Nonlinear Hypothesis Research Articles

Nonlinearities in business cycle: SETAR models and G7 industrial production data

In this paper we enquire if nonlinear or linear models produce iid residuals using the BDS test for the G7 industrial production series. We found that nonlinear models produce iid residual for the USA, and evidence of NL are also detected for Canada and Germany, while Japanese data does not reject the alternatives, and the L model is rejected for Italy, France and the UK. On this evidence, ‘white chaos’ data generation processes cannot be rejected. We evaluate the linear and nonlinear impulse response functions finding that: long-run multipliers are smaller for European countries; long-run asymmetries are evident for the USA, Canada and West Germany. Differently from previous research, our results show that the non-linear hypothesis has to be taken seriously, but with some caution because of not entirely satisfactory forecast performance and asymmetries (this is especially true for the US series). On the other hand, the hypothesis of linearity can be rejected with greater confidence, since it almost alway...

Conductivity discontinuities in the upper mantle beneath a stable craton

We present evidence for approximate collocation of seismic and electrical transitions in the upper mantle. More than two years of very long period magnetotelluric (MT) data were recorded at a lakebottom observatory in the central Canadian Shield. After processing to contend with non‐stationary source effects, and removal of galvanic distortion, the underlying structure is 1D for periods of one hour to four days. The response was extended to periods of 100 days by appending Geomagnetic Depth Sounding data to the MT curves. Minimum structure linearised inversion, nonlinear extremal inversion, and a new genetic algorithm for nonlinear hypothesis testing, reveal discrete jumps in conductivity at depths near the major upper mantle seismic discontinuities. The jumps occur over limited depth ranges.

On the construction of a nonlinear damage accumulation hypothesis

A nonlinear damage accumulation hypothesis that generalizes the well-known Palmgren-Miner theory is considered. The new theory is nonstationary and leads to changes of the shape of the lifetime distribution under random load. A scaled nonstationary damage accumulation theory is also studied. Examples of lifetime distributions under random load with increasing, decreasing and bathtub shaped failure rates are considered.

Modelling of transverse crack growth and saturation in cross-ply laminates

A model of transverse cracking in cross-ply laminates is presented. The model describes the onset of cracking, the development of the number of cracks, the saturation phase of this damage mode and the final crack distribution, as well as the dependency of these phenomena on the 90° ply thickness. This analysis is based on an effective flaw size distribution and a non-linear interlaminar behaviour hypothesis. The theoretical prediction of the process and the saturation of cracking was well correlated with the experiments conducted on [O2/90 n ]s graphite/epoxy. However, there was considerable dispersion in the experimental results concerning the onset of cracking. Experimental work and part of the theoretical investigations were made at ONERA, 29 av. Division, Leclerc 92322, Chatillan, Cedex, France.

Extended wave-particle description of longitudinal photons

On the basis of the two-wave particle model, the nonlinear wave hypothesis and the tachyonic theory of elementary particle structure, the propagation of electromagnetic fields in phase-locked cavities and waveguides has been investigated. It is shown that in a pull-phase-locked cavity, a Doppler-shifted radiation may be considered as a nonlinear system of time-like and space-like waves which lock to form the plane photo-like wave. In the particle picture, it may be interpreted as photon conversion into a system composed of both bradyonic and tachyonic components which trap each other in a relativistically invariant way. The considerations are extended to include the case of radiation transmitted inside waveguides. The relativistic mechanics and field description of longitudinal massive photons associated with trapped radiation have been developed. The time-like Proca wave equation and its space-like counterpart are derived.

The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models

This paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis. The paper is organized around a lemma which characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test. We then present two examples which illustrate several implications of this lemma. We also discuss the impact of these properties on the empirical implementation and interpretation of these test procedures.

Unitary Information Ether and its Possible Applications

AbstractThe idea of information ether as the unitary information field is developed. It rests on the assumption that the notion of information is a fundamental category in the description of reality and that it can be defined independently from the notion of probability itself. It is shown that the information ether provides a deterministic background for the nonlinear wave hypothesis and quantum cybernetics.

Is a massive particle a compound bradyon-pseudotachyon system?

The spacetime two-wave description of a massive particle presented earlier is considered in the context of the nonlinear wave hypothesis and tachyon theory. It is shown that the description implies that the massive particle in motion can be regarded as a system composed of both bradyonic and pseudotachyonic components. A physical interpretation of the pseudotachyonic component is proposed.

A simple statistical method for the comparison of accumulated dose in ESR dating

It is generally recognized that estimates of accumulated dose (AD) for ESR dating are vulnerable to variations in sample preparation and measurement procedures: it is therefore desirable to be able to compare AD's derived by different methods as a first step in establishing universally acceptable methods. However, because AD is calculated by dividing two variables, the distribution of AD is non-linear and standard linear hypothesis tests cannot be applied directly. The method developed here by the addition of another assumption (which can be tested) allows AD's to be compared using Student's t -test. Hence, sample preparation and measurement procedures can be tested for equivalence. The technique also allows AD of different samples to be compared, provided the values of the additional radiation are the same or similar for each sample. Confidence limits for AD may also be derived. Existing linear regression programs can be easily modified to accomodate the method.

