This dissertation examines the forecast model selection problem in economics in both theoretical and empirical settings. The forecast model selection problem is that there often exists a menu of different suitable models to forecast the same economic variable of interest. The theoretical portion of this dissertation considers agents who face this problem in two distinct scenarios. The first scenario considers the case where agents possess a menu of different forecast techniques which includes rational expectations but where the selection of rational expectations is costly. The assumptions that are necessary to include rational expectations as a choice are characterized and the equilibrium dynamics of a model under the appropriate assumptions is studied and shown to exhibit chaotic dynamics. The second scenario considers agents who possess a menu of econometric forecast models and examines the equilibrium outcomes when agents combine the different forecasts using strategies suggested by the forecasting literature. The equilibrium outcomes under these forecasting assumptions are shown to exhibit time-varying volatility and endogenous structural breaks, which are common features of macroeconomic data. The empirical portion of the dissertation proposes a new dynamic combination strategy for the forecast model selection problem to forecast inflation. The procedure builds on recent research on inflation persistence in the U.S. and on explanations for the efficacy of simple combination strategies, often referred to as the forecast combination puzzle. The new combination strategy is shown to forecast well in real-time out-of-sample forecasting exercises.

We provide a comprehensive study of out-of-sample forecasts for the EUR/USD exchange rate based on multivariate macroeconomic models and forecast combinations. We use profit maximization measures based on directional accuracy and trading strategies in addition to standard loss minimization measures. When comparing predictive accuracy and profit measures, data snooping bias free tests are used. The results indicate that forecast combinations, in particular those based on principal components of forecasts, help to improve over benchmark trading strategies, although the excess return per unit of deviation is limited.

Combining multiple forecasts in order to generate a single, more accurate one is a well-known approach. A simple average of forecasts has been found to be robust despite theoretically better approaches, increasing availability in the number of expert forecasts, and improved computational capabilities. The dominance of a simple average is related to the small sample sizes and to the estimation errors associated with more complex methods. We study the role that expert correlation, multiple experts, and their relative forecasting accuracy have on the weight estimation error distribution. The distributions we find are used to identify the conditions when a decision maker can confidently estimate weights versus using a simple average. We also propose an improved expert weighting approach that is less sensitive to covariance estimation error while providing much of the benefit from a covariance optimal weight. These two improvements create a new heuristic for better forecast aggregation that is simple to use. This heuristic appears new to the literature and is shown to perform better than a simple average in a simulation study and by application to economic forecast data.

We provide a systematic comparison of the out-of-sample forecasts based on multivariate macroeconomic models and forecast combinations for the euro against the US dollar, the British pound, the Swiss franc and the Japanese yen. We use profit maximization measures based on directional accuracy and trading strategies in addition to standard loss minimization measures. When comparing predictive accuracy and profit measures, data snooping bias free tests are used. The results indicate that forecast combinations help to improve over benchmark trading strategies for the exchange rate against the US dollar and the British pound, although the excess return per unit of deviation is limited. For the euro against the Swiss franc or the Japanese yen, no evidence of generalized improvement in profit measures over the benchmark is found. (authors' abstract) / Series: Department of Economics Working Paper Series

A obtenção de previsões com maior acuracidade é uma necessidade constantemente requerida, em tempos onde há imensa disponibilidade de dados e recursos computacionais cada dia mais eficientes. Tais critérios possibilitaram o desenvolvimento de muitas técnicas de previsão individual ou de métodos de combinação que são considerados eficientes no intuito de reduzir erros. O desenvolvimento de novas técnicas, por sua vez, promove questionamentos quanto à identificação de quantas ou quais técnicas de previsão individual combinar. A literatura não é unânime ao tentar responder a estes questionamentos e indica a importância da correlação entre os erros de previsão na precisão da combinação. Posto isso, esta tese apresenta uma alternativa aos métodos atuais de combinar previsões, contemplando a correlação entre os erros de previsão, além de propor uma forma de identificar técnicas de previsão que sejam distintas quanto à modelagem de características da série de dados. Para identificar grupos de técnicas de previsão individual que sejam similares, utilizou-se a Análise de Agrupamentos em erros gerados por 15 técnicas de previsão que modelaram uma mesma série de dados real com tendência e sazonalidade. O resultado indicou a formação de 3 agrupamentos. Como alternativa aos métodos atuais de combinar previsão e selecionar a quantidade adequada de técnicas, utilizou-se a Análise de Componentes Principais. O método proposto mostrou-se viável quando comparado com outros métodos de combinação e quando submetido à modelagem de séries com maior variabilidade. / The obtaining of more accurate forecasts is a necessity often required in times where there is a huge availability of data and computing resources becoming more efficient every day. These criteria allowed the development of many individual forecasting techniques or combination methods that are considered efficient in order to reduce errors. The development of new techniques, in turn, promotes questioning as the identification of how many or which techniques to combine individual forecasts. The literature is not unanimous when trying to answer these questions and indicates the importance of the correlation between forecast errors on the accuracy of the combination. That said, this presents an alternative to current methods of combining forecasts, considering the correlation between forecast errors, and propose a way to identify predictive techniques that are different about the modeling features of the data series. To identify groups of individual forecasting techniques that are similar, it was used the cluster analysis on errors generated by 15 forecasting techniques that shaped the same series of real data with trend and seasonality. The result indicated the formation of 3 clusters. As an alternative to current methods of combining forecasting and selecting the appropriate amount of techniques, it was used the Principal Component Analysis. The proposed method has proved feasible when compared to other methods of combining and when subjected to modeling of series with greater variability.

