Search

Thomas and Legge have proposed amatching hypothesis for two-alternative detection and recognition tasks. Given symmetric payoff, S is supposed to match his unconditional response probabilities to the presentation probabilities. More generally, even when payoff is asymmetric, S is supposed to keep his unconditional response probabilities constant across different discriminability levels. Time series analysis is applied here to the response sequences from two auditory amplitude recognition tasks to test both hypotheses. Experiment I obtains a single sequence from each of 16 Ss. Experiment II obtains two sequences at different discriminability levels from each of 24 Ss. Departures from the matching hypothesis are extremely gross in both cases. In addition, Experiment II shows clear changes in the response probabilities across discriminability conditions, though these are not systematic in direction across Ss.

A new method for modeling the human operator from actual input-output data utilizing time series analysis is discussed in this applications oriented paper. The technique first identifies the form of the model, then estimates the parameters of the identified model based on actual data. Finally it checks the fitted model in relation to the data with the aim of revealing model inadequacies, thus providing model improvement. The methodology for applying the time series technique for determining the model of the human element in a feedback system is discussed. In addition, an approach for determining the human model under various levels of stress is discussed. The time series approach is a useful method for modeling any set of discrete observables corrupted with noise, be it human or some other deterministic/stochastic process. Since this is the first time that the human model has ever been obtained from the time series method, it is quite understandable that the results described shed new light on certain aspects of this problem, reveal new insights into the human model, and ask other probing questions.

The natural, groundwater hydrograph of water-table levels reflects the dynamic response of the groundwater flow system to climatic stimuli. Consequently time-series analysis has been employed to examine the frequency structure of long-term climatological and hydrogeological records, and to compare hydrographs from different parts of Northern Ontario, which are known to experience considerably different climatic regimes. The results of the study show that the soil–moisture zone filters out high-frequency climatic cycles before they reach the water table. Furthermore by dividing groundwater hydrographs into a deterministic component, the mean annual hydrograph, and a stochastic component, the residual time series, it is shown that only hydrographs of observation wells within the same hydrogeological subregion have deterministic components with coincidental inflection points and stochastic components that are inphase and coherent. It is also shown that the amplitudes of the deterministic components vary rather unpredictably, and that the variance spectra of the stochastic component of hydrographs from the same hydrogeological region tend to be similar irrespective of climatic differences within the region.

The analysis of time series data can be significantly eased by the use of orthogonal polynomials. This technique is based on traditional regression analysis, but the necessity for solving the associated normal equations is eliminated. Also, the orthogonal polynomial technique includes a means to statistically test the level of fit of the independent terms in a forecast model (e.g., constant, linear, or quadratic). This paper shows the application of orthogonal polynomial technique to the analysis of time series data, but more importantly develops a mathematical means for updating the forecast model from one period to the next without completely recomputing the model from stored historical data. This result considerably improves the ease of application of the orthogonal polynomial technique and increases the value of the technique in practice.

This article presents a data analysis approach consisting of a synthesis of experimental design methods and spectral methods of time series analysis which is appropriate in exploratory situations where the recording process generates a long sequence of correlated observations.

The method of time series analysis is used to study rawinsonde data in middle latitudes. The spectra reveal baroclinically unstable traveling waves with a preferred period of four to five days and a large amount of variance at lower frequencies. The preferred period of the longer-period waves is roughly 30 days, although the character of the disturbances in this range is highly variable. For the waves of periods between three and seven days, phase relations are derived for the northward component of the wind, the temperature, and the height of constant pressure surfaces. The phase relations are characteristic of traveling baroclinic waves and possess reasonable statistical significance. No stable phases were obtained for the eastward component of the wind or for the longer-period oscillations.

It is natural to think of estimating distributed lag models from time series data since it is in time series contexts that such models arise. This article studies the estimation of rational distributed lags in the context of hospital admissions and discharges where a relevant body of cross-section data exists in the form of lengths-of-stay and appears to be more appropriate for this purpose than do the available time series data. The cross-section approach presumably has applications in many situations in which length-of-stay in the system or its counterpart can be observed.

