Fully Bayesian analysis of ARMA time series models

Statistical analysis of autoregressive-moving average (ARMA) models is an important non-standard problem. No classical approach is widely accepted; legitimacy for most classical approaches is based solely on asymptotic grounds, while small sample sizes are common. The only obstacle to the Bayesian approach are designing a structure through which prior information can be incorporated and designing a practical computational method. The objective of this work is to overcome these two obstacles. In addition to the standard results, the Bayesian approach gives a different method of determining the order of the ARMA model, that is (p, q).     

Trends and cycles in economic time series: A Bayesian approach

Trends and cyclical components in economic time series are modeled in a Bayesian framework. This enables prior notions about the duration of cycles to be used, while the generalized class of stochastic cycles employed allows the possibility of relatively smooth cycles being extracted. The posterior distributions of such underlying cycles can be very informative for policy makers, particularly with regard to the size and direction of the output gap and potential turning points. From the technical point of view a contribution is made in investigating the most appropriate prior distributions for the parameters in the cyclical components and in developing Markov chain Monte Carlo methods for both univariate and multivariate models. Applications to US macroeconomic series are presented.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

Urbanisation,fiscal decentralisation and economic development: A time series evidence

Several empirical tests using Multiple Regression Analyses were conducted on several hypotheses using time series data obtained from the federal and state governments. The results of our analyses establish that the degree of fiscal decentralisation is dependent on intergovernmental transfers and states income per capita. However intergovernmental transfers were not dependent on expenditure decentralisationper se. The degree of urbanisation was found to be inversely related to fiscal decentralisation. The variable measuring the degree of openess was found not statistically significant as an explanatory variable for fiscal decentralisation. However, the share of agriculture was found significant in revenue decentralisation but loses its importance in expenditure decentralisation.The policy implications of the study are that: (i) There is need for the states to develop plans to increase their per capita income, improve their tax collection system, introduce new tax bases and reduce the high degree of free ridership in public goods and services exhibited by the urban population. (ii) The Federal Government should provide specific grants to state governments for urban development, because of the high per capita cost of public goods and services. (iii) The existing Revenue Allocation Act should be reviewed to reflect state government efforts in generating their own revenue from internal sources.     

The second time around: reaching for the right package

There are several key questions to ask when replacing a software package. Taking the time to get the answers will save a lot of time, money and grief.     

Econometric modelling on microcomputers: A review of major software packages

In their present state, both in terms of price and power, microcomputers are taking over applied econometics. Now even model simulation is feasible. This paper tries to help the model-builder in determining which of the following modelling software is appropriate to his/her specific needs: AREMOS, ESP, Micro-TSP, MODLER and SORITEC. Tables devoted to data management, estimation, model specification, simulation, and presentation of results, detail the availability of desirable features. Finally, individual short reviews stress the best and worst points of each software.     

Structured low-rank matrix completion for forecasting in time series analysis

This paper considers the low-rank matrix completion problem, with a specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a rank constraint. We consider a matrix completion problem for Hankel matrices and a convex relaxation based on the nuclear norm. Based on new theoretical results and a number of numerical and real examples, we investigate the cases in which the proposed approach can work. Our results highlight the importance of choosing a proper weighting scheme for the known observations.     

Model selection in univariate time series forecasting using discriminant analysis

When a large number of time series are to be forecast on a regular basis, as in large scale inventory management or production control, the appropriate choice of a forecast model is important as it has the potential for large cost savings through improved accuracy. A possible solution to this problem is to select one best forecast model for all the series in the dataset. Alternatively one may develop a rule that will select the best model for each series. Fildes (1989) calls the former an aggregate selection rule and the latter an individual selection rule. In this paper we develop an individual selection rule using discriminant analysis and compare its performance to aggregate selection for the quarterly series of the M-Competition data. A number of forecast accuracy measures are used for the evaluation and confidence intervals for them are constructed using bootstrapping. The results indicate that the individual selection rule based on discriminant scores is more accurate, and sometimes significantly so, than any aggregate selection method.     

Nonparametric analysis of financial time series by the Kernel methodology

This paper aims to study, in the most recent historical time period, the efficiency of the Paris Stock Exchange market. We test its weak form while analysing the stock exchange returns series by nonparametric methods, using kernel methodology in particular. In doing so, our approach extends the traditional view treating the observed cyclical fluctuations on this market.     

Detecting shocks: Outliers and breaks in time series

A single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares. An equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question. Similarly, for unobserved components or structural time-series models, the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter, such as trend or level changes. Because such time-series models contain more than one variance, the effect of the intervention is measured by the change in individual variances.We examine the effect on the estimated parameters of moving various kinds of intervention along the series. The horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing. Interpretation of the resulting time-series plots of diagnostics is aided by simulation envelopes.Our procedures, illustrated with four example, permit keen insights into the fragility of inferences to specific shocks, such as outliers and level breaks. Although the emphasis is mostly on parameter estimation, forecast are also considered. Possible extensions include seasonal adjustment and detrending of series.     

A flexible approach to parametric inference in nonlinear and time varying time series models

Many structural break and regime-switching models have been used with macroeconomic and financial data. In this paper, we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications. We build on earlier work showing the relationship between flexible functional forms and random variation in parameters. Our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring (reordered) observations. The range of priors produced in this way can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the amount of random variation in parameters to depend on the distance between (reordered) observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). Bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering. Conditional on a hypothetical reordering and distance function, a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation. We use artificial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth.     

A literature review on business process modelling: new frontiers of reusability

Business process modelling (BPM) has become fundamental for modern enterprises due to the increasing rate of organisational change. As a consequence, business processes need to be continuously (re-)designed as well as subsequently aligned with the corresponding enterprise information systems. One major problem associated with the design of business processes is reusability. Reuse of business process models has the potential of increasing the efficiency and effectiveness of BPM. This article critically surveys the existing literature on the problem of BPM reusability and more specifically on that State-of-the-Art research that can provide or suggest the ‘elements’ required for the development of a methodology aimed at discovering reusable conceptual artefacts in the form of patterns. The article initially clarifies the definitions of business process and business process model; then, it sets out to explore the previous research conducted in areas that have an impact on reusability in BPM. The article concludes by distilling directions for future research towards the development of apatterns-based approach to BPM; an approach that brings together the contributions made by the research community in the areas of process mining and discovery, declarative approaches and ontologies.     

A heteroscedasticity-consistent covariance matrix estimator for time series regressions

This paper provides a covariance matrix estimator for the ordinary least squares coefficients of a linear time series model which is consistent even when the disturbances are heteroscedastic. This estimator does not require a formal model of the heteroscedasticity. One can also obtain a direct test of heteroscedasticity, although Monte Carlo experiments show that it may have low power.     

Pricing-to-market in U.S. imports and exports: A time series and cross-sessional study

This paper provides a comparative study of how U.S. imports and exports prices react to exchange rate changes. It finds, through time series analyses, that while both U.S. and foreign exporters price to market, foreign exporters in general absorb a large portion of exchange rate changes by themselves while U.S. exporters pass through most of the exchange rate change to foreign currency prices. Pricing behavior of U.S. imports and, to a lesser extent, of U.S. exports varies across industries and such variation relates to industry characteristics such as market shares, product d differentiation, and capital-to-labor ratio.