ASYMPTOTIC PROPERTIES OF SOME PRELIMINARY ESTIMATORS FOR AUTOREGRESSIVE MOVING AVERAGE TIME SERIES MODELS

Abstract. Some simple preliminary estimators for the coefficients of mixed autoregressive moving average time series models are considered. As the first step the estimators require the fitting of a long autoregression to the data. The first two methods of the paper are non-iterative and generally inefficient. The estimators are Yule-Walker type modifications of the least squares estimators of the coefficients in auxiliary linear regression models derived, respectively, for the coefficients of the long autoregression and for the coefficients of the corresponding long moving average approximation of the model. Both of these estimators are shown to be strongly consistent and their asymptotic distributions are derived. The asymptotic distributions are used in studying the loss in efficiency and in constructing the third estimator of the paper which is an asymptotically efficient two-step estimator. A numerical illustration of the third estimator with real data is given.     

Chemical Ecology Mediated by Fungal Endophytes in Grasses

Defensive mutualism is widely accepted as providing the best framework for understanding how seed-transmitted, alkaloid producing fungal endophytes of grasses are maintained in many host populations. Here, we first briefly review current knowledge of bioactive alkaloids produced by systemic grass-endophytes. New findings suggest that chemotypic diversity of the endophyte-grass symbiotum is far more complex, involving multifaceted signaling and chemical cross-talk between endophyte and host cells (e.g., reactive oxygen species and antioxidants) or between plants, herbivores, and their natural enemies (e.g., volatile organic compounds, and salicylic acid and jasmonic acid pathways). Accumulating evidence also suggests that the tight relationship between the systemic endophyte and the host grass can lead to the loss of grass traits when the lost functions, such as plant defense to herbivores, are compensated for by an interactive endophytic fungal partner. Furthermore, chemotypic diversity of a symbiotum appears to depend on the endophyte and the host plant life histories, as well as on fungal and plant genotypes, abiotic and biotic environmental conditions, and their interactions. Thus, joint approaches of (bio)chemists, molecular biologists, plant physiologists, evolutionary biologists, and ecologists are urgently needed to fully understand the endophyte-grass symbiosis, its coevolutionary history, and ecological importance. We propose that endophyte-grass symbiosis provides an excellent model to study microbially mediated multirophic interactions from molecular mechanisms to ecology.     

A Microevaporation Method and Its Application in Determination of Boiling Points of Carboxylic Acids and Esters

A microevaporation method using a thermoanalyzer equipment was developed for the determination of vapor pressure/boiling points o.f fat derivatives. Boiling points of samples smaller than 10 mg can be used in the method. Methyl oleate was used to test the method and boiling points of cyclized fatty acid isomers and their esters were determined. Evaporation enthalpies could be calculated from the results with a precision of 3 to 5% using the Clausius equation.     

Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break

Abstract. A test for the cointegrating rank of a vector autoregressive (VAR) process with a possible shift and broken linear trend is proposed. The break point is assumed to be known. Our test is not a likelihood ratio test but the deterministic terms including the broken trends are removed first by a generalized least squares procedure. Then, a likelihood ratio‐type test is applied to the adjusted series. The asymptotic null distribution of the test is derived and it is shown by a Monte Carlo experiment that the test has better small‐sample properties in many cases than a corresponding Gaussian likelihood ratio test for the cointegrating rank. Moreover, response surface techniques can be used to easily obtain p‐values of the test for any possible break date.     

Multilevel analysis of the educational use of technology: Quantity and versatility of digital technology usage in Finnish basic education schools

The adoption of technology in teaching has been identified to relate to various factors from attitudes and self-efficacy to subjective norms and digital references. The aim of this study is to broaden the perspective to hierarchical grouping effects. Multilevel modelling of the study utilizes the data of 2355 Finnish basic education teachers. The results show that, before the coronavirus pandemic, Finnish teachers used digital devices in teaching at least once a week, on average, and many times on a daily basis, varying according to the subject being taught. The variation in teachers' technology usage occurs mainly at the individual level, with a small proportion between schools; higher-level hierarchies proved redundant in the context of Finland. At the teacher level, digital skills, age, and digital self-efficacy increase technology usage in teaching. At the end, the significance and limitations of the research and the direction of future research in the post-pandemic era are discussed.     

