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Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear hierarchy in terms of the methods, with approaches that adequately approximate the states yielding superior accuracy over methods that do not. We also document numerically that over small out-of-sample evaluation periods the inferential discrepancies between the various methods often yield only small discrepancies in predictive accuracy. Nevertheless, in certain settings, and over a longer out-of-sample period, these predictive discrepancies can become meaningful. This finding indicates that the invariance of predictive results to inferential inaccuracy, which has been an oft-touted point made by practitioners seeking to justify the use of variational inference, is not ubiquitous and must be assessed on a case-by-case basis. Supplementary materials for this article are available online.

Data from the Household Income and Labour Dynamics in Australia Survey is used to estimate distributions for the level of educational attainment for Australian indigenous and nonindigenous populations for the years 2001, 2006, 2014 and 2017. Bayesian inference is used to analyse how these ordinal categorical distributions have changed over time and to compare indigenous and nonindigenous distributions. Both the level of educational attainment and inequality in educational attainment are considered. To compare changes in levels over time, as well as inequality between the two populations, first order stochastic dominance and an index of educational poverty are used. To examine changes in inequality over time, two inequality indices and generalised Lorenz dominance are considered. Results are presented in terms of posterior densities for the indices and posterior probabilities for dominance for the dominance comparisons. We find some evidence of improvement over time, especially in the lower parts of the indigenous distribution and that inequality has significantly increased from 2001 to 2017.

Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different scoring rules rewarding distinct aspects of forecast performance. Herein, we re-investigate the practice of using proper scoring rules to produce probabilistic forecasts that are ‘optimal’ according to a given score and assess when their out-of-sample accuracy is superior to alternative forecasts, according to that score. Particular attention is paid to relative predictive performance under misspecification of the predictive model. Using numerical illustrations, we document several novel findings within this paradigm that highlight the important interplay between the true data generating process, the assumed predictive model and the scoring rule. Notably, we show that only when a predictive model is sufficiently compatible with the true process to allow a particular score criterion to reward what it is designed to reward, will this approach to forecasting reap benefits. Subject to this compatibility, however, the superiority of the optimal forecast will be greater, the greater is the degree of misspecification. We explore these issues under a range of different scenarios and using both artificially simulated and empirical data.

This published article reviews 4 different statistical software systems for utility as tools for introductory statistical education. The paper has been published as: Abbasnasab Sardareh, S., Brown, G. T. L., & Denny, P. (2021). Comparing four contemporary statistical software tools for introductory data science and statistics in the social sciences. Teaching Statistics, 43(S1), S157-S172. https://doi.org/10.1111/test.12274

This thesis explores three different but interconnected issues relating to the identification of fiscal policy shocks. Grounded on several extensions of the structural vector autoregressive (SVAR) framework, the three essays provide empirical analyses of the macroeconomic impacts of fiscal policy shocks. They also shed light on the role of nonlinearity as well as its implications for the transitional dynamics of the U.S. economy during the financial crisis and the zero effective lower bound of interest rate. Beyond its contribution to the literature, this thesis also provides meaningful insights for effective policy targeting from a practical perspective.

The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain Monte Carlo: for instance, models with unavailable likelihoods, high-dimensional models, and models featuring large data sets. These approximate methods are the subject of this review. The aim is to help new researchers in particular -- and more generally those interested in adopting a Bayesian approach to empirical work -- distinguish between different approximate techniques; understand the sense in which they are approximate; appreciate when and why particular methods are useful; and see the ways in which they can can be combined., Comment: arXiv admin note: text overlap with arXiv:2004.06425

This thesis investigates three topics in stochastic frontier models using panel data via Bayesian simulations. First, the marginal posterior density of inefficiencies is approximated by a conditional density. The simulation result shows that the predictive inefficiency distribution derived from this model can capture information about inefficiencies very well. Further, we propose a data-driven adaptive bandwidth kernel estimator for the unknown frontier function. The application and simulation results imply that the adaptive bandwidth model outperforms the fixed bandwidth model. Finally, we present two sampling algorithms to model the unobserved grouped heterogeneity in the stochastic frontier mode with a latent class structure. Using the algorithms, we find evidence supporting the grouped heterogeneity in the cost frontier function.

This thesis presents dimension reduction methods for empirical probability distributions to explore the underlying structure of high-dimensional data, and these methods are applied to detect households with anomalous electricity usage patterns. The first main chapter deal with the non-Euclidean distance estimation when the data objects are probability distributions and the associated computational efficiency. The second main chapter shows how to correct the distortion from dimension reduction when estimating the density of the underlying structure. And the third main chapter explores the change in the distribution of electricity consumption brought by COVID-19 in Melbourne.

In this thesis we analyse the effect on random sampling variation on distributional forecasts and values extracted from those distributional forecasts, in a particular statistical context. Particular focus was paid to financial applications, particularly in banking, where we analysed how random sampling variation affects estimation of the size of a 1-in-100-day loss required to be calculated daily by banking institutions, and whether sampling variation alone can lead to failure of tests of models imposed by financial regulators and on the interplay between sampling variation and model selection on statistical model performance.