Arbitrage Pricing Theory as a Restricted Nonlinear Multivariate Regression Model Iterated Nonlinear Seemingly Unrelated Regression Estimates

By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of asset sensitivities and their associated APT risk “prices.” Without the assumption of normally distributed errors, these estimators are strongly consistent and asymptotically normal. With the additional assumption of normal errors, they are also full-information maximum likelihood estimators. Classical asymptotic nonlinear nested hypothesis tests are supportive of the APT with measured macroeconomic factors.

Obtaining any Wald statistic you want

While the Wald test can be used to test a non-linear hypothesis in a linear or non-linear regression model it is known that a particular hypothesis can be written in many ways when non-linear forms are permitted. This paper illustrates that it is possible to obtain virtually any value of the Wald statistic at different significance levels. It is also shown that in small samples the use of the χ 2 or F approximation for the distribution of the Wald statistic can be misleading for some forms of the non-linear Wald test.

Biomedical engineering approach of pharmacokinetic problems: computer-aided design in pharmacokinetics and bioprocessing

In complex or nonlinear processes the identifiability of classical models fails because of too many parameters. To reduce this number and to keep a description which is significant to the user in pharmacokinetics or bioprocessing a modular representation model is built up. To define all parameters and internal variables of those models, the authors have chosen an electrical equivalent representation. This electrical representation leads to linear and nonlinear associative modules, and this strategy allows them to realise a computer-aided design well suited to biological processes. On the one hand, it allows optimal therapeutic drug control after defining optimal criteria. On the other hand, it may be used for biomedicine, ecology and bioprocessing problems. The CAD system is conceived like a ‘Lego’ game and it can be used with minimal or no knowledge of programming and computer science. Its main goals are to formulate, resolve and simulate quickly any linear or nonlinear hypothesis of biological processes, and give time for innovation in biological research. Pharmacokinetic models are founded on the hypothesis of transmembrane drug transfer and modelled by differential equations. These differential equations allow the description of drug kinetics or in vivo drug behaviour by a compartment model. This compartment model, which is a representative or descriptive model, tries to give a concrete physiological picture of transmembrane drug transfers. In the usual pharmacokinetic studies, the compartment model is a satisfactory approach to the treatment of simple linear diffusion and elimination processes. In these cases, the canonical form (diagonal form Σ aie-λit) deduced from those models includes a number of parameters approaching the number of parameters of the representative model. Then, for a set of experimental data, when the canonical form is identified, it is possible to reconstruct the original compartment model with few structural hypotheses. For more complex or nonlinear processes, the compartment model fails because of its large number of parameters with regard to the number of identified parameters in the diagonal form. To treat these processes, the paper presents a modular model which is a representative model. In such a model, the number of parameters approach the number of canonical form parameters. On the other hand, this modular network allows a simple extension to nonlinear functions included in the linear network. The definition of this model leads to a computer-aided-design tool, suitable for any linear or nonlinear pharmacokinetic problem. To define all components of the modular model it is necessary to unify all pharmacokinetic parameters; so the authors have established an analogy table between classical pharmacokinetic and electrical parameters. This equivalence table suggests an electrical representation with physiological meaning similar to the physiological compartment concept. In this electrical model, the physiological parameters, such as elimination clearance, volume of distribution and transfer clearance between several diffusion areas, are the constitutive parameters of the model. Then, this analogy allows the inclusion of major limiting parameters like arterial or hepatic blood flow in the model.

Non-bank public and commercial bank portfolio behavior in the Brunner-Meltzer model: A review and clarification

This paper investigates the relationship between a portfolio theoretic model of non-bank public and commercial bank behavior and the Brunner-Meltzer non-linear money supply hypothesis. We examine the recent modification of the Brunner-Meltzer macroeconomic model suggested by Friedman and Froewiss (1977), discuss its shortcomings, and argue that the unmodified model is valid if one adopts the monetary sector equilibria definition of Saving (1977).

Short-Run Fluctuations in the Money Multiplier and Monetary Control

An increasing number of monetary economists now describe the money supply process within the framework of the Brunner-Meltzer nonlinear hypothesis. For a detailed description of the hypothesis see [4, 5, 6]. Several aspects of this general approach to analyzing the behavior of the money stock are considered in this article. In section 1, the relative merits of different ways of decomposing the money supply into a monetary multiplier and a base are discussed. The difficult task of separating the effects of reserve requirement changes from the monetary multiplier is discussed in section 2. A problem with Brunner and Meltzer's reserve adjustment variable is pointed out and an alternative logarithmic reserve adjustment variable is suggested. These two reserve adjustment variables are then compared in section 3. In section 4, the behavior of the monetary multiplier during the period 1961-74 is examined and an explanation is presented for the marked increase in the variance of the monetary multiplier. The final section considers some simple forecasting models that utilize the basic framework of the Brunner-Meltzer nonlinear hypothesis. It is shown that, despite the large variance in the monetary multiplier, it is possible for the Federal Reserve to control the money supply quite accurately over periods of one or two quarters.

