On multistep prediction error methods for time series models

Multistep prediction error methods for linear time series models are considered from both a theoretical and a practical standpoint. The emphasis is on autoregressive moving-average (ARMA) models for which a multistep prediction error estimation method (PEM) is developed. The results of a Monte Carlo simulation study aimed at establishing the possible merits of the multistep PEM are presented.     

A role for spatiotemporal scales in modeling

Bogen and Woodward's distinction between data and phenomena raises the need to understand the structure of the data-to-phenomena and theory-to-phenomena inferences. I suggest that one way to study the structure of these inferences is to analyze the role of the assumptions involved in the inferences: What kind of assumptions are they? How do these assumptions contribute to the practice of identifying phenomena? In this paper, using examples from atmospheric dynamics, I develop an account of the practice of identifying the target in the data-to-phenomena and theory-to-phenomena inferences in which assumptions about spatiotemporal scales play a central role in the identification of parameters that describe the target system. I also argue that these assumptions are not only empirical but they are also idealizing and abstracting. I conclude the paper with a reflection on the role of idealizations in modeling.     

The diverse aims of science

There is increasing attention to the centrality of idealization in science. One common view is that models and other idealized representations are important to science, but that they fall short in one or more ways. On this view, there must be an intermediary step between idealized representation and the traditional aims of science, including truth, explanation, and prediction. Here I develop an alternative interpretation of the relationship between idealized representation and the aims of science. I suggest that continuing, widespread idealization calls into question the idea that science aims for truth. If instead science aims to produce understanding, this would enable idealizations to directly contribute to science's epistemic success. I also use the fact of widespread idealization to motivate the idea that science's wide variety aims, epistemic and non-epistemic, are best served by different kinds of scientific products. Finally, I show how these diverse aims—most rather distant from truth—result in the expanded influence of social values on science.     

Multi-model approaches to phylogenetics: Implications for idealization

Phylogenetic models traditionally represent the history of life as having a strictly-branching tree structure. However, it is becoming increasingly clear that the history of life is often not strictly-branching; lateral gene transfer, endosymbiosis, and hybridization, for example, can all produce lateral branching events. There is thus motivation to allow phylogenetic models to have a reticulate structure. One proposal involves the reconciliation of genealogical discordance. Briefly, this method uses patterns of disagreement – discordance – between trees of different genes to add lateral branching events to phylogenetic trees of taxa, and to estimate the most likely cause of these events. I use this practice to argue for: (1) a need for expanded accounts of multiple-models idealization, (2) a distinction between automatic and manual de-idealization, and (3) recognition that idealization may serve the meso-level aims of science in a different way than hitherto acknowledged.     

Seeking representations of phenomena: Phenomenological models

A distinction is made between theory-driven and phenomenological models. It is argued that phenomenological models are significant means by which theory is applied to phenomena. They act both as sources of knowledge of their target systems and are explanatory of the behaviors of the latter. A version of the shell-model of nuclear structure is analyzed and it is explained why such a model cannot be understood as being subsumed under the theory structure of Quantum Mechanics. Thus its representational capacity does not stem from its close link to theory. It is shown that the shell model yields knowledge about the target and is explanatory of certain behaviors of nuclei. Aspects of the process by which the shell model acquires its representational capacity are analyzed. It is argued that these point to the conclusion that the representational status of the model is a function of its capacity to function as a source of knowledge and its capacity to postulate and explain underlying mechanisms that give rise to the observed behavior of its target.     

Big data and prediction: Four case studies

Has the rise of data-intensive science, or ‘big data’, revolutionized our ability to predict? Does it imply a new priority for prediction over causal understanding, and a diminished role for theory and human experts? I examine four important cases where prediction is desirable: political elections, the weather, GDP, and the results of interventions suggested by economic experiments. These cases suggest caution. Although big data methods are indeed very useful sometimes, in this paper's cases they improve predictions either limitedly or not at all, and their prospects of doing so in the future are limited too.     

Giving up on convergence and autonomy: Why the theories of psychology and neuroscience are codependent as well as irreconcilable

There is a long-standing debate in the philosophy of mind and philosophy of science regarding how best to interpret the relationship between neuroscience and psychology. It has traditionally been argued that either the two domains will evolve and change over time until they converge on a single unified account of human behaviour, or else that they will continue to work in isolation given that they identify properties and states that exist autonomously from one another (due to the multiple-realizability of psychological states). In this paper, I argue that progress in psychology and neuroscience is contingent on the fact that both of these positions are false. Contra the convergence position, I argue that the theories of psychology and the theories of neuroscience are scientifically valuable as representational tools precisely because they cannot be integrated into a single account. However, contra the autonomy position, I propose that the theories of psychology and neuroscience are deeply dependent on one another for further refinement and improvement. In this respect, there is an irreconcilable codependence between psychology and neuroscience that is necessary for both domains to improve and progress. The two domains are forever linked while simultaneously being unable to integrate.     