A forecast combination is produced by taking a weighted average of forecasts from different sources, such as different statistical models. This thesis proposes a novel method for the production of forecast combinations, and shows that this method has superior predictive accuracy relative to the traditional method most commonly used today. This finding is driven primarily by the relationship between sampling variability and predictive accuracy. A systematic exploration and comparison of these two methods is undertaken based on statistical theory, Monte Carlo simulation, and empirical data, with several implications arising for the use of forecast combination techniques in practice.

Fundamental changes have been happening in healthcare organizations and delivery in these decades, including more accessible physician information, the low-cost collection and sharing of clinical records, and decision support systems, among others. Emerging information systems and technologies play a signification role in these transformations. To extend the understanding and the implications of information systems on healthcare, my dissertation investigates the influence of information systems on enhancing healthcare operations. The findings reveal the practical value of digitalization in indicating healthcare providers' cognitive behaviors, responding to healthcare crises, and improving medical performance. The first essay investigates the unrevealed value of a special type of user-generated content in healthcare operations. In today's social media world, individuals are willing to express themselves on various online platforms. This user-generated content posted online help readers get easy assess to individuals' features, including but not limited to personality traits. To study the impact of physicians' personality traits on medicine behaviours and performance, we take a view from the perspective of user generated content posted by their supplier side as well as using physician statements which have been made available in medical review websites. It has been found that a higher openness score leads to lower mortality rates, reduced lab test costs, shorter time usage in hospitals treated by physicians with greater openness scores. Furthermore, taking these personality traits into consideration in an optimization problem of ED scheduling, the estimation of counterfactual analysis shows an average of 11.4%, 18.4%, and 17.8% reduction in in-hospital mortality rates, lab test expenditures, and lengths of stay, respectively. In future operation of healthcare, physicians' personalities should be taken into account when healthcare resources are insufficient in times of healthcare pandemics like COVID-19, as our study indicates that health service providers personality is an actual influence on clinical quality. In the second essay, we focus on the influences of the most severe healthcare pandemic in these decades, COVID-19, on digital goods consumption and examine whether digital goods consumption is resilient to an individual’s physical restriction induced by the pandemic. Leveraging the enforced quarantine policy during the COVID-19 pandemic as a quasi-experiment, we identify the influence of a specific factor, quarantine policy, on mobile app consumption in every Apple app store category in the short and long terms. In the perspective of better responding in the post-pandemic era, the quantitative findings provide managerial implications to the app industry as well as the stock market for accurately understanding the long-term impact of a significant intervention, quarantine, in the pandemic. Moreover, by using the conditional exogenous quarantine policy to instrument app users’ daily movement patterns, we are able to further investigate the digital resilience of physical mobility in different app categories and quantify the impact of an individual’s physical mobility on human behavior in app usage. For results, we find that the reduction in 10% of one’s physical mobility (measured in the radius of gyration) leads to a 2.68% increase in general app usage and a 5.44% rise in app usage time dispersion, suggesting practitioners should consider users’ physical mobility in future mobile app design, pricing, and marketing. In the third essay, we investigate the role of an emerging AI-based clinical treatment method, robot-assisted surgery (RAS), in transforming the healthcare delivery. As an advanced technique to help diminish the human physical and intellectual limitations in surgeries, RAS is expected to but has not been empirically proven to improve clinical performance. In this work, we first investigate the effect of RAS on clinical outcomes, controlling physicians' self-selection behavior in choosing whether or not to use RAS treatment methods. In particular, we focus on the accessibility of RAS and explore how physician and patient heterogeneity affect the adoption of the RAS method, including learning RAS and using RAS. Investigating the decision-making process on RAS implementation in both the learning and using stages, we show the synergy of RAS implementation in alleviating healthcare racial disparity. Ultimately, the mechanism analysis will be conducted to reveal the underlying mechanism that induces the enhancement of surgical outcomes. For instance, the estimations tend to reveal that, more than surging clinical performance, RAS tends to increase standardization in time and steps when applying the treatment procedures.

A forecast combination is produced by taking a weighted average of forecasts from different sources, such as different statistical models. This thesis proposes a novel method for the production of forecast combinations, and shows that this method has superior predictive accuracy relative to the traditional method most commonly used today. This finding is driven primarily by the relationship between sampling variability and predictive accuracy. A systematic exploration and comparison of these two methods is undertaken based on statistical theory, Monte Carlo simulation, and empirical data, with several implications arising for the use of forecast combination techniques in practice.

This paper develops a time--varying coefficient spatial autoregressive panel data model with individual fixed effects to capture the nonlinear effects of the regressors, which vary over the time. To effectively estimate the model, we propose a method that incorporates local linear estimation and concentrated quasi-maximum likelihood estimation to obtain consistent estimators for the spatial autoregressive coefficient, variance of error term and nonparametric time-varying coefficient function. The asymptotic properties of these estimators are derived as well, showing regular the standard rate of convergence for the parametric parameters and common standard rate of convergence for the time-varying component, respectively. Monte Carlo simulations are conducted to illustrate the finite sample performance of our proposed method. Meanwhile, we apply our method to study the Chinese labor productivity to identify the spatial influences and the time--varying spillover effects among 185 Chinese cities with comparison to the results on a subregion--East China.

