow definitive conclusions to be drawn on the predominance or relative importance of these four sets of factors, this paper identifies three related research areas for which particularly severe gaps seem to emerge and for which additional investigation appears necessary. These are: over-time studies, studies for low-income, high-mortality countries of Africa, for middle-income countries and for high-income, high-mortality countries, and studies measuring impact on the basis of indicators of welfare other than infant mortality rates.

Is Income Overrated in Determining Adequate Nutrition?

There is now a wide measure of agreement on several broad propositions. Serious and extensive nutritional deficiencies occur in virtually all developing countries, though they are worst in low-income countries. They are usually caused by undernourishment-a shortage of food-not by an imbalance between calories and protein. ... Malnutrition affects old and young, male and female, urban and rural dwellers.... Malnutrition is largely a reflection of poverty: people do not have enough income for food. Given the slow income growth that is likely for the poorest people in the foreseeable future, large numbers will remain malnourished for decades to come. The most efficient long-term policies are those that raise the incomes of the poor, and those that raise food production per person. Other relevant policies include food subsidies, nutrition education, adding minerals or vitamins to salt and other processed foods, and increasing emphasis on producing foods typically consumed by the poor.'