Robert B. Miller

Unit Roots in Time Series Models: Tests and Implications

Abstract The decision on whether or not to include a unit root in an autoregressive operator has profound implications. Formal tests for the presence of unit roots give analysts objective guidance in this decision. This article is a practical guide to the use of these tests.

On the Stable Paretian Behavior of Stock-Market Prices

Abstract In this article we present some empirical evidence which indicates that attempts to represent the probability distribution of the rates of return on common stocks by a member of the stable Paretian family of distributions, with 1 < α < 2, may be misleading and in fact may not produce an adequate fit to observed rates of return. We offer an alternative probability model for describing rates of return based on the hypothesized phenomenon of a changing variance. We test the “goodness of fit” of our model vis-a-vis a stable Paretian model for several series of rates of return. Finally we propose an extension of the stability test of Fama and Roll [6].

Statistics for business : data analysis and modeling

PART ONE: DATA COLLECTION 1. Data Analysis and Model Building: An Introduction 2. Plotting Process Data 3. Plotting Distributions 4. Summarizing Continuous Data 5. Describing Categorical Variables 6. Relating Continuous Variables PART TWO: ELEMENTS OF MODELING 7. Straight Line Models 8. Multiple Regression Models 9. Normal Distributions 10. Control Charts for Continuous Variables 11. Binomial distributions 12. Control Charts for Binary Data PART THREE: RANDOMIZED DATA COLLECTION AND INFERENCE 13. Data Collection Tools 14. Introduction to Surveys 15. Survey Designs 16. Reading the Results of a Survey 17. Significance Tests and Confidence Intervals 18. Completely Randomized and Randomized Block Designs and the Analysis of Variance 19. Factorial and Fractional Factorial Designs PART FOUR: MODELING AND INFERENCE 20. Inference and Regression Models 21. Regression Diagnostics and Transformations 22. Regression Model Selection 23. Time Series Models 24. Seasonal Time Series Models PART FIVE: STATISTICS AND ORGANIZATIONS 25. A Perspective on Statistics in Organization Appendices / References / Glossary / Answers to Selected Exercises / Data Set Index / Index

Bayesian Analysis of the Two-Parameter Gamma Distribution

This paper presents a Bayesian analysis of shape, scale, and mean of the two-parameter gamma distribution. Attention is given to conjugate and “non-informative” priors, to simplifications of the numerical analysis of posterior distributions, and to comparison of Bayesian and classical inferences.

The pretectum mediates rapid eye movement sleep regulation by light.

A variety of sensory stimuli (e.g., visual, auditory, and thermal) are known to induce rapid eye movement (REM) sleep in mammals. Studies have examined the induction of REM sleep in albino rats by light-to-dark transitions, a phenomenon referred to as REM sleep triggering. Recent research has demonstrated that aspiration lesions of the superior colliculus (SC) and pretectal area attenuated REM sleep triggering. To define more specifically the area or areas involved in mediating REM sleep responses to changes in illumination, fiber-sparing neurotoxic lesions were made to the pretectum (PT) or the SC. Lesions of the PT attenuated REM sleep triggering, whereas lesions of the SC did not. Thus, the role of the PT may be expanded to include the regulation of REM sleep in response to photic stimulation in albino rats. These findings provide a paradigm in which to study mechanisms of REM sleep generation and the effects of light on behavioral state.

Multivariate Time Series Projections of Parameterized Age-Specific Fertility Rates

1 solution to the dimensionality problem raised by projection of individual age-specific fertility rates is the use of parametric curves to approximate the annual age-specific rates and a multivariate time series model to forecast the curve parameters. Such a method reduces the number of time series to be modeled for women 14-45 years of age from 32 to 40 (the number of curve parameters). In addition, the curves force even longterm fertility projections to exhibit the same smooth distribution across age as historical data. The data base used to illustrate this approach was age-specific fertility rates for US white women in 1921-84. An important advantage of this model is that it permits investigation of the interactions among the total fertility rate, the mean age of childbearing, and the standard deviation of age at childbearing. In the analysis of this particular data base, the contemporaneous relationship between the mean and standard deviation of age at childbearing was the only significant relationship. The addition of bias forecasts to the forecast gamma curve improves forecast accuracy, especially 1-2 years ahead. The most recent US Census Bureau projections have combined a time series model with longterm projections based on demographic judgment. These official projections yielded a slightly higher ultimate mean age and slightly lower standard deviation than those resulting from the model described in this paper.

Repeated Time Series Analysis of ARIMA–Noise Models

This article develops a theory and methodology for repeated time series (RTS) measurements on autoregressive integrated moving average-noise (ARIMAN) process. The theory enables us to relax the normality assumption in the ARIMAN model and to identify models for each component series of the process. We discuss the properties, estimation, and forecasting of RTS ARIMAN models and illustrate with examples.

A Strategy to Complete a Time Series with Missing Observations

The problem introduced in this paper originated from a water pollution study of the Menomenee River in Milwaukee, Wisconsin. The final goal of the study was to estimate the total pollutant load deposited in Lake Michigan, for a given season. However, the information on the concentration of pollutants was not complete. Concentration data were available for only 20% of the days in the study period. Complete data were available on two related series: river flow rate and water equivalent of precipitation. Those series were used along with the pollutant concentration data to create a model for pollutant behavior (for the different pollutants and years), to estimate the missing observations and to estimate total pollutant loading for several seasons. (See Miller, et al (1980).)

An evaluation of two doses of isocarboxazid in depression

Two fixed doses of isocarboxazid were studied over a 4-week period in depressed in-patients. Thirty-five patients completed treatment, 20 of whom received 30 mg isocarboxazid per day, and 15 of whom received 50 mg isocarboxazid per day. No overall difference between the two doses was observed. When patients were subdivided into melancholia/endogenous depression or non-melancholia/non-endogenous depression, the higher dose exerted significantly greater antidepressant effects in the latter groups. Diagnostic type is considered to be an important variable in studies of dose-effect relationships with antidepressant drugs. The side effects of isocarboxazid at the two doses studied did not differ materially, although there was a suggestion of greater anticholinergic effect at 50 mg.

Comments on "Grosch's law re-revisited: CPU power and the cost of computation"

Taking Ein-Dors recent reevaluation of Groschs law one step further, the authors find evidence of different slopes for different classes of computers and the utility of an additional variable: the IBM or IBM-compatible factor. The analysis indicates that Groschs law no longer applies to minicomputers.