The results of a time series analysis of earthquakes in the New Guinea region are presented. Two basic sets of data are used, the second being a subset of the first such that all estimated related earthquakes have been removed from the first set, leaving a residue of supposedly unrelated events. The primary results are as follows. Positive trends exist in the number of earthquakes as a function of time and there are slight indications of periodicity in the activity. The distribution of earthquakes does not approximate the Poisson distribution at all well for the raw data although this distribution is a much better model with all aftershocks and foreshocks removed from the series. The different seismic natures of the regions studied are reflected in the results of the analyses.

The characterization of biological data during sleepwaking state changes requires the utilization of time series and point process techniques of analysis. The time series procedures that have been found useful in describing biological activity during sleep include frequency domain techniques, such as the autospectrum, digital filtering, complex demodulation, coherence, and cross-spectrum calculations, as well as time domain procedures, such as autocorrelation and matched filtering. The point process techniques include interval distributions, intensity functions, serial correlations, and cross-intensity functions. In addition, applications of frequency domain techniques such as the interval spectrum and spectrum of counts have been implemented for point process data.

The existence of factor intensity reversals between industrial countries has sometimes been attributed to differences in intra-industry specialisation. The industries studied are in fact quite heterogeneous. Consequently the relationships between the specialisation pattern of individual countries and differences in technology between industries may be obscured. In this paper a new method is presented with which specialisation of engineering trade can be studied in great detail. The method rests on the hypothesis that so called (metric) ton prices can be used as a proxy variable for differences in technology in a cross-section of engineering products. This hypothesis is further specified and tested in the paper for a cross-section of engineering products consisting of 40 subindustries of the Swedish engineering industry. If the outcome of the test can be assumed to hold both for a lower level of commodity aggregation and for other countries as well, the new method can be used to test different trade theories (including the factor proportions theory) on the engineering trade of industrial countries. It uses among other variables three variables constructed from the ton prices in engineering exports of OECD-Europe. The results of this paper carry major implications also on the construction and earlier use of price indices of engineering products. The results seem to imply that ton prices fo not measure product prices of engineering goods but rather the technology used in converting tons of metals into units of engineering goods. The price indices used in studies estimating price elasticities in foreign trade or production functions on time series data rest, however, im part on such an assumption.

GIVEN THE LIMITED AVAILABILITY OF MONTHLY DATA, opinions may differ whether it is feasible to construct a monthly econometric model of the U.S. economy at the present time. There may also be different views regarding the method of constructing a monthly model on time series data. Few economists, however, would disagree with the desirability of having a monthly model if it could be constructed satisfactorily.2 The advantages of having a monthly econometric model are numerous. First, important government policy decisions have often been influenced by the latest change in monthly economic data. A more systematic and rigorous analysis of monthly data through the construction of a monthly econometric model would reduce the hazard in using monthly data in an ad hoc manner as is ususally done. Second, short term forecasts are likely to be more accurate if they are made on a monthly model than on equally good quarterly or annual models. If this is true, then a monthly model can contribute to policy formulation in a way in which quarterly and annual models cannot. Third, the application of the Cowles Foundation maximum likelihood simultaneous equation estimating procedures [11] or Theil's k-class estimators [19] to small samples is of uncertain merit, especially with regard to statistical efficiency.3 The Cowles and k-class estimates of the regression coefficients in a system of simultaneous equations merely have the desirable property of consistency for large samples. In a monthly model, there would be much less simultaneity involved in the system of economic relationships than in quarterly or annual models so that the estimation of monthly recursive relationships by the ordinary least squares method would suffer little in inconsistency but would perhaps gain in efficiency. Finally but perhaps more importantly, a recursive monthly model, compared to quarterly and annual models, may involve the least specification error concerning causal directions; and at the same time, it may not give rise to greater serial correlations in the disturbance terms than those involved in models of longer unit periods of observation. This point was argued strongly by one of the authors of the present paper, but it may not be shared by others.4 A test of the feasibility of constructing a monthly econometric model was

This paper describes the development of a quarterly econometric model for the monetary sector oft the Austrian economy. The model consists of 8 behavioural equations and 3 definitions. The equations were estimated by OLS using absolute differences on an annual basis of quarterly time series data. The sample period covers 44 quarters (1st quarter of 1960 to 4th quarter of 1970).