The multinomial probit model is a popular tool for analyzing choice behaviour as it allows for correlation between choice alternatives. Because current model specifications employ a full covariance matrix of the latent utilities for the choice alternatives, they are not scalable to a large number of choice alternatives. This paper proposes a factor structure on the covariance matrix, which makes the model scalable to large choice sets. The main challenge in estimating this structure is that the model parameters require identifying restrictions. We identify the parameters by a trace-restriction on the covariance matrix, which is imposed through a reparametrization of the factor structure. We specify interpretable prior distributions on the model parameters and develop an MCMC sampler for parameter estimation. The proposed approach significantly improves performance in large choice sets relative to existing multinomial probit specifications. Applications to purchase data show the economic importance of including a large number of choice alternatives in consumer choice analysis., Comment: 39 pages, 12 figures. We corrected an error in coding in the previous version of the paper. The overall conclusions of the paper did not change after correction of the error

This paper proposes a novel forecast reconciliation framework using Bayesian state-space methods. It allows for the joint reconciliation at all forecast horizons and uses predictive distributions rather than past variation of forecast errors. Informative priors are used to assign weights to specific predictions, which makes it possible to reconcile forecasts such that they accommodate specific judgmental predictions or managerial decisions. The reconciled forecasts adhere to hierarchical constraints, which facilitates communication and supports aligned decision-making at all levels of complex hierarchical structures. An extensive forecasting study is conducted on a large collection of 13,118 time series that measure Swiss merchandise exports, grouped hierarchically by export destination and product category. We find strong evidence that in addition to producing coherent forecasts, reconciliation also leads to substantial improvements in forecast accuracy. The use of state-space methods is particularly promising for optimal decision-making under conditions with increased model uncertainty and data volatility. © 2020 Elsevier B.V., European Journal of Operational Research, 291 (2), ISSN:0377-2217, ISSN:1872-6860

We use the jackknife to bias correct the log-periodogram regression(LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as `optimal' in this sense. The theoretical results are valid under both the non-overlapping and moving-block sub-sampling schemes that can be used in the jackknife technique, and do not require the assumption of Gaussianity for the data generating process. A Monte Carlo study explores the finite sample performance of different versions of the jackknife estimator, under a variety of scenarios. The simulation experiments reveal that when the weights are constructed using the parameter values of the true data generating process, a version of the optimal jackknife estimator almost always out-performs alternative semi-parametric bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using estimates of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases. Even when misspecified short run dynamics are assumed in the construction of the weights, the feasible jackknife still shows significant reduction in bias under certain designs. As is not surprising, parametric maximum likelihood estimation out-performs all semi-parametric methods when the true values of the short memory parameters are known, but is dominated by the semi-parametric methods (in terms of bias) when the short memory parameters need to be estimated, and in particular when the model is misspecified., Comment: 57 pages

In this paper, we consider a panel data model which allows for heterogeneous time trends at different locations. We propose a new estimation method for the panel data model before we establish an asymptotic theory for the proposed estimation method. For inferential purposes, we develop a bootstrap method for the case where weak correlation presents in both dimensions of the error terms. We examine the finite-sample properties of the proposed model and estimation method through extensive simulated studies. Finally, we use the newly proposed model and method to investigate rainfall, temperature and sunshine data of U.K. respectively. Overall, we find the weather of winter has changed dramatically over the past fifty years. Changes may vary with respect to locations for the other seasons.

This paper presents a new approach to hypothesis testing based on a vector of statistics. It involves simulating the statistics under the null hypothesis and then estimating the joint density of the statistics. This allows the p-value of the smallest acceptance region test to be estimated. We prove this p-value is a consistent estimate under some regularity conditions. The small-sample properties of the proposed procedure are investigated in the context of testing for autocorrelation, testing for normality, and testing for model misspecification through the information matrix. We find that our testing procedure has appropriate sizes and good powers.

The size of China’s financial system raises the possibility that the liberalization of its capital account could have a large effect on the global financial system. This paper provides a counterfactual scenario analysis that estimates what the size and direction of China’s overseas portfolio investments would have been in 2015 if China had had no restrictions on these outflows. In such a scenario, China’s holdings of overseas portfolio assets would have been between US$1.5 trillion and US$3.2 trillion (13 to 29 per cent of Chinese GDP), or 5 to 12 times its actual holdings of US$281 billion. Our model estimates that these additional holdings would have been predominantly directed to the world’s deepest financial markets, especially the United States, while emerging-market economies would have received little additional portfolio investment. These results suggest that the liberalization of Chinese portfolio outflows may not prove disruptive to the global financial system, although it could have important implications for China., Vu la taille du système financier chinois, la libéralisation du compte de capital du pays pourrait avoir une grande incidence sur le système financier mondial. Cette étude s’appuie sur une analyse contrefactuelle pour estimer ce qu’auraient été la taille et la destination des placements étrangers de la Chine en 2015 si ces sorties de capitaux n’étaient soumises à des restrictions. Selon ce scénario, le portefeuille d’actifs étrangers de la Chine aurait été compris entre 1,5 et 3,2 billions de dollars US (de 13 à 29 % du PIB du pays), soit de 5 à 12 fois la taille du portefeuille actuel de 281 milliards. D’après les estimations de nos modèles, ces avoirs supplémentaires auraient surtout été investis dans les marchés financiers les plus profonds du monde, en particulier le marché des États-Unis. Les pays émergents, pour leur part, n’auraient reçu qu’une fraction limitée de ce surcroît. Ces résultats semblent montrer que la libéralisation des placements étrangers de la Chine ne perturberait pas le système financier mondial, mais pourrait avoir d’importantes conséquences pour le pays.

