Top-down strategies based on adaptive fuzzy rule-based systems for daily time series forecasting

This paper presents a data-driven approach applied to the long term prediction of daily time series in the Neural Forecasting Competition. The proposal comprises the use of adaptive fuzzy rule-based systems in a top-down modeling framework. Therefore, daily samples are aggregated to build weekly time series, and consequently, model optimization is performed in a top-down framework, thus reducing the forecast horizon from 56 to 8 steps ahead. Two different disaggregation procedures are evaluated: the historical and daily top-down approaches. Data pre-processing and input selection are carried out prior to the model adjustment. The prediction results are validated using multiple time series, as well as rolling origin evaluations with model re-calibration, and the results are compared with those obtained using daily models, allowing us to analyze the effectiveness of the top-down approach for longer forecast horizons.     

Accounting for time-dependent treatment use when developing a prognostic model from observational data: A review of methods

Failure to account for time-dependent treatment use when developing a prognostic model can result in biased future predictions. We reviewed currently available methods to account for treatment use when developing a prognostic model. First, we defined the estimands targeted by each method and examined their mechanisms of action with directed acyclic graphs (DAGs). Next, methods were implemented in data from 1,906 patients; 325 received selective β-blockers (SBBs) during follow-up. We demonstrated seven Cox regression modeling strategies: (a) ignoring SBB treatment; (b) excluding SBB users or (c) censoring them when treated; (d) inverse probability of treatment weighting after censoring (IPCW), including SBB treatment as (e) a binary or (f) a time-dependent covariate; and (g) marginal structural modeling (MSM). Using DAGs, we demonstrated IPCW and MSM have the best properties and target a similar estimand. In the case study, compared to (a), approaches (b) and (e) provided predictions that were 1% and 2% higher on average. Performance (c-statistic, Brier score, calibration slope) varied minimally between approaches. Our review of methods confirmed that ignoring treatment is theoretically inferior, but differences between the prediction models obtained using different methods can be modest in practice. Future simulation studies and applications are needed to assess the value of applying IPCW or MSM to adjust for treatments in different treatment and disease settings.     

金融时序数据建模的模型设定问题分析

W．J．Granger与D．F．Hendry（2004）关于建模思路的对话引起了国际计量经济学界关于模型设定问题的争论，本文就这一问题分析讨论了在金融时序数据实证研究中得以广泛应用的ARCH／GARCH模型的设定问题，认为在金融时序数据的建模中，ARMA族模型不宜作为数据生成过程的模型设定，其统计性质也不能直接扩展到ARMA-GARCH族数据生成过程。虽然ARCH／GARCH族模型作为金融时序数据的生成过程有着良好的统计性质，但不宜单纯采用一般到特殊的建模思路，而应是一般到特殊和特殊到一般两种建模思路的结合。ARCH／GARCH族模型的设定应当包含事前检验、事后检验等设定检验步骤。     

How to handle missing data in regression models using information criteria*

An important application of multiple regression is predictor selection. When there are no missing values in the data, information criteria can be used to select predictors. For example, one could apply the small‐sample‐size corrected version of the Akaike information criterion (AIC), the (AICC). In this article, we discuss how information criteria should be calculated when the dependent variable and/or the predictors contain missing values. Therewith, we extensively discuss and evaluate three models that can be employed to deal with the missing data, that is, to predict the missing values. The most complex model, that is, the model with all available predictors, outperforms the other models. These results also apply to more general hypotheses than predictor selection and also to structural equation modeling (SEM) models.     

Exchange-rate forecasts with simultaneous nearest-neighbour methods: evidence from the EMS

In this paper we extend nearest-neighbour predictors to allow for information content in a wider set of simultaneous time series. We apply these simultaneous nearest-neighbour (SNN) predictors to nine EMS currencies, using daily data for the 1st January 1978–31st December 1994 period. When forecasting performance is measured by Theil's U statistic, the (nonlinear) SNN predictors perform marginally better than both a random walk and the traditional (linear) ARIMA predictors. Furthermore, the SNN predictors outperform the random walk and the ARIMA models when producing directional forecasts.When formally testing for forecast accuracy, in most of the cases the SNN predictor outperforms the random walk at the 1% significance level, while outperforming the ARIMA model in three of the nine cases. On the other hand, our results suggest that the probability of correctly predicting the sign of change is higher for the SNN predictions than the ARIMA case.     

