Testing for the Cointegrating Rank of a Vector Autoregressive Process with Uncertain Deterministic Trend Term

When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to be orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second one is based on a misspecified model if the linear trend is not orthogonal to the cointegration relations. Hence, the treatment of the linear trend term is crucial for the outcome of the rank determination procedure. We compare two alternative testing strategies which are applicable if there is uncertainty regarding the proper trend specification. In the first one a specific cointegrating rank is rejected if one of the two tests rejects and in the second one the trend term is decided upon by a pretest. The first strategy is shown to be preferable in applied work.Cointegration analysis, likelihood ratio test, vector autoregressive model, vector error correction model

Real GDP Per Capita in Developed Countries

Growth rate of real GDP per capita is represented as a sum of two components – a monotonically decreasing economic trend and fluctuations related to a specific age population change. The economic trend is modeled by an inverse function of real GDP per capita with a numerator potentially constant for the largest developed economies. Statistical analysis of 19 selected OECD countries for the period between 1950 and 2004 shows a very weak linear trend in the annual GDP per capita increment for the largest economies: the USA, Japan, France, Italy, and Spain. The UK, Australia, and Canada show a larger positive linear trend. The fluctuations around the trend values are characterized by a quasi-normal distribution with potentially Levy distribution for far tails. Developing countries demonstrate the increment values far below the mean increment for the most developed economies. This indicates an underperformance in spite of large relative growth rates

Geometric analysis of the linear Boltzmann equation I. Trend to equilibrium

This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the associated collision kernel may vanish in a large subset of the phase space; (2) we do not assume that it is bounded below by a Maxwellian at infinity in velocity. We study how the association of transport and collision phenomena can lead to convergence to equilibrium, using concepts and ideas from control theory. We prove two main classes of results. On the one hand, we show that convergence towards an equilibrium is equivalent to an almost everywhere geometric control condition. The equilibria (which are not necessarily Maxwellians with our general assumptions on the collision kernel) are described in terms of the equivalence classes of an appropriate equivalence relation. On the other hand, we characterize the exponential convergence to equilibrium in terms of the Lebeau constant, which involves some averages of the collision frequency along the flow of the transport. We handle several cases of phase spaces, including those associated to specular reflection in a bounded domain, or to a compact Riemannian manifold

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The application of spectral analysis in some related varieties is a new and important trend in the theory of functional equations; especially they have successful applications in case of homogeneous linear functional equations. The foundation of the theory can be found in M. Laczkovich and G. Kiss \cite{KL}, see also G. Kiss and A. Varga \cite{KV}. We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to T. Szostok \cite{KKSZ08}, see also \cite{KKSZ} and \cite{KKSZW}. They are motivated by quadrature rules of approximate integration

ANALISIS PRODUKSI SUSU SAPI PERAH DI INDONESIA

Cow's milk is large in contributing to meeting the needs of people in developing countries to meet nutritional fulfillment. Cow's milk has increased imports due to the problem of cow disease which cannot meet the needs of the Indonesian people who increase every year milk consumption every year. This study aims to analyze milk production trends and factors affecting milk production of dairy cows in Indonesia. The type of data used is secondary data with a vulnerable time of 2012-2021. The analysis methods used are trend analysis and multiple linear regression analysis. The results showed that the trend of milk production of dairy cows decreased from 2012-2015 and rose again from 2016-2021. Milk prices and cows population simultaneously affect the volume of milk production of dairy cows in Indonesia

An I(2) Cointegration Model With Piecewise Linear Trends: Likelihood Analysis And Application

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.Cointegration, I(2); piecewise linear trends; likelihood analysis; US consumption

Semiparametric Trending Panel Data Models with Cross-Sectional Dependence

A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A semiparametric profile likelihood approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the time trend function.cross-sectional dependence, nonlinear time trend, panel data, profile likelihood, semiparametric regression