We introduce a Bayesian approach for assessing Lorenz and stochastic dominance. For two income distributions, say X and Y, estimated via Markov chain Monte Carlo, we describe how to compute posterior probabilities for: (i) X dominates Y, (ii) Y dominates X and (iii) neither Y nor X dominates. The proposed approach is applied to Indonesian income distributions using mixtures of gamma densities that ensure flexible modelling. Probability curves depicting the probability of dominance at each population proportion are used to explain changes in dominance probabilities over restricted ranges relevant for poverty orderings. They also explain some seemingly contradictory outcomes from the p-values of some sampling theory tests. Resume: Evaluation bayesienne des dominances stochastiques et de Lorenz. Dans cet article, nous presentons une approche bayesienne pour evaluer les dominances stochastiques et de Lorenz. Pour deux distributions de revenus estimees par la methode de Monte-Carlo par chaines de Markov, X et Y par exemple, nous decrivons la fac¸on de calculer les probabilites a posteriori lorsque (i) X domine Y, (ii) Y domine X et (iii) ni Y ni X ne sont dominants. Nous avons applique l’approche proposee a la distribution des revenus en Indonesie en utilisant une variete de densites gamma pour garantir une modelisation flexible. Des courbes de probabilite illustrant la probabilite de dominance sur chaque proportion de population sont utilisees pour expliquer les changements de probabilite de dominance sur des fourchettes restreintes necessaires a l’evaluation des niveaux de pauvrete. Ces courbes permettent egalement d’expliquer les resultats apparemment contradictoires des valeurs p de certains tests theoriques en matiere d’echantillonnage.

The sum of forecasts of a disaggregated time series are often required to equal the forecast of the aggregate. The least squares solution for finding coherent forecasts uses a reconciliation approach known as MinT, proposed by Wickramasuriya, Athanasopoulos and Hyndman (2019). The MinT approach and its variants do not guarantee that the coherent forecasts are nonnegative, even when all of the original forecasts are non-negative in nature. This has become aserious issue in applications that are inherently non-negative such as with sales data or tourism numbers. While overcoming this difficulty, we consider the analytical solution of MinT as a least squares minimization problem. The non-negativity constraints are then imposed on the minimization problem to ensure that the coherent forecasts are strictly non-negative. Considering the dimension and sparsity of the matrices involved, and the alternative representation of MinT, this constrained quadratic programming problem is solved using three algorithms. They are the block principal pivoting algorithm, projected conjugate gradient algorithm, and scaled gradient projection algorithm. A Monte Carlo simulation is performed to evaluate the computational performances of these algorithms. The results demonstrate that the block principal pivoting algorithm clearly outperforms the rest, and projected conjugate gradient is the second best. The superior performance of the block principal pivoting algorithm can be partially attributed to the alternative representation of the weight matrix in the MinT approach. An empirical investigation is carried out to assess the impact of imposing non-negativity constraints on forecast reconciliation. It is observed that slight gains in forecast accuracy have occurred at the most disaggregated level. At the aggregated level slight losses are also observed. Although the gains or losses are negligible, the procedure plays an important role in decision and policy implementation processes.

We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according to criterion functions based on proper scoring rules, which are chosen to reward the form of forecast accuracy that matters for the problem at hand, and forecast performance is measured using the out-of-sample expectation of said scoring rule. Our results provide novel insights into the behavior of estimated forecast combinations. Firstly, we show that, asymptotically, the sampling variability in the performance of standard forecast combinations is determined solely by estimation of the constituent models, with estimation of the combination weights contributing no sampling variability whatsoever, at first order. Secondly, we show that, if computationally feasible, forecast combinations produced in a single step -- in which the constituent model and combination function parameters are estimated jointly -- have superior predictive accuracy and lower sampling variability than standard forecast combinations -- where constituent model and combination function parameters are estimated in two steps. These theoretical insights are demonstrated numerically, both in simulation settings and in an extensive empirical illustration using a time series of S&P500 returns., 42 pages, 8 figures, 1 table; the views expressed in this paper are those of the authors alone, and do not in any way represent the Methodology Division, the Australian Bureau of Statistics, the Australian Public Service, or the Australian Government

Decreases in stock market returns often lead to higher increases in volatility than increases in returns of the same magnitude, and it is common to incorporate these so-called leverage effects in GARCH and stochastic volatility models. Recent research has also found it useful to account for leverage in models of realized volatility, as well as in models of the continuous and jump components of realized volatility. This paper explores the use of smooth transition autoregressive (STAR) models for capturing leverage effects in multiple series of the continuous components of realized volatility. We find that the leverage effect is well captured by a common nonlinear factor driven by returns, even though the persistence in each country’s volatility is country specific. A three country model that incorporates both country specific persistence and a common leverage effect offers slight forecast improvements for mid-range horizons, relative to other models that do not allow for the common nonlinearity.