Product diversification and attitudes toward risk in agricultural production

In this article we analyze the relationship between risk-avoidance behavior and economic jointness in a multi-output agricultural technology. We focus on farmer specific heterogeneity in attitudes towards risk-taking, while treating production uncertainty as unobserved stochastic error that is common to all region specific farms. We furthermore utilize a new flexible functional form, the Constant Elasticity of Transformation, Constant Elasticity of Substitution, Generalized Leontief (Behrman, Lovell, Pollak, and Sickles, [1992]) which has the appealing property of relative flexibility while ensuring proper curvature properties of the estimated multi-output technology over a larger sample region of the price/quantity space than a flexible form such as the Generalized Leontief [Diewert, 1971].Our empirical study deals with small-scale agriculture in the Indian Semi-Arid Tropics (SAT), partly because of the importance of yield-related risk in this region, but also because we have measures of farmer specific risk attitudes in the SAT data. Our modeling approach allows for the calculation of the shadow cost of farmer specific risk attitudes in terms of foregone profits, while at the same time controlliing for the technical factors that give rise to multi-output production in the absence of risk. We are thus able to estimate these opportunity costs while modeling a multiple output technology in which cost complementarities can lead to diversified production and in which joint production is not always undertaken.     

Linear transformations of vector ARMA processes

Linear transformations of stochastic processes are used in many ways in economic analyses, for example when linear aggregates or subprocesses are considered. It is demonstrated that a linear transformation of a vector ARMA process is again an ARMA process and conditions for stationarity are given. Three different predictors for a linearly transformed process are compared. Forecasting the original process and transforming the predictions is superior to forecasting the transformed process directly and to transforming univariate predictions of the components of the original process. Conditions for equality of the three different forecasts are provided.     

On modeling panels of time series*

This paper reviews research issues in modeling panels of time series. Examples of this type of data are annually observed macroeconomic indicators for all countries in the world, daily returns on the individual stocks listed in the S&P500, and the sales records of all items in a retail store. A panel of time series concerns the case where the cross‐sectional dimension and the time dimension are large. Often, there is no a priori reason to select a few series or to aggregate the series over the cross‐sectional dimension. The use of, for example, a vector autoregression or other types of multivariate models then becomes cumbersome. Panel models and associated estimation techniques are more useful. Due to the large time dimension, one should however incorporate the time‐series features. And, the models should not have too many parameters to facilitate interpretation. This paper discusses representation, estimation and inference of relevant models and discusses recently proposed modeling approaches that explicitly aim to meet these requirements. The paper concludes with some reflections on the usefulness of large data sets. These concern sample selection issues and the notion that more detail also requires more complex models.     

Nowcasting Indian GDP

Nowcasting has become a useful tool for making timely predictions of gross domestic product (GDP) in a data‐rich environment. However, in developing economies this is more challenging due to substantial revisions in GDP data and the limited availability of predictor variables. Taking India as a leading case, we use a dynamic factor model nowcasting method to analyse these two issues. Firstly, we propose to compare nowcasts of the first release of GDP to those of the final release to assess differences in their predictability. Secondly, we expand a standard set of predictors typically used for nowcasting GDP with nominal and international series, in order to proxy the variation in missing employment and service sector variables in India. We find that the factor model improves over several benchmarks, including bridge equations, but only for the final GDP release and not for the first release. Also, the nominal and international series improve predictions over and above real series. This suggests that future studies of nowcasting in developing economies which have similar issues of data revisions and availability as India should be careful in analysing first‐ vs. final‐release GDP data, and may find that predictions are improved when additional variables from more timely international data sources are included.     