Application of the sliding correlation technique has permitted detailed stratigraphic correlation over entire basins. The main values of the technique are to (1) demonstrate correlation statistically, (2) extend the range of visual correlation, and (3) establish precise correlation where correlation is known to exist but is difficult to establish visually. The technique is especially valuable in aiding correlation of stratigraphic sequences such as varves and turbidites, which are characterized by monotonous repetition of two or more lithologic components. The moving correlation technique is a valuable aid in examining variations in degree of correlation between correlative sections, and in analysis of component associations within a single stratigraphic sequence.

In recent years there has been increasing interest in autoregressive spectrum estimation. This procedure fits a finite autoregression to the time series data, and calculates the spectrum from the estimated autoregression coefficients and the one step prediction error variance. For multivariate time series, the estimated autoregressive matrices and one step prediction covariance matrix produce estimates of the spectra, coherences, phases, and group delays. The use of Akaike's information criterion (AIC) for identification of the order of the autoregression to be used makes the procedure objective. Experience gained from analyzing large amounts of data from the biological and physical sciences has indicated that AIC works very well for model identification when compared to more subjective procedures such as the examination of partial F -statistics. This experience has also indicated that using both autoregressive spectrum estimation and classical spectrum estimation and superimposing the plots gives a much stronger feeling for the shape of the true spectrum being estimated. The results of some of these analyses are presented.

Some key theorems in the asymptotic theory for multivariate time series, using spectrl methods, are established. These theorems relate to various estimation situations including multiple systems of regressions, the determination of the frequency of a periodic signal and the determination of the velocity of a signal propagated through a dispersive medium and received with noise at a number of recorders. The theorems are of a general kind and relate to the almost sure convergence of averages of the periodogram and to the limiting covariance properties and the central limit theorem for such averages. Some brief indications are given concerning extensions of the results to cases where processes are observed that are stationary in time and homogenous with respect to spatial translation.

A comparison between the theoretical backgrounds of the Cosinor Test and the periodogram method suggested that in many cases the use of the periodogram method is preferable and safer (Van Cauter and Huyberechts, 1972). This work refers particularly to the analysis of multifrequential phenomena, which are commonly encountered in biology and medicine. Statistical analysis of computer‐generated time‐series and 24‐hr cortisol paterns is performed by both methods; comparison between the obtained results strongly support our previous theoretical conclusions. The periodogram method appears to be particularly well‐suited to period estimation in biological data; in some cases, simple additional compulations may improve the approximation of the period.

It is very common to see reported in applied econometric literature time series regression equations with an apparently high degree of fit, as measured by the coefficient of multiple correlation R2 or the corrected coefficient R2, but with an extremely low value for the Durbin-Watson statistic. We find it very curious that whereas virtually every textbook on econometric methodology contains explicit warnings of the dangers of autocorrelated errors, this phenomenon crops up so frequently in well-respected applied work. Numerous examples could be cited, but doubtless the reader has met sufficient cases to accept our point. It would, for example, be easy to quote published equations for which R2 = 0.997 and the Durbin-Watson statistic (d) is 0.53. The most extreme example we have met is an equation for which R2 = 0.99 and d = 0.093. I-Iowever, we shall suggest that cases with much less extreme values may well be entirely spurious. The recent experience of one of us [see Box and Newbold (1971)] has indicated just how easily one can be led to produce a spurious model if sufficient care is not taken over an appropriate formulation for the autocorrelation structure of the errors from the regression equation. We felt, then, that we should undertake a more detailed enquiry seeking to determine what, if anything, could be inferred from those regression equations having the properties just described. There are, in fact, as is well-known, three major consequences of autocorrelated errors in regression analysis : (i) Estimates of the regression coefficients are inefficient. (ii) Forecasts based on the regression equations are sub-optimal. (iii) The usual significance tests on the coefficients are invalid.

The procedure of maximum‐entropy spectral analysis (MESA), used in the processing of time series data, also applies to wavenumber (bearing) analysis of signals received from a spatially distributed linear array of sensors. The method is precisely the use of autoregressive spectral analysis in the space dimension rather than in time. There are also close links to the predictive deconvolution method used in geophysical work, and to the process of constructing noise‐whitening filters in communication theory, as well as to least‐squares model building. In this note, we review the maximum‐entropy procedure pointing out all these links. The specific algorithm appropriate to a uniformly spaced line array of sensors is given, as well as one possible algorithm for use in the case of nonuniform sensor spacing.