Genetic and Environmental Factors Behind Foliar Chemistry of the Mature Mountain Birch

Previous studies of mountain birch (Betula pubescens spp. czerepanovii) repeatedly have found differences between individual trees in herbivory-related traits, but rarely have yielded estimates of the additive genetic variation of these traits or of their relationship to habitat. We used thirty-year-old birch half-sibs in a northern common garden to estimate the effect of genetics and local microhabitat on resistance-related traits. Genetic estimates of foliar chemistry have been studied only rarely with trees as old as these. Moth performance (Epirrita autumnata), rust (Melampsoridium betulinum) incidence levels, and the general level of natural herbivory damage to individual trees were used as direct measures of birch resistance. Chemical resistance-related traits in plant chemistry included 15 individual phenolics, 16 amino acids, and phenoloxidase activities in the foliage. We also followed birch phenology and growth. Our results show that the genotype of the birch was the most important determinant of phenolic composition and phenoloxidase activity, but that amino acid levels were best explained by the microhabitat of the birch. We also found that the phenology of the birch had a high heritability, although its variation was low. Our results reveal rich genetic variation in birch chemistry.     

A Gaussian Mixture Autoregressive Model for Univariate Time Series

The Gaussian mixture autoregressive model studied in this article belongs to the family of mixture autoregressive models, but it differs from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the definition of the model, conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. Another major advantage is that, for a pth‐order model, explicit expressions of the stationary distributions of dimension p + 1 or smaller are known and given by mixtures of Gaussian distributions with constant mixing weights. In contrast, the conditional distribution given the past observations is a Gaussian mixture with time‐varying mixing weights that depend on p lagged values of the series in a natural and parsimonious way. Because of the known stationary distribution, exact maximum likelihood estimation is feasible and one can assess the applicability of the model in advance by using a non‐parametric estimate of the stationary density. An empirical example with interest rate series illustrates the practical usefulness and flexibility of the model, particularly in allowing for level shifts and temporary changes in variance. Copyright © 2014 Wiley Publishing Ltd     

Trend Adjustment Prior to Testing for the Cointegrating Rank of a Vector Autoregressive Process

Testing the cointegrating rank of a vector autoregressive process that may have a deterministic linear trend is considered. Previous proposals for dealing with such a situation are either to allow for a deterministic trend term in computing a suitable test statistic or else to remove the linear trend first and then derive the test statistic from the trend-adjusted data. In this study the latter approach is considered and a new method for trend removal is proposed that is based on estimating the trend parameters under the null hypothesis. Likelihood ratio and Lagrange multiplier type test statistics are derived on the basis of the trend-adjusted data and their asymptotic distributions are considered under the null hypothesis and under local alternatives. A simulation comparison with other proposals is performed.     

Enabling Remote Testing: Embedded Test Controller and Mixed-signal Test Architecture

Remote testing requires embedded test infrastructure, consisting of communication, test control and test access. This article presents an embedded test solution for a low-frequency audio board. Supporting analog testing, the solution consists of a measurement and calculation method for passive component characterization, analog test bus solution and an embedded test controller for controlling embedded tests and providing test stimuli. Moreover, the solution, which supports the presented test plan, was compared to a test plan supporting traditional testing. It was found that the embedded test solution provided a 29% test coverage of the audio board components and substituted flying probe testing included in the traditional test plan. Besides such benefits as improved fault diagnostics and lower manufacturing costs, the paper also discusses the drawbacks of the presented solution, including reduced measurement accuracy. This paper also presents a correction to a previously presented passive component measurement and calculation method.