A obtenção de previsões com maior acuracidade é uma necessidade constantemente requerida, em tempos onde há imensa disponibilidade de dados e recursos computacionais cada dia mais eficientes. Tais critérios possibilitaram o desenvolvimento de muitas técnicas de previsão individual ou de métodos de combinação que são considerados eficientes no intuito de reduzir erros. O desenvolvimento de novas técnicas, por sua vez, promove questionamentos quanto à identificação de quantas ou quais técnicas de previsão individual combinar. A literatura não é unânime ao tentar responder a estes questionamentos e indica a importância da correlação entre os erros de previsão na precisão da combinação. Posto isso, esta tese apresenta uma alternativa aos métodos atuais de combinar previsões, contemplando a correlação entre os erros de previsão, além de propor uma forma de identificar técnicas de previsão que sejam distintas quanto à modelagem de características da série de dados. Para identificar grupos de técnicas de previsão individual que sejam similares, utilizou-se a Análise de Agrupamentos em erros gerados por 15 técnicas de previsão que modelaram uma mesma série de dados real com tendência e sazonalidade. O resultado indicou a formação de 3 agrupamentos. Como alternativa aos métodos atuais de combinar previsão e selecionar a quantidade adequada de técnicas, utilizou-se a Análise de Componentes Principais. O método proposto mostrou-se viável quando comparado com outros métodos de combinação e quando submetido à modelagem de séries com maior variabilidade. / The obtaining of more accurate forecasts is a necessity often required in times where there is a huge availability of data and computing resources becoming more efficient every day. These criteria allowed the development of many individual forecasting techniques or combination methods that are considered efficient in order to reduce errors. The development of new techniques, in turn, promotes questioning as the identification of how many or which techniques to combine individual forecasts. The literature is not unanimous when trying to answer these questions and indicates the importance of the correlation between forecast errors on the accuracy of the combination. That said, this presents an alternative to current methods of combining forecasts, considering the correlation between forecast errors, and propose a way to identify predictive techniques that are different about the modeling features of the data series. To identify groups of individual forecasting techniques that are similar, it was used the cluster analysis on errors generated by 15 forecasting techniques that shaped the same series of real data with trend and seasonality. The result indicated the formation of 3 clusters. As an alternative to current methods of combining forecasting and selecting the appropriate amount of techniques, it was used the Principal Component Analysis. The proposed method has proved feasible when compared to other methods of combining and when subjected to modeling of series with greater variability.