The solutions of $$\ddot x = F(x,t)$$ , and also $$\dot x = F(x,t)$$ , are developed in truncated series in timet whose coefficients are found empirically. The series ending in thet 6 term yields a position at a final prechosen time that is accurate through 9th order in the sequence size. This is achieved by using Gauss-Radau and Gauss-Lobatto spacings for the several substeps within each sequence. This timeseries method is the same in principle as implicit Runge-Kutta forms, including some not described previously. In some orders these methods are unconditionally stable (A-stable). In the time-series formulation the implicit system converges rapidly. For integrating a test orbit the method is found to be about twice as fast as high-order explicit Runge-Kutta-Nystrom-Fehlberg methods at the same accuracies. Both the Cowell and the Encke equations are solved for the test orbit, the latter being 35% faster. It is shown that the Encke equations are particularly well-adapted to treating close encounters when used with a single-sequence integrator (such as this one) provided that the reference orbit is re-initialized at the start of each sequence. This use of Encke equations is compared with the use of regularized Cowell equations.

Methods of time series analysis were applied to half-hourly plasma levels of aldosterone, growth hormone, and renin activity in four normal volunteers and one patient (CH) with aldosterone producing adenoma. The evidence suggests that the hormonal time series of normal subjects are homologous, when their mean levels are made equal; therefore, they can be concatenated in a single series. Analysis in the time domain and in the frequency domain suggest a predominant 24-hr periodicity. Cross-correlation indicates synchrony of aldosterone with renin and of cortisol with corticosterone, suggesting common regulatory mechanisms; it also shows a 5-hr lag difference between the two pairs, indicative of their phase relation. In CH, lag-correlation and spectral analysis of aldosterone, and renin differ from the normal, those of cortisol and of corticosterone are similar to the normal group. These results indicate that time series analysis may be a useful, objective and quantitative approach to the analysis of complex hormonal patterns in plasma.

In order to avoid distorting the spectrum and introducing spurious coherency, time series shouid be filtered until they approximate white noise.2 Smith and Marcis filter interest rates by detrending with linear regression. Trend, however, is not the major problem in most economic time series. Even in the absence of trend, most economic time series contain strong positive autocorrelation and, as a result, most of the power is concentrated in the low frequencies. First differencing converts most economic time series to a reasonable approximation of white noise. Figures 1 and 2 show that detrending interest rates does not effectively eliminate the concentration of power in the low frequencies while first differencing does eliminate the concentration. Using regression techniques to remove trend also involves applying different filters to the two series, which tends to distort the phase estimates.3 In addition, from a purely practical standpoint, it generally is easier to interpret the spectrum for economic time series after the series have been converted to approximately white noise by first differencing.

The attempt to preserve seasonal characteristics in the modeling of streamflow time series has given rise to a decomposition scheme wherein a random process is superimposed on another periodic process. Strong empirical evidence indicates that under this hypothesis, the amplitude and phase of the periodic component are quite variable. The nature of this variability is examined using simulated time series whose structure is assumed known. It is found that the random component tend to distort estimates of the amplitude and phase so that a relatively long series is needed to estimate parameters (60 years of simulated monthly data to give coefficients of variation of 0.16 for the amplitude and 0.20 for the phase angle). The variation of the phase angle and amplitude, as determined by demodulation is highly dependent on a “signal-to-noise” measure defined as the ratio of the variance explained by the periodic component to the variance of the random component.

A procedure is described for the identification of multiinput-multioutput transfer function and the disturbance model from closed-loop data. The basic step of the identification procedure is to obtain a multivariate time series model for the input and the output series. A new method-viz., the method of successive orthogonalization is given for the modeling of multiple time series. Real data on closed-loop operation of a blast furnace are analyzed.