In this paper, we study a class of high dimensional moment restriction panel data models with interactive effects, where factors are unobserved and factor loadings are nonparametrically unknown smooth functions of individual characteristics variables. We allow the dimension of the parameter vector and the number of moment conditions to diverge with sample size. This is a very general framework and includes many existing linear and nonlinear panel data models as special cases. In order to estimate the unknown parameters, factors and factor loadings, we propose a sieve-based generalized method of moments estimation method and we show that under a set of simple identification conditions, all those unknown quantities can be consistently estimated. Further we establish asymptotic distributions of the proposed estimators. In addition, we propose tests for over-identification, specification of factor loading functions, and establish their large sample properties. Moreover, a number of simulation studies are conducted to examine the performance of the proposed estimators and test statistics in finite samples. An empirical example on stock return prediction is studied to demonstrate the usefulness of the proposed framework and corresponding estimation methods and testing procedures.

This paper examines the identification power of instrumental variables (IVs) for average treatment effect (ATE) in partially identified models. We decompose the ATE identification gains into components of contributions driven by IV relevancy, IV strength, direction and degree of treatment endogeneity, and matching via exogenous covariates. Our decomposition is demonstrated with graphical illustrations, simulation studies and an empirical example of childbearing and women's labour supply. Our analysis offers insights for understanding the complex role of IVs in ATE identification and for selecting IVs in practical policy designs. Simulations also suggest potential uses of our analysis for detecting irrelevant instruments.

Calendars are broadly used in society to display temporal information, and events. This paper describes a new R package with functionality to organize and display temporal data, collected on sub-daily resolution, into a calendar layout. The function `frame_calendar` uses linear algebra on the date variable to restructure data into a format lending itself to calendar layouts. The user can apply the grammar of graphics to create plots inside each calendar cell, and thus the displays synchronize neatly with ggplot2 graphics. The motivating application is studying pedestrian behavior in Melbourne, Australia, based on counts which are captured at hourly intervals by sensors scattered around the city. Faceting by the usual features such as day and month, was insufficient to examine the behavior. Making displays on a monthly calendar format helps to understand pedestrian patterns relative to events such as work days, weekends, holidays, and special events. The layout algorithm has several format options and variations. It is implemented in the R package sugrrants., 31 pages, 19 figures

We propose a common features approach and establish that global temperatures and greenhouse gases share a common trend without conditioning on the exact nature of their trends. We also find deterministic cycles in global temperature series with a period of 72 years whose amplitude is non-negligible compared to the warming effect caused by anthropogenic greenhouse gas emissions. We also explore the direction of causation in the co-trending relationship by establishing an error correction mechanism, which shows that greenhouse gas emissions do not respond to the equilibrium errors whereas the global temperature responds to equilibrium errors so as to maintain the co-trending relationship. Finally, we forecast future temperatures conditional on representative concentration pathways (RCP) of greenhouse gases considered by the intergovernmental panel on climate change (IPCC). Our forecasts show that the cyclical component could play a significant role in the next 30 years in such a way that would make the politics of effective emission control policy making more challenging.

The stochastic frontier model used for continuous dependent variables is extended to accommodate output measured as a discrete ordinal outcome variable. Conditional on the inefficiency error, the assumptions of the ordered probit model are adopted for the log of output. Bayesian estimation utilizing a Gibbs sampler with data augmentation is applied to a convenient re-parameterisation of the model. Using panel data from an Australian longitudinal survey, demographic and socioeconomic characteristics are specified as inputs to health production, whereas production efficiency is made dependent on lifestyle factors. Posterior summary statistics are obtained for selected health status probabilities, efficiencies, and marginal effects.

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of linear statistics. The methods are then applied to the problem of estimating the sampling distribution of the sample mean under long memory, in an experimental setting. The pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding.

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

This paper examines real exchange rate responses to shocks in exchange rate determinants for fourteen Asian developing countries. The analysis is based on a panel structural vector error correction model, and the shocks are identified using sign and zero restrictions. We find that trade liberalization generates permanent depreciation, and higher government consumption causes persistent appreciation. Traded-sector productivity gains induce appreciation but their effects are not immediate and last only for a few years. Real exchange rate responses to unexpected monetary tightening are consistent with the long-run neutrality of money. The evidence suggests that trade liberalization and government consumption have a strong effect on real exchange rates, while the effects of traded-sector productivity shocks are much weaker.

This paper focuses on the estimation of the location of level breaks in time series whose shocks display non-stationary volatility (permanent changes in unconditional volatility). We propose a new feasible weighted least squares (WLS) estimator, based on an adaptive estimate of the volatility path of the shocks. We show that this estimator belongs to a generic class of weighted residual sum of squares which also contains the ordinary least squares (OLS) and WLS estimators, the latter based on the true volatility process. For fixed magnitude breaks we show that the consistency rate of the generic estimator is unaffected by non-stationary volatility. We also provide local limiting distribution theory for cases where the break magnitude is eitherlocal-to-zero at some polynomial rate in the sample size or is exactly zero. The former includes the Pitman drift rate which is shown via Monte Carlo experiments to predict well the key features of the finite sample behaviour of both the OLS and our feasible WLS estimators. The simulations highlight the importance of the break location, break magnitude, and the form of non-stationary volatility for the finite sample performance of these estimators, and show that our proposed feasible WLS estimator can deliver significant improvements over the OLS estimator under heteroskedasticity. We discuss how these results can be applied, by using level break fraction estimators on the first differences of the data, when testing for a unit root in the presence of trend breaks and/or non-stationary volatility. Methods to select between the break and no break cases, using standard information criteria and feasible weighted information criteria based on our adaptive volatility estimator, are also discussed. Simulation evidence suggests that unit root tests based on these weighted quantities can display significantly improved finite sample behaviour under heteroskedasticity relative to their unweighted counterparts. An empirical illustration to U.S. and U.K. real GDP is also considered.

