A univariate time varying analysis of periodic ARMA processes

The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time varying univariate process and obviates the need for vector analysis. The specification, interpretation, and solution of a periodic ARMA process enable us to formulate a forecasting method which avoids recursion and allows us to obtain analytic expressions of the optimal predictors. Our results on periodic models are general, analogous to those for stationary specifications, and place the former on the same computational basis as the latter.Comment: 26 pages, no figures. arXiv admin note: text overlap with arXiv:1403.335

Time Varying Cyclical Analysis for Economies in Transition

The identification of a possible European business cycle has been inconclusive and is complicated by the enlargement to the new member states and their transition to market economies. This paper shows how to decompose a business cycle into a time-frequency framework in a way that allows us to accommodate structural breaks and nonstationary variables. To illustrate, calculations of the growth rate spectrum and coherences for the Hungarian, Polish, German and French economies show the instability of the transition period. However, since then there has been convergence on the Eurozone economy at short cycle lengths, but little convergence in long cycles. We argue that this shows evidence of nominal convergence, but little real convergence. The Maastricht criteria for membership of the Euro therefore need to be adapted to test for real convergence.Time-Frequency Analysis, Coherence, Growth Rates, Business Cycle

Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For discrete time nonlinear systems satisfying an exponential or finite time controllability assumption, we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints. Based on our formula, we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

Panel Data Analysis of the Time-Varying Determinants of Corruption

There is a long history of models attempting to identify the causes of corruption, yet empirical analysis is complicated. Not only is data difficult to obtain and often available only for few countries and a limited number of years, but such estimation involves inherent complexities. This paper focuses on the use of panel data techniques to better identify factors that affect bureaucratic corruption. Furthermore, this paper identifies an endogeneity problem which arises in the analysis of the causes of corruption, and a new instrumental variable is proposed to solve it. To help in this endeavor, a data set is employed which provides information for as many as 135 countries over a span of sixteen years. Results show that neglecting the endogeneity problem leads to severely biased results. Using panel data techniques reveals that the availability of rents is a crucial determinant of corruption and that previous research may have underestimated the economic significance of rents on corruption. Furthermore, corruption is shown to be procyclical. Depuis longtemps, des modèles sont utilisés dans le but de déterminer les causes de la corruption. Toutefois, l’analyse empirique demeure complexe. Qui plus est, les données sont difficiles à recueillir et couvrent souvent un nombre restreint de pays et une période limitée. Ce genre d’évaluation présente aussi des complexités inhérentes. Le présent document met l’accent sur le recours à des techniques de données de panels dans le but de mieux connaître les facteurs qui influent sur la corruption bureaucratique. En outre, cette analyse souligne le problème d’endogénéité qui ressort de l’analyse des causes de la corruption et propose une nouvelle variable instrumentale permettant de contrer celui-ci. Pour faciliter la démarche, ce document utilise un ensemble de données fournissant des renseignements sur au moins 135 pays et pour une période de seize ans. Les résultats indiquent que si le problème d’endogénéité n’est pas pris en compte, les résultats sont sérieusement biaisés. De plus, la corruption est décrite comme étant procyclique.corruption, endogeneity, income, rents, corruption, endogénéité

Functional Principal Component Analysis for Non-stationary Dynamic Time Series

Motivated by a highly dynamic hydrological high-frequency time series, we propose time-varying Functional Principal Component Analysis (FPCA) as a novel approach for the analysis of non-stationary Functional Time Series (FTS) in the frequency domain. Traditional FPCA does not take into account (i) the temporal dependence between the functional observations and (ii) the changes in the covariance/variability structure over time, which could result in inadequate dimension reduction. The novel time-varying FPCA proposed adapts to the changes in the auto-covariance structure and varies smoothly over frequency and time to allow investigation of whether and how the variability structure in an FTS changes over time. Based on the (smooth) time-varying dynamic FPCs, a bootstrap inference procedure is proposed to detect significant changes in the covariance structure over time. Although this time-varying dynamic FPCA can be applied to any dynamic FTS, it has been applied here to study the daily processes of partial pressure of CO2 in a small river catchment in Scotland

Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).Comment: 49 pages, 16 figure

A perturbation analysis of some Markov chains models with time-varying parameters

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process developed in the literature and that can be used for studying a wide class of Markov processes. To this end, for some families of V-geometrically ergodic Markov kernels indexed by a real parameter u, we give conditions under which the invariant probability distribution is differentiable with respect to u, in the sense of signed measures. Our results also complete the existing literature for the perturbation analysis of Markov chains, in particular when exponential moments are not finite. Our conditions are checked on several original examples of locally stationary processes such as integer-valued autoregressive processes, categorical time series or threshold autoregressive processes