The purpose of this study is to forecast the market shares of alternative home-heating units: oil-burners, gas-burners and electric-heating units for the United States. The forecasting method used is The Markov Process with estimated transition probability matrices. The transition probabilities represent whether households will continue to use the same heating unit which they have used in the recent past or switch to another type unit. Maximum likelihood and Bayesian estimation techniques have been used to estimate these transition probabilities from aggregate historical market shares of alternative home-heating units.

The Box-Jenkins method, a time-based technique for time series analysis, is shown to be successful in modeling chloride and dissolved oxygen data for the St. Clair River near Corunna, Ontario. This is thought to be the first application of the method to water quality data. The technique is demonstrated to be superior in this situation to either a frequency-based approach or a deterministic causative model. The description of the model building process includes the identification, estimation, and diagnostic checking stages. Forecasting and interpretation follow the derivation of the successful models. It is found that an autoregressive type of model best represents the chloride data, and a moving average process the dissolved oxygen following removal of nonstationarity. Similar causative mechanisms appear to influence June and December chloride and June dissolved oxygen.

The identification of a multivariable stochastic system, usually, involves the estimation of a transfer function matrix, which is a general function of frequency. This estimation involves inversion of a large Hermitian matrix, which sometimes may become unwieldly. In this paper we describe how "principal component analysis" in the frequency domain may be used to replace the input/output variables by some function of smaller dimensions without much "loss of information." The analogy between the "factor analysis" of time series in frequency domain and the minimal realization of state space models is pointed out. The principal component approach described in this paper is applied in the case of a simulated system.

Box and Pierce [3] showed that the residual autocorrelations computed from an autoregressive-moving average time series model (single variate) can be successfully utilized for testing the goodness of fit. Here we extend their results to multiple autoregressive time series models. It is shown that the residual autocorrelations can be approximately represented as a singular linear transform of the corresponding white noise autocorrelations and that they possess a multivariate singular normal distribution. Finally a simple, approximate chi-square statistic is proposed to test the fit.

This paper establishes a procedure for estimating the various spectral parameters in an echo type situation where both the signal is received as well as lagged and attenuated forms of the signal. The lag parameters are assumed frequency dependent and the basic assumption made is that these lags are sufficiently large to cause significant variation in the spectrum over the narrow band of frequencies considered. The asymptotic properties of the estimates of these parameters are established and some simulations and an analysis of real data are considered.

A method is presented for solving agricultural sector models under risk to obtain perfectly competitive levels of outputs and prices in all product markets when producers behave according to an E, V decision criterion. The deterministic model is based on the assumption that individual farmers are profit maximizers and that they compete in a perfectly competitive way. The basic source of risk to be introduced is confined to yields. A number of difficult issues exist with respect to both the design and implementation of aggregate risk models. First, market equilibrium is considerably more complicated under risk than in a deterministic setting. Second, an aggregate model must be defined in terms of variables that are inherently difficult to measure. However, these problems are seemingly overcome by using statistical estimates of the aggregate variable obtained from time series data. 21 references.

Cross-spectral analysis is recognized as a powerful analytical tool for the analysis of time-varying behavior in a number of disciplines. Applications in business have been limited, however, and the potential usefulness of this new approach to time series analysis has received relatively little attention in advertising. The purpose of this paper is to explain cross-spectral analysis and illustrate the use of this new technique in studying the interaction between advertising and sales.

Many qualitative properties of the spectral measure of a stationary Gaussian sequence are spectral properties of the underlying shift transformation. This has implications in time series analysis.

This paper deals with a treatment of spatial correlation, especially spatial correlation in the disturbances of a linear model. In section 1, a brief review of regionalization is presented together with the notion of contiguity. In section 2, definitions of first and higher order contiguity are proposed. Three different concepts of a contiguity coefficient are examined. A choice has been made in favour of the Moran coefficient. Section 3 deals with the topic of estimating the parameters in a linear model with spatially correlated disturbances. An extension of Durbin's method (known from time series analysis) to spatial cross section analysis is suggested. Section 4 presents an application of the theory of section 3 to a model developed by Somermeyer and Lammers (1960)

This article is an exploratory study on the question: Does consumer advertising increase retail availability of a new product? Nerlove's procedure is used to estimate a dynamic model. Cross-section and time series data for one product class are pooled. The managerial implications of the model are discussed.