Forecast reconciliation involves adjusting forecasts to ensure coherence with aggregation constraints. We extend this concept from point forecasts to probabilistic forecasts by redefining forecast reconciliation in terms of linear functions in general, and projections more specifically. New theorems establish that the true predictive distribution can be recovered in the elliptical case by linear reconciliation, and general conditions are derived for when this is a projection. A geometric interpretation is also used to prove two new theoretical results for point forecasting; that reconciliation via projection both preserves unbiasedness and dominates unreconciled forecasts in a mean squared error sense. Strategies for forecast evaluation based on scoring rules are discussed, and it is shown that the popular log score is an improper scoring rule with respect to the class of unreconciled forecasts when the true predictive distribution coheres with aggregation constraints. Finally, evidence from a simulation study shows that reconciliation based on an oblique projection, derived from the MinT method of Wickramasuriya, Athanasopoulos and Hyndman (2018) for point forecasting, outperforms both reconciled and unreconciled alternatives.

This paper establishes vector autoregressive moving average (VARMA) models for Malaysian monetary policy analysis by efficiently identifying and simultaneously estimating the model parameters using full information maximum likelihood. The monetary literature is largely dominated by vector autoregressive (VAR) and structural vector autoregressive (SVAR).models, and to the best of our knowledge, this is the first paper to use VARMA modelling to investigate monetary policy. Malaysia is an interesting small open economy to study because of the capital control measures imposed by the government following the 1997 Asian financial crisis. A comparison of the impulse responses generated by these three models for the pre- and post-crisis periods indicates that the VARMA model impulse responses are consistent with prior expectations based on economic theories and policies pursued by the Malaysian government, particularly in the post-crisis period. Furthermore, uncovering the way in which various intermediate channels work would help Bank Negara Malaysia to steer the economy in the right direction so that monetary policy can still remain an effective policy measure in achieving sustainable economic growth and price stability.

We propose a powerful quadratic test for the overall significance of many weak exogenous variables in a dense autoregressive model. By shrinking the classical weighting matrix on the sample moments to be identity, the test is asymptotically correct in high dimensions even when the number of coefficients is larger than the sample size. Our theory allows a non-parametric error distribution and estimation of the autoregressive coefficients. Using random matrix theory, we show that the test has the optimal asymptotic testing power among a large class of competitors against local dense alternatives whose direction is free in the eigenbasis of the sample covariance matrix among regressors. The asymptotic results are adaptive to the predictors' cross-sectional and temporal dependence structure, and do not require a limiting spectral law of their sample covariance matrix. The method extends beyond autoregressive models, and allows more general nuisance parameters. Monte Carlo studies suggest a good power performance of our proposed test against high dimensional dense alternative for various data generating processes. We apply our tests to detect the overall significance of over one hundred exogenous variables in the latest FRED-MD database for predicting the monthly growth in the US industrial production index.

We estimate the effect of Bitcoin ownership on the level of cash holdings of Canadian consumers. Bitcoin ownership positively correlates with cash holdings even after accounting for selection into ownership via a control function approach. On average, Bitcoin owners hold 83 percent (in 2018) to 95 percent (in 2017) more cash than non-owners. Focusing on the quantiles of cash holdings, we find that Bitcoin ownership has a highly nonlinear effect. For example, the difference in cash holdings between Bitcoin owners and non-owners in 2017 varies from 63 percent at the 25th quantile of cash to 176 percent at the 95th quantile of cash. Our results provide some evidence to reject the hypothesis that new digital currencies or technologies, such as Bitcoin, will lead to a decline in cash holdings., Nous estimons l’effet de la détention de bitcoins sur la propension des consommateurs canadiens à détenir de l’argent comptant. Il existe une corrélation positive entre la détention de bitcoins et les avoirs en argent liquide même après la prise en compte d’un biais de sélectivité à l’aide d’une fonction de contrôle. En moyenne, les détenteurs de bitcoins ont plus d’argent liquide que les non-détenteurs (83 % plus en 2018 et 95 % plus en 2017). En mettant l’accent sur les quantiles d’avoirs en argent liquide, nous constatons que la détention de bitcoins a un effet fortement non linéaire. Par exemple, la différence entre les sommes d’argent comptant des détenteurs et des non détenteurs en 2017 varie de 63 % au 25e quantile d’argent liquide à 176 % au 95e quantile d’argent liquide. Nos résultats fournissent certains éléments pour rejeter l’hypothèse voulant que l’adoption de nouvelles monnaies numériques ou technologies, comme le bitcoin, mènera au déclin de l’argent liquide.