The causal structure of natural kinds

One primary goal for metaphysical theories of natural kinds is to account for their epistemic fruitfulness. According to cluster theories of natural kinds, this epistemic fruitfulness is grounded in the regular and stable co-occurrence of a broad set of properties. In this paper, I defend the view that such a cluster theory is insufficient to adequately account for the epistemic fruitfulness of kinds. I argue that cluster theories can indeed account for the projectibility of natural kinds, but not for several other epistemic operations that natural kinds support. Natural kinds also play a role in scientific explanations and categorizations. A theory of natural kinds can only account for these additional kind-based epistemic practices if it also analyzes their causal structure.     

Observation and prediction in ancient astrology

What is the relationship between observations, predictions, texts, and instruments in ancient astrology? By distinguishing between two distinct kinds of observation claim in astrological texts, I show on the one hand the rhetorical and theoretical importance of each kind of observation claim to ancient astrological traditions, and on the other hand how practices of ancient astrology break from observation once astronomical phenomena become reliably predictable. We thus see a shift in practice from observationally derived predictions to a reliance on textual and instrumental authority, even though the rhetoric of ancient astrology still tries to maintain an emphasis on observation.     

Re-orienting discussions of scientific explanation: A functional perspective

Philosophy of science offers a rich lineage of analysis concerning the nature of scientific explanation, but the vast majority of this work, aiming to provide an analysis of the relation that binds a given explanans to its corresponding explanandum, presumes the proper analytic focus rests at the level of individual explanations. There are, however, other questions we could ask about explanation in science, such as: What role(s) does explanatory practice play in science? Shifting focus away from explanations, as achievements, toward explaining, as a coordinated activity of communities, the functional perspective aims to reveal how the practice of explanatory discourse functions within scientific communities given their more comprehensive aims and practices. In this paper, I outline the functional perspective, argue that taking the functional perspective can reveal important methodological roles for explanation in science, and consequently, that beginning here provides resources for developing more adequate responses to traditional concerns. In particular, through an examination of the ideal gas law, I emphasize the normative status of explanations within scientific communities and discuss how such status underwrites a compelling rationale for explanatory power as a theoretical virtue.     

Distinctively mathematical explanation and the problem of directionality: A quasi-erotetic solution

The increasing preponderance of opinion that some natural phenomena can be explained mathematically has inspired a search for a viable account of distinctively mathematical explanation. Among the desiderata for an adequate account is that it should solve the problem of directionality —the reversals of distinctively mathematical explanations should not count as members among the explanatory fold but any solution must also avoid the exclusion of genuine explanations. In what follows, I introduce and defend what I refer to as a quasi-erotetic solution which provides a remedy to the problem in the form of an additional necessary condition on explanation.     

Estimation and prediction under structural instability: The case of the U.S. pulp and paper market

The objectives of this paper are: first, to show empirically the relevance of using adaptive estimation techniques over more traditional estimation approaches when economic systems are believed to be structurally unstable over time; and secondly, to compare in an empirical framework two adaptive estimation techniques: Kalman filtering and the Carbone–Longini filter. For that purpose, an econometric model for the U.S. pulp and paper market is examined under the assumption of structural instability and, hence, constitutes the basis for comparing forecasting performances and estimation accuracy achieved by each technique. A version of Kalman filtering, modified in line with the basic idea of ‘tracking’ characterizing the Carbone–Longini filter, is also presented and applied. The analysis of the results shows that it may be worth using adapative estimation methods to estimate structurally unstable models, even if there is no prior knowledge about the patterns of variation of the parameters. Also, it shows the Carbone–Longini filter and Kalman filtering as being complementary estimation techniques. An estimation/forecasting methodology involving a sequential application mode of these two techniques is suggested.     

Quantum state holism: a case for holistic causation

I propose to interpret quantum state holism as a view concerning possibilities: the degree of possibility of a compound's outcome is not determined by the degrees of possibility of the components' outcomes. To analyze this proposal I sketch the modal framework of branching space-times with probabilities understood as weights of possibility. These probabilities serve to define holistic events. A holistic event produces its outcomes subluminally; yet the degree of possibility of its outcome is not determined by the degrees of possibility imposed by the event's components.     