A obtenção de previsões com maior acuracidade é uma necessidade constantemente requerida, em tempos onde há imensa disponibilidade de dados e recursos computacionais cada dia mais eficientes. Tais critérios possibilitaram o desenvolvimento de muitas técnicas de previsão individual ou de métodos de combinação que são considerados eficientes no intuito de reduzir erros. O desenvolvimento de novas técnicas, por sua vez, promove questionamentos quanto à identificação de quantas ou quais técnicas de previsão individual combinar. A literatura não é unânime ao tentar responder a estes questionamentos e indica a importância da correlação entre os erros de previsão na precisão da combinação. Posto isso, esta tese apresenta uma alternativa aos métodos atuais de combinar previsões, contemplando a correlação entre os erros de previsão, além de propor uma forma de identificar técnicas de previsão que sejam distintas quanto à modelagem de características da série de dados. Para identificar grupos de técnicas de previsão individual que sejam similares, utilizou-se a Análise de Agrupamentos em erros gerados por 15 técnicas de previsão que modelaram uma mesma série de dados real com tendência e sazonalidade. O resultado indicou a formação de 3 agrupamentos. Como alternativa aos métodos atuais de combinar previsão e selecionar a quantidade adequada de técnicas, utilizou-se a Análise de Componentes Principais. O método proposto mostrou-se viável quando comparado com outros métodos de combinação e quando submetido à modelagem de séries com maior variabilidade. / The obtaining of more accurate forecasts is a necessity often required in times where there is a huge availability of data and computing resources becoming more efficient every day. These criteria allowed the development of many individual forecasting techniques or combination methods that are considered efficient in order to reduce errors. The development of new techniques, in turn, promotes questioning as the identification of how many or which techniques to combine individual forecasts. The literature is not unanimous when trying to answer these questions and indicates the importance of the correlation between forecast errors on the accuracy of the combination. That said, this presents an alternative to current methods of combining forecasts, considering the correlation between forecast errors, and propose a way to identify predictive techniques that are different about the modeling features of the data series. To identify groups of individual forecasting techniques that are similar, it was used the cluster analysis on errors generated by 15 forecasting techniques that shaped the same series of real data with trend and seasonality. The result indicated the formation of 3 clusters. As an alternative to current methods of combining forecasting and selecting the appropriate amount of techniques, it was used the Principal Component Analysis. The proposed method has proved feasible when compared to other methods of combining and when subjected to modeling of series with greater variability.

The gross domestic product (GDP) is an essential measure of the state of economic activity and serves as a crucial tool for policymakers, investors, or businesses. However, the official GDP estimate in the Czech Republic is only available with a lag of approximately 60 days, and the Czech National Bank (CNB) announces its GDP forecast once in each quarter. This thesis focuses on predicting GDP growth in the current quarter, referred to as nowcasting. I employ several methods to nowcast the real GDP growth in the Czech Republic in a pseudo-real-time setting and compare their performance. Additionally, I investigate the possibility of creating an ensemble model by using a weighted average of several nowcasting models. The results suggest that the Dynamic Factor Model (DFM) performs best in the GDP nowcasting task, and its predictive accuracy is comparable with the official CNB nowcast. Furthermore, the model averaging process yields accuracy close to the best individual model while addressing model uncertainty. The GDP nowcast of the DFM will be made available to the public in real-time on a website and updated with a daily frequency.

Commodities primárias, tais como metais, petróleo e agricultura, constituem matérias-primas fundamentais para a economia mundial. Dentre os metais, destaca-se o alumínio, usado em uma ampla gama de indústrias, e que detém o maior volume de contratos na London Metal Exchange (LME). Como o preço não está diretamente relacionado aos custos de produção, em momentos de volatilidade ou choques econômicos, o impacto financeiro na indústria global de alumínio é significativo. Previsão de preços do alumínio é fundamental, portanto, para definição de política industrial, bem como para produtores e consumidores. Este trabalho propõe um modelo ótimo de previsões para preços de alumínio, por meio de combinações de previsões e de seleção de modelos através do Model Confidence Set (MCS), capaz de aumentar o poder preditivo em relação a métodos tradicionais. A abordagem adotada preenche uma lacuna na literatura para previsão de preços de alumínio. Foram ajustados 5 modelos individuais: AR(1), como benchmarking, ARIMA, dois modelos ARIMAX e um modelo estrutural, utilizando a base de dados mensais de janeiro de 1999 a setembro de 2014. Para cada modelo individual, foram geradas 142 previsões fora da amostra, 12 meses à frente, por meio de uma janela móvel de 36 meses. Nove combinações de modelos foram desenvolvidas para cada ajuste dos modelos individuais, resultando em 60 previsões fora da amostra, 12 meses à frente. A avaliação de desempenho preditivo dos modelos foi realizada por meio do MCS para os últimos 60, 48 e 36 meses. Um total de 1.250 estimações foram realizadas e 1.140 variáveis independentes e suas transformadas foram avaliadas. A combinação de previsões usando ARIMA e um ARMAX foi o único modelo que permaneceu no conjunto de modelos com melhor acuracidade de previsão para 36, 48 e 60 meses a um nível descritivo do MCS de 0,10. Para os últimos 36 meses, o modelo combinado proposto apresentou resultados superiores em relação a todos os demais modelos. Duas co-variáveis identificadas no modelo ARMAX, preço futuro de três meses e estoques mundiais, aumentaram a acuracidade de previsão. A combinação ótima apresentou um intervalo de confiança pequeno, equivalente a 5% da média global da amostra completa analisada, fornecendo subsídio importante para tomada de decisão na indústria global de alumínio. iii / Primary commodities, including metals, oil and agricultural products are key raw materials for the global economy. Among metals, aluminum stands out for its large use in several industrial applications and for holding the largest contract volume on the London Metal Exchange (LME). As the price is not directly related to production costs, during volatility periods or economic shocks, the financial impact on the global aluminum industry is significant. Aluminum price forecasting, therefore, is critical for industrial policy as well as for producers and consumers. This work has proposed an optimal forecast model for aluminum prices by using forecast combination and the Model Confidence Set for model selection, resulting in superior performance compared to tradicional methods. The proposed approach was not found in the literature for aluminum price forecasting. Five individual models were developed: AR(1) for benchmarking, ARIMA, two ARIMAX models and a structural model, using monthly data from January 1999 to September 2014. For each individual model, 142 out-of-sample, 12 month ahead, forecasts were generated through a 36 month rolling window. Nine foreast combinations were deveoped for each individual model estimation, resulting in 60 out-of-sample, 12 month ahead forecasts. Model predictive performace was assessed through the Model Confidence Set for the latest 36, 48, and 60 months, through 12-month ahead out-of-sample forecasts. A total of 1,250 estimations were performed and 1,140 independent variables and their transformations were assessed. The forecast combination using ARMA and ARIMAX was the only model among the best set of models presenting equivalent performance at 0.10 MCS p-value in all three periods. For the latest 36 months, the proposed combination was the best model at 0.1 MCS p-value. Two co-variantes, identified for the ARMAX model, namely, 3-month forward price and global inventories increased forecast accuracy. The optimal forecast combination has generated a small confidence interval, equivalent to 5% of average aluminum price for the entire sample, proving relevant support for global industry decision makers.