Optimal error and GMDH predictors: A comparison with some statistical techniques

This paper presents some results obtained in time series forecasting using two nonstandard approaches and compares them with those obtained by usual statistical techniques. In particular, a new method based on recent results of the General Theory of Optimal Algorithm is considered. This method may be useful when no reliable statistical hypotheses can be made or when a limited number of observations is available. Moreover, a nonlinear modelling technique based on Group Method of Data Handling (GMDH) is also considered to derive forecasts. The well-known Wolf Sunspot Numbers and Annual Canadian Lynx Trappings series are analyzed; the Optimal Error Predictor is also applied to a recently published demographic series on Australian Births. The reported results show that the Optimal Error and GMDH predictors provide accurate one step ahead forecasts with respect to those obtained by some linear and nonlinear statistical models. Furthermore, the Optimal Error Predictor shows very good performances in multistep forecasting.     

Continuous time modeling of panel data: SEM versus filter techniques

Although convincing arguments have been put forward for continuous-time modeling, its use in panel research is rare. In one approach, classical N  = 1 state-space modeling procedures are adapted for panel analysis to estimate the exact discrete model (EDM) by means of filter techniques. Based on earlier less satisfactory indirect methods, a more recent approach uses structural equation modeling (SEM) to get the maximum likelihood estimate of the EDM by the direct method. After an introduction into continuous-time state-space modeling for panel data and the EDM, a thorough comparison is made between the two distinct approaches with quite different histories by means of Monte Carlo simulation studies. The model used in the simulation studies is the damped linear oscillator with and without random subject effects.     

Modeling Clustered Ordered Categorical Data: A Survey

This article surveys various strategies for modeling ordered categorical (ordinal) response variables when the data have some type of clustering, extending a similar survey for binary data by Pendergast, Gange, Newton, Lindstrom, Palta & Fisher (1996). An important special case is when repeated measurement occurs at various occasions for each subject, such as in longitudinal studies. A much greater variety of models and fitting methods are available than when a similar survey for repeated ordinal response data was prepared a decade ago (Agresti, 1989). The primary emphasis of the review is on two classes of models, marginal models for which effects are averaged over all clusters at particular levels of predictors, and cluster-specific models for which effects apply at the cluster level. We present the two types of models in the ordinal context, review the literature for each, and discuss connections between them. Then, we summarize some alternative modeling approaches and ways of estimating parameters, including a Bayesian approach. We also discuss applications and areas likely to be popular for future research, such as ways of handling missing data and ways of modeling agreement and evaluating the accuracy of diagnostic tests. Finally, we review the current availability of software for using the methods discussed in this article.     

Measuring scale efficiency from a parametric hyperbolic distance function

This paper shows how scale efficiency can be measured from an arbitrary parametric hyperbolic distance function with multiple outputs and multiple inputs. It extends the methods introduced by Ray (J Product Anal 11:183–194, 1998), and Balk (J Product Anal 15:159–183, 2001) and Ray (2003) that measure scale efficiency from a single-output multi-input distance function and from a multi-output and multi-input distance function, respectively. The method developed in the present paper is different from Ray’s and Balk’s in that it allows for simultaneous contraction of inputs and expansion of outputs. Theorems applicable to an arbitrary parametric hyperbolic distance function are introduced first, and then their uses in measuring scale efficiency are illustrated with the translog functional form.     

Efficient big data model selection with applications to fraud detection

As the volume and complexity of data continues to grow, more attention is being focused on solving so-called big data problems. One field where this focus is pertinent is credit card fraud detection. Model selection approaches can identify key predictors for preventing fraud. Stagewise Selection is a classic model selection technique that has experienced a revitalized interest due to its computational simplicity and flexibility. Over a sequence of simple learning steps, stagewise techniques build a sequence of candidate models that is less greedy than the stepwise approach.This paper introduces a new stochastic stagewise technique that integrates a sub-sampling approach into the stagewise framework, yielding a simple tool for model selection when working with big data. Simulation studies demonstrate the proposed technique offers a reasonable trade off between computational cost and predictive performance. We apply the proposed approach to synthetic credit card fraud data to demonstrate the technique’s application.     