This paper considers modelling and detecting structure breaks associated with cross-sectional dependence for large dimensional panel data models, which are popular

This paper concerns the forecasting of seasonal intraday time series. An extension of Holt-Winters exponential smoothing has been proposed that smoothes an intraday cycle and an intraweek cycle. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce an exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms than the other two exponential smoothing methods. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. By contrast with the previously proposed exponential smoothing methods, our new method can model in a straightforward way this situation, where the number of periods on each day of the week is not the same.

This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate of the long memory parameter. Theoretical justification for using the bootstrap techniques to bias adjust log-periodogram and semi-parametric local Whittle estimators of the memory parameter is provided. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias correction techniques is also presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which analytical adjustments have already been used. The empirical coverage of confidence intervals based on the bias-adjusted estimators is very close to the nominal, for a reasonably large sample size, more so than for the comparable analytically adjusted estimators. The precision of inferences (as measured by interval length) is also greater when the bootstrap is used to bias correct rather than analytical adjustments., Comment: 38 pages

The paper presents estimates of price elasticities of demand for twelve disaggregated alcohol beverages in Australia: premium beer, full strength beer, low alcohol beer, and mid strength beer; red bottled wine, white bottled wine, sparkling wine, cask wine, and dark and light ready-to-drink (RTD); and dark and light spirits. These disaggregated categories correspond closely to the commodities of interest to public policymakers with respect to taxation and health policies. The system of demand equations is estimated with Nielsen data from Australia using the semiflexible AIDS model in order to impose negative semidefiniteness on the demand parameters. Results indicate elastic own-price elasticities for virtually all commodities. Morishma elasticities of substitution indicate premium beer, mid strength beer, and cask wine exhibit the largest elasticities of substitution. Low alcohol beer, light RTD, and light spirits show the lowest substitution. The elasticity estimates are used to illustrate the effect of a change in the current tax system toward taxation equalisation based on alcohol content. The policy simulation highlights the importance of having a complete system of demand elasticities because the mix of consumption of alcohol beverages changes in response to the type of alcohol policy.

This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from short-term operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments.

Forecasting hierarchical or grouped time series usually involves two steps: computing base forecasts and reconciling the forecasts. Base forecasts can be computed by popular time series forecasting methods such as Exponential Smoothing (ETS) and Autoregressive Integrated Moving Average (ARIMA) models. The reconciliation step is a linear process that adjusts the base forecasts to ensure they are coherent. However using ETS or ARIMA for base forecasts can be computationally challenging when there are a large number of series to forecast, as each model must be numerically optimized for each series. We propose a linear model that avoids this computational problem and handles the forecasting and reconciliation in a single step. The proposed method is very flexible in incorporating external data, handling missing values and model selection. We illustrate our approach using two datasets: monthly Australian domestic tourism and daily Wikipedia pageviews. We compare our approach to reconciliation using ETS and ARIMA, and show that our approach is much faster while providing similar levels of forecast accuracy.

In this paper, we propose three new predictive models: the multi-step nonparametric predictive regression model and the multi-step additive predictive regression model, in which the predictive variables are locally stationary time series; and the multi-step time-varying coefficient predictive regression model, in which the predictive variables are stochastically nonstationary. We also establish the estimation theory and asymptotic properties for these models in the short horizon and long horizon case. To evaluate the effectiveness of these models, we investigate their capability of stock return prediction. The empirical results show that all of these models can substantially outperform the traditional linear predictive regression model in terms of both in-sample and out-of-sample performance. In addition, we find that these models can always beat the historical mean model in terms of in-sample fitting, and also for some cases in terms of the out-of-sample forecasting.

This paper proposes two new weighting schemes that average forecasts using different estimation windows to account for structural change. We let the weights reflect the probability of each time point being the most-recent break point, and we use the reversed ordered Cusum test statistics to capture this intuition. The second weighting method simply imposes heavier weights on those forecasts that use more recent information. The proposed combination forecasts are evaluated using Monte Carlo techniques, and we compare them with forecasts based on other methods that try to account for structural change, including average forecasts weighted by past forecasting performance and techniques that first estimate a break point and then forecast using the post break data. Simulation results show that our proposed weighting methods often outperform the others in the presence of structural breaks. An empirical application based on a NAIRU Phillips curve model for the United States indicates that it is possible to outperform the random walk forecasting model when we employ forecasting methods that account for break uncertainty.

Formulas are derived for the Gini, Theil and Pietra coefficients for a population-weighted mixture of double Pareto-lognormal distributions; they are applied to South America for two years. Results are also provided for the special case Pareto-lognormal and lognormal distributions. The formulas are useful for measuring regional or global inequality in large-scale projects that utilise double Pareto-lognormal distributions or their special cases.