Types of experiments and causal process tracing: What happened on the Kaibab Plateau in the 1920s

In a well-cited book chapter, ecologist Jared Diamond characterizes three main types of experiment performed in community ecology: laboratory experiment, field experiment, and natural experiment. Diamond argues that each form of experiment has strengths and weaknesses, with respect to, for example, realism or the ability to follow a causal trajectory. But does Diamond's typology exhaust the available kinds of cause-finding practices? Some social scientists have characterized something they call “causal process tracing.” Is this a fourth type of experiment or something else? I examine Diamond's typology and causal process tracing in the context of a case study concerning the dynamics of wolf and deer populations on the Kaibab Plateau in the 1920s, a case that has been used as a canonical example of a trophic cascade by ecologists but which has also been subject to controversy. I argue that ecologists have profitably deployed causal process tracing together with other types of experiment to help settle questions of causality in this case. It remains to be seen how widespread the use of causal process tracing outside of the social sciences is (or could be), but there are some potentially promising applications, particularly with respect to questions about specific causal sequences.     

Folk judgments of causation

Experimental studies suggest that people’s ordinary causal judgments are affected not only by statistical considerations but also by moral considerations. One way to explain these results would be to construct a model according to which people are trying to make a purely statistical judgment but moral considerations somehow distort their intuitions. The present paper offers an alternative perspective. Specifically, the author proposes a model according to which the very same underlying mechanism accounts for the influence of both statistical and moral considerations. On this model, it appears that ordinary causal judgments are quite different from the sorts of judgments one might find in the systematic sciences.     

Rehabilitating the regulative use of reason: Kant on empirical and chemical laws

In his Kritik der reinen Vernunft, Kant asserts that laws of nature “carry with them an expression of necessity” (A159/B198). There is, however, widespread interpretive disagreement regarding the nature and source of the necessity of empirical laws of natural sciences in Kant's system. It is especially unclear how chemistry—a science without a clear, straightforward connection to the a priori principles of the understanding—could contain such genuine, empirical laws. Existing accounts of the necessity of causal laws unfortunately fail to illuminate the possibility of non-physical laws. In this paper, I develop an alternative, ‘ideational’ account of natural laws, according to which ideas of reason necessitate the laws of some non-physical sciences. Chemical laws, for instance, are grounded on ideas of the elements, and the chemist aims to reduce her phenomena to these elements via experimentation. Although such ideas are beyond the possibility of experience, their postulation is necessary for the achievement of reason's theoretical ends: the unification and explanation of the cognitions of science.     

Evaluation of the predictive performance of biased regression estimators

Regression models are widely used in forecasting, either directly as prediction equations, or indirectly as the basis of other procedures. The predictive performance of a regression model can be adversely affected by both multicollinearity and high-leverage data points. Although biased estimation procedures have been proposed as an alternative to least squares, there has been little analysis of the predictive performance of the resulting equations. This paper discusses the predictive performance of various biased estimators, emphasizing the concept that the predictive region, as well as the strength of the multicollinearity, dictates the choice of appropriate coefficient estimators.     

Causal forces: Structuring knowledge for time-series extrapolation

This paper examines a strategy for structuring one type of domain knowledge for use in extrapolation. It does so by representing information about causality and using this domain knowledge to select and combine forecasts. We use five categories to express causal impacts upon trends: growth, decay, supporting, opposing, and regressing. An identification of causal forces aided in the determination of weights for combining extrapolation forecasts. These weights improved average ex ante forecast accuracy when tested on 104 annual economic and demographic time series. Gains in accuracy were greatest when (1) the causal forces were clearly specified and (2) stronger causal effects were expected, as in longer-range forecasts. One rule suggested by this analysis was: ‘Do not extrapolate trends if they are contrary to causal forces.’ We tested this rule by comparing forecasts from a method that implicitly assumes supporting trends (Holt's exponential smoothing) with forecasts from the random walk. Use of the rule improved accuracy for 20 series where the trends were contrary; the MdAPE (Median Absolute Percentage Error) was 18% less for the random walk on 20 one-year ahead forecasts and 40% less for 20 six-year-ahead forecasts. We then applied the rule to four other data sets. Here, the MdAPE for the random walk forecasts was 17% less than Holt's error for 943 short-range forecasts and 43% less for 723 long-range forecasts. Our study suggests that the causal assumptions implicit in traditional extrapolation methods are inappropriate for many applications.