LoMEF: A framework to produce local explanations for global model time series forecasts

Global forecasting models (GFMs) that are trained across a set of multiple time series have shown superior results in many forecasting competitions and real-world applications compared with univariate forecasting approaches. One aspect of the popularity of statistical forecasting models such as ETS and ARIMA is their relative simplicity and interpretability (in terms of relevant lags, trend, seasonality, and other attributes), while GFMs typically lack interpretability, especially relating to particular time series. This reduces the trust and confidence of stakeholders when making decisions based on the forecasts without being able to understand the predictions. To mitigate this problem, we propose a novel local model-agnostic interpretability approach to explain the forecasts from GFMs. We train simpler univariate surrogate models that are considered interpretable (e.g., ETS) on the predictions of the GFM on samples within a neighbourhood that we obtain through bootstrapping, or straightforwardly as the one-step-ahead global black-box model forecasts of the time series which needs to be explained. After, we evaluate the explanations for the forecasts of the global models in both qualitative and quantitative aspects such as accuracy, fidelity, stability, and comprehensibility, and are able to show the benefits of our approach.     

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

A REFLECTION ON THE EFFECTS OF TRANSPORT COSTS WITHIN THE NEW ECONOMIC GEOGRAPHY

This paper analyzes, in the light of recent contributions of New Economic Geography models, the spatial consequences of transport cost reductions. So far, the role of transport costs have been only partially unveiled; papers focused either on the Dixit-Stiglitz-Iceberg framework or on the alternative framework put forth by Ottaviano et al. (2002) ,—which departs from the former in preferences and transport modeling. This paper goes a step further, offering a comprehensive view that includes the two approaches, in contexts both of two and of more than two locations. Contrary to other revisions of the literature focused mainly on the centripetal forces included in these models, we emphasize the role of dispersion forces. In a two-location setting, the results seem quite robust against changes in transportation modeling, so that considering either multiplicative transport costs or additive the predictions are identical. However, when allowing for a multilocation setup, the analysis becomes more complex.     

A UNIFYING VIEW ON MULTI‐STEP FORECASTING USING AN AUTOREGRESSION

Abstract This paper unifies two methodologies for multi‐step forecasting from autoregressive time series models. The first is covered in most of the traditional time series literature and it uses short‐horizon forecasts to compute longer‐horizon forecasts, while the estimation method minimizes one‐step‐ahead forecast errors. The second methodology considers direct multi‐step estimation and forecasting. In this paper, we show that both approaches are special (boundary) cases of a technique called partial least squares (PLS) when this technique is applied to an autoregression. We outline this methodology and show how it unifies the other two. We also illustrate the practical relevance of the resultant PLS autoregression for 17 quarterly, seasonally adjusted, industrial production series. Our main findings are that both boundary models can be improved by including factors indicated from the PLS technique.     

Elasticities of substitution and complementarity

This paper develops a classification scheme of the many different definitions of elasticities of substitution and complementarity in the production case based on primal and dual representations of technology and their related direct and inverse demand functions, gross and net substitution, elasticity type, and three different basic concepts of substitution and complementarity. The ten elasticities of substitution are derived from the cost, profit, input distance, and revenue functions. All the elasticities are equally valid for single and multi-output technologies. The classic Berndt-Wood dataset is used to show the considerable variation across the elasticities.     

A fuzzy clustering approach used in evaluating technical efficiency measures in manufacturing

Comparing analytical approaches is crucial when important policy decisions of corporations or government agencies may be influenced by results that depend on the methodologies certain disciplines customarily use. Technical efficiency can be measured by a full-frontier production function model or by linear programming specifications. By using these modeling approaches observations pertaining to three linerboard manufacturing facilities are classified as efficient, inefficient, scale inefficient, and other. However, observations may or may not be consistently classified into these four groups when employing the two modeling approaches. In order to validate the efficiency designations of the two modeling approaches and to determine the uniqueness of observations, a fuzzy K-means clustering approach that uses a modified hat matrix H ^* as a similarity or information matrix is employed. This approach permits observations to be allocated to clusters in a fuzzy way by defining a membership function from 0 to 1. As the degree of fuzziness increases, a sensitivity analysis with respect to individual observations belonging to some cluster can be evaluated. At the same time, this fuzzy approach assists the analyst to assess the inconsistencies that can arise when using the mathematical programming and full-frontier modeling approaches of technical efficiency.The refereeing process of this paper was handled through Rolf Färe. The majority of this research work was completed when Bill Seaver was at the Department of Management Information Resources, College of Business Administration, Western Illinois University, Macomb, IL 61455.