This dissertation comprises of three original contributions to empirical forecasting research. Chapter 1 introduces the dissertation. Chapter 2 contributes to the literature on hierarchical time series (HTS) modelling by proposing a disaggregated forecasting system for both inflation rate and its volatility. Using monthly data that underlies the Retail Prices Index for the UK, we analyse the dynamics of the inflation process. We examine patterns in the time-varying covariation among product-level inflation rates that aggregate up to industry-level inflation rates that in turn aggregate up to the overall inflation rate. The aggregate inflation volatility closely tracks the time path of this covariation, which is seen to be driven primarily by the variances of common shocks shared by all products, and by the covariances between idiosyncratic product-level shocks. We formulate a forecasting system that comprises of models for mean inflation rate and its variance, and exploit the index structure of the aggregate inflation rate using the HTS framework. Using a dynamic model selection approach to forecasting, we obtain forecasts that are between 9 and 155 % more accurate than a SARIMA-GARCH(1,1) for the aggregate inflation volatility. Chapter 3 is on improving forecasts using forecast combinations. The paper documents the software implementation of the open source R package for forecast combination that we coded and published on the official R package depository, CRAN. The GeomComb package is the only R package that covers a wide range of different popular forecast combination methods. We implement techniques from 3 broad categories: (a) simple non-parametric methods, (b) regression-based methods, and (c) geometric (eigenvector) methods, allowing for static or dynamic estimation of each approach. Using S3 classes/methods in R, the package provides a user-friendly environment for applied forecasting, implementing solutions for typical issues related to forecast combination (multicollinearity, missing values, etc.), criterion-based optimisation for several parametric methods, and post-fit functions to rationalise and visualise estimation results. The package has been listed in the official R Task Views for Time Series Analysis and for Official Statistics. The brief empirical application in the paper illustrates the package’s functionality by estimating forecast combination techniques for monthly UK electricity supply. Chapter 4 introduces HTS forecasting and forecast combination to a healthcare staffing context. A slowdown of healthcare budget growth in the UK that does not keep pace with growth of demand for hospital services made efficient cost planning increasingly crucial for hospitals, in particular for staff which accounts for more than half of hospitals’ expenses. This is facilitated by accurate forecasts of patient census and churn. Using a dataset of more than 3 million observations from a large UK hospital, we show how HTS forecasting can improve forecast accuracy by using information at different levels of the hospital hierarchy (aggregate, emergency/electives, divisions, specialties), compared to the naïve benchmark: the seasonal random walk model applied to the aggregate. We show that forecast combination can improve accuracy even more in some cases, and leads to lower forecast error variance (decreasing forecasting risk). We propose a comprehensive parametric approach to use forecasts in a nurse staffing model that has the aim of minimising cost while satisfying that the care requirements (e.g. nurse hours per patient day thresholds) are met.