Inequality and Discontent: A Nonlinear Hypothesis

At least since Aristotle, theorists have believed that political dis-content and its consequents—protest, instability, violence, revolution—depend not only on the absolute level of economic well-being, but also on the distribution of wealth. Contemporary political analysts have tried to test this ancient assumption using modern statistical methods. Their results are distressingly confusing. One cross-national investigation finds the commonsensical positive linear relation: the more the inequality, the greater the instability. A second study purports to show the opposite relation in the important case of South Vietnam: the greater the inequality, the less the support for revolution. And a third analysis, also of South Vietnam, detects no relation at all between inequality and rebellion.

Auditory nonlinearity: audible subjective difference tones fh − f1 and 2f1 − fh

The polynomial nonlinearity hypothesis of the previous paper equates growth rates of equal-order difference and summation tones. Growth rates for 2f1 − fh and possibly fh − f1(fh/f1 = 1.2;f1 = 1000 Hz) have been found to approximate 1 dB/dB, contradicting the classical nonlinear hypothesis. At least three possible explanations of these discrepancies exist. Only one method, cancellation [E. Zwieker, Acustica 5, 67–74 (1955)], has been used previously, suggesting a possible methodological artifact. Agreement between the psychoacoustic results and some of the physiological data suggests possible real disparities between the generation of audible and inaudible subjective tones. Finally, these difference tones may be processed in some special manner after their generation. To explore the first possibility, a new method was developed incorporating alternating binaural loudness balances between the subjective tone and a contralateral pure tone of equal frequency under conditions of equivalent masking. Cancellation estimates corrected for masking (a correction not previously incorporated) agree closely with loudness balance measures of 2f1 − fh from the same subjects. Both methods produced 1 dB/dB growth functions, an unlikely result if the discrepancies were methodological. Grewth and audibility of these subjective tones suggest a difference in processing after generation to account for the discrepancies.

Wage Inflation and the Structure of Regional Unemployment: Comment

Frank Brechling's paper could well serve as a model for other authors. It is both imaginative and clear in its development of formal theory, and follows through with relevant econometric testing and estimation. Such basic work on the underpinnings of the Phillips relation is badly needed. Taking off from the work by Lipsey and Archibald that stresses the importance of the geographic segmentation of the labor market, Brechling considers two hypotheses for relating sectoral imbalances to the wage inflation-unemployment trade-off of the American economy. The first is the familiar aggregation of nonlinear local Phillips curves. The second provides for spillover effects through expectations from tight sectors to looser ones. One minor slip in the theoretical derivation should be avoided in the future. The aggregation of wage rates in equation (2) should use the fraction of earnings for sectoral weighting while in equation (6) the fraction of labor force should be used for sectoral weighting instead. In the theory development for the nonlinear aggregation hypothesis, the assumption is used that all sectoral Phillips relations are identical. However, empirical evidence indicates that this is not likely to be true, particularly because of different turnover rates in different sectors.l Since it is the nonlinearity of the local curves that causes the aggregate inflation rate to be increased by the dispersion of unemployment, Brechling only needs to assume identical slopes for local curves. Their levels may differ. Uniform sectoral unemployment rates would still give the minimum aggregate wage inflation rate, but the wage inflation rates would differ systematically by sector and his second deftnition of long run which leads to equation (11) would be suspect, i.e., that the expected inflation rate in each sector was equal to the aggregate inflation rate. Clearly, if inflation rates differ by sector, the relative wage structure will drift and this would induce the movement of demand and supply between sectors. Thus we need to develop the theory of the intersectoral adjustment process on a much more basic level than simply through the expectation formation process. One may question the label of dynamic market interdependence which Brech-

Note on the MacAdam Nonlinear Hypothesis

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text Yoshio Sugiyama, "Note on the MacAdam Nonlinear Hypothesis," J. Opt. Soc. Am. 54, 127-127 (1964) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

CHROMATIC ADAPTATION. II. NONLINEAR HYPOTHESIS.

The von Kries coefficient law of chromatic adaptation—that there is linear proportionality between stimulus and response for each of three types of visual receptor—results in systematic discrepancies between prediction and experiment. A hypothesis that the responses of the receptors are nonlinear was fairly successful when applied to three sets of experimental data obtained independently by quite different methods. Analysis of additional data confirms the earlier conclusions that (1) discrepancies of predictions of corresponding colors by the linear hypothesis are significantly large and systematic; (2) the discrepancies are less systematic and are significantly reduced by the nonlinear hypothesis; (3) the most successful forms of the mathematical relations expressing the nonlinearities are systematically dependent on the chromaticities of the adaptations. These forms are substantially the same as those for the three sets of experimental data previously studied.

Nonlinear Relations of Psychometric Scale Values to Chromaticity Differences*

Psychometric scale values for color differences are correlated with physically measured chromaticity differences by use of a formula which postulates that the scale values are proportional to some power, less than unity, of distance in a subjectively isotropic, projective transformation of the CIE chromaticity diagram. Exponents ranging from 0.38 to 0.80 are reported. Eleven to 37% smaller root-mean-square errors of fit to psychometric scale values are obtained with the nonlinear hypothesis than with a linear hypothesis.