This dissertation address two significant challenges in the causal inference workflow for Big Observational Data. The first is designing Big Observational Data with high-dimensional and heterogeneous covariates. The second is performing uncertainty quantification for estimates of causal estimands that are obtained from the application of black box machine learning algorithms on the designed Big Observational Data. The methodologies developed by addressing these challenges are applied for the design and analysis of Big Observational Data from a large public university in the United States. Distributed Design A fundamental issue in causal inference for Big Observational Data is confounding due to covariate imbalances between treatment groups. This can be addressed by designing the study prior to analysis. The design ensures that subjects in the different treatment groups that have comparable covariates are subclassified or matched together. Analyzing such a designed study helps to reduce biases arising from the confounding of covariates with treatment. Existing design methods, developed for traditional observational studies consisting of a single designer, can yield unsatisfactory designs with sub-optimum covariate balance for Big Observational Data due to their inability to accommodate the massive dimensionality, heterogeneity, and volume of the Big Data. We propose a new framework for the distributed design of Big Observational Data amongst collaborative designers. Our framework first assigns subsets of the high-dimensional and heterogeneous covariates to multiple designers. The designers then summarize their covariates into lower-dimensional quantities, share their summaries with the others, and design the study in parallel based on their assigned covariates and the summaries they receive. The final design is selected by comparing balance measures for all covariates across the candidates and identifying the best amongst the candidates. We perform simulation studies and analyze datasets from the 2016 Atlantic Causal Inference Conference Data Challenge to demonstrate the flexibility and power of our framework for constructing designs with good covariate balance from Big Observational Data. Designed Bootstrap The combination of modern machine learning algorithms with the nonparametric bootstrap can enable effective predictions and inferences on Big Observational Data. An increasingly prominent and critical objective in such analyses is to draw causal inferences from the Big Observational Data. A fundamental step in addressing this objective is to design the observational study prior to the application of machine learning algorithms. However, the application of the traditional nonparametric bootstrap on Big Observational Data requires excessive computational efforts. This is because every bootstrap sample would need to be re-designed under the traditional approach, which can be prohibitive in practice. We propose a design-based bootstrap for deriving causal inferences with reduced bias from the application of machine learning algorithms on Big Observational Data. Our bootstrap procedure operates by resampling from the original designed observational study. It eliminates the need for additional, costly design steps on each bootstrap sample that are performed under the standard nonparametric bootstrap. We demonstrate the computational efficiency of this procedure compared to the traditional nonparametric bootstrap, and its equivalency in terms of confidence interval coverage rates for the average treatment effects, by means of simulation studies and a real-life case study. Case Study We apply the distributed design and designed bootstrap methodologies in a case study involving institutional data from a large public university in the United States. The institutional data contains comprehensive information about the undergraduate students in the university, ranging from their academic records to on-campus activities. We study the causal effects of undergraduate students’ attempted course load on their academic performance based on a selection of covariates from these data. Ultimately, our real-life case study demonstrates how our methodologies enable researchers to effectively use straightforward design procedures to obtain valid causal inferences with reduced computational efforts from the application of machine learning algorithms on Big Observational Data.

A large body of the forecasting literature so far has been focused on forecasting the conditional mean of future observations. However, there is an increasing need for generating the entire conditional distribution of future observations in order to effectively quantify the uncertainty in time series data. We present two different methods for probabilistic time series forecasting that allow the inclusion of a possibly large set of exogenous variables. One method is based on forecasting both the conditional mean and variance of the future distribution using a traditional regression approach. The other directly computes multiple quantiles of the future distribution using quantile regression. We propose an implementation for the two methods based on boosted additive models, which enjoy many useful properties including accuracy, flexibility, interpretability and automatic variable selection. We conduct extensive experiments using electricity smart meter data, on both aggregated and disaggregated scales, to compare the two forecasting methods for the challenging problem of forecasting the distribution of future electricity consumption. The empirical results demonstrate that the mean and variance forecasting provides better forecasts for aggregated demand, while the flexibility of the quantile regression approach is more suitable for disaggregated demand. These results are particularly useful since more energy data will become available at the disaggregated level in the future.

Kernel density estimation is an important technique for understanding the distributional properties of data. Some investigations have found that the estimation of a global bandwidth can be heavily affected by observations in the tail. We propose to categorize data into low- and high-density regions, to which we assign two different bandwidths called the low-density adaptive bandwidths. We derive the posterior of the bandwidth parameters through the Kullback-Leibler information. A Bayesian sampling algorithm is presented to estimate the bandwidths. Monte Carlo simulations are conducted to examine the performance of the proposed Bayesian sampling algorithm in comparison with the performance of the normal reference rule and a Bayesian sampling algorithm for estimating a global bandwidth. According to Kullback-Leibler information, the kernel density estimator with low-density adaptive bandwidths estimated through the proposed Bayesian sampling algorithm outperforms the density estimators with bandwidth estimated through the two competitors. We apply the low-density adaptive kernel density estimator to the estimation of the bivariate density of daily stock-index returns observed from the U.S. and Australian stock markets. The derived conditional distribution of the Australian stock-index return for a given daily return in the U.S. market enables market analysts to understand how the former market is associated with the latter.

This paper considers a semiparametric panel data model with heterogeneous coefficients

Optimal probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of the integer autoregressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth and death process or branching process. The theoretical proofs of asymptotic optimality are supplemented by simulation results which demonstrate the overall superiority of the nonparametric method relative to a misspecified parametric maximum likelihood estimator, in large but .nite samples. The method is applied to counts of wage claim benefits, stock market iceberg orders and civilian deaths in Iraq, with bootstrap methods used to quantify sampling variation in the estimated forecast distributions.