The tourism forecasting competition

We evaluate the performances of various methods for forecasting tourism data. The data used include 366 monthly series, 427 quarterly series and 518 annual series, all supplied to us by either tourism bodies or academics who had used them in previous tourism forecasting studies. The forecasting methods implemented in the competition are univariate and multivariate time series approaches, and econometric models. This forecasting competition differs from previous competitions in several ways: (i) we concentrate on tourism data only; (ii) we include approaches with explanatory variables; (iii) we evaluate the forecast interval coverage as well as the point forecast accuracy; (iv) we observe the effect of temporal aggregation on the forecasting accuracy; and (v) we consider the mean absolute scaled error as an alternative forecasting accuracy measure. We find that pure time series approaches provide more accurate forecasts for tourism data than models with explanatory variables. For seasonal data we implement three fully automated pure time series algorithms that generate accurate point forecasts, and two of these also produce forecast coverage probabilities which are satisfactorily close to the nominal rates. For annual data we find that Naïve forecasts are hard to beat.     

Forecasting spare part demand with installed base information: A review

The classical spare part demand forecasting literature studies methods for forecasting intermittent demand. However, the majority of these methods do not consider the underlying demand-generating factors. The demand for spare parts originates from the replacement of parts in the installed base of machines, either preventively or upon breakdown of the part. This information from service operations, which we refer to as installed base information, can be used to forecast the future demand for spare parts. This paper reviews the literature on the use of such installed base information for spare part demand forecasting in order to asses (1) what type of installed base information can be useful; (2) how this information can be used to derive forecasts; (3) the value of using installed base information to improve forecasting; and (4) the limits of the existing methods. This serves as motivation for future research.     

Forecasting television ratings

Despite the state of flux in media today, television remains the dominant player globally for advertising spending. Since television advertising time is purchased on the basis of projected future ratings, and ad costs have skyrocketed, there is increasingly pressure to forecast television ratings accurately. The forecasting methods that have been used in the past are not generally very reliable, and many have not been validated; also, even more distressingly, none have been tested in today’s multichannel environment. In this study we compare eight different forecasting models, ranging from a naïve empirical method to a state-of-the-art Bayesian model-averaging method. Our data come from a recent time period, namely 2004-2008, in a market with over 70 channels, making the data more typical of today’s viewing environment. The simple models that are commonly used in industry do not forecast as well as any econometric models. Furthermore, time series methods are not applicable, as many programs are broadcast only once. However, we find that a relatively straightforward random effects regression model often performs as well as more sophisticated Bayesian models in out-of-sample forecasting. Finally, we demonstrate that making improvements in ratings forecasts could save the television industry between $250 and $586 million per year.     

Applications of machine learning for corporate bond yield spread forecasting

This article considers nine different predictive techniques, including state-of-the-art machine learning methods for forecasting corporate bond yield spreads with other input variables. We examine each method’s out-of-sample forecasting performance using two different forecast horizons: (1) the in-sample dataset over 2003–2007 is used for one-year-ahead and two-year-ahead forecasts of non-callable corporate bond yield spreads; and (2) the in-sample dataset over 2003–2008 is considered to forecast the yield spreads in 2009. Evaluations of forecasting accuracy have shown that neural network forecasts are superior to the other methods considered here in both the short and longer horizon. Furthermore, we visualize the determinants of yield spreads and find that a firm’s equity volatility is a critical factor in yield spreads.     

A disaster response model driven by spatial–temporal forecasts

In this research, we propose a disaster response model combining preparedness and responsiveness strategies. The selective response depends on the level of accuracy that our forecasting models can achieve. In order to decide the right geographical space and time window of response, forecasts are prepared and assessed through a spatial–temporal aggregation framework, until we find the optimum level of aggregation. The research considers major earthquake data for the period 1985–2014. Building on the produced forecasts, we develop accordingly a disaster response model. The model is dynamic in nature, as it is updated every time a new event is added in the database. Any forecasting model can be optimized though the proposed spatial–temporal forecasting framework, and as such our results can be easily generalized. This is true for other forecasting methods and in other disaster response contexts.     

Large time-varying parameter VARs

In this paper, we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints, we draw on ideas from the dynamic model averaging literature which achieve reductions in the computational burden through the use forgetting factors. We then extend the TVP-VAR so that its dimension can change over time. For instance, we can have a large TVP-VAR as the forecasting model at some points in time, but a smaller TVP-VAR at others. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting factor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output and interest rates demonstrates the feasibility and usefulness of our approach.     

Parameter-efficient deep probabilistic forecasting

Probabilistic time series forecasting is crucial in many application domains, such as retail, ecommerce, finance, and biology. With the increasing availability of large volumes of data, a number of neural architectures have been proposed for this problem. In particular, Transformer-based methods achieve state-of-the-art performance on real-world benchmarks. However, these methods require a large number of parameters to be learned, which imposes high memory requirements on the computational resources for training such models. To address this problem, we introduce a novel bidirectional temporal convolutional network that requires an order of magnitude fewer parameters than a common Transformer-based approach. Our model combines two temporal convolutional networks: the first network encodes future covariates of the time series, whereas the second network encodes past observations and covariates. We jointly estimate the parameters of an output distribution via these two networks. Experiments on four real-world datasets show that our method performs on par with four state-of-the-art probabilistic forecasting methods, including a Transformer-based approach and WaveNet, on two point metrics (sMAPE and NRMSE) as well as on a set of range metrics (quantile loss percentiles) in the majority of cases. We also demonstrate that our method requires significantly fewer parameters than Transformer-based methods, which means that the model can be trained faster with significantly lower memory requirements, which as a consequence reduces the infrastructure cost for deploying these models.     

Relative performance of judgmental methods for forecasting the success of megaprojects

Forecasting the success of megaprojects, such as the Olympic Games or space exploration missions, is a very difficult but important task, due to their complexity and the large capital investment they require. Typically, megaproject stakeholders do not employ formal forecasting methods, but instead rely on impact assessments and/or cost–benefit analysis; however, as these tools do not necessarily include forecasts, there is no accountability. This study evaluates the effectiveness of judgmental methods for successfully forecasting the accomplishment of specific megaproject objectives, where the measure of success is the collective accomplishment of such objectives. We compare the performances of three judgmental methods used by a group of 69 semi-experts: unaided judgement (UJ), semi-structured analogies (s-SA), and interaction groups (IG). The empirical evidence reveals that the use of s-SA leads to accuracy improvements relative to UJ. These improvements are amplified further when we introduce the pooling of analogies through teamwork in IG.     

FRED-SD: A real-time database for state-level data with forecasting applications

We construct a real-time dataset (FRED-SD) with vintage data for the U.S. states that can be used to forecast both state-level and national-level variables. Our dataset includes approximately 28 variables per state, including labor-market, production, and housing variables. We conduct two sets of real-time forecasting exercises. The first forecasts state-level labor-market variables using five different models and different levels of industrially disaggregated data. The second forecasts a national-level variable exploiting the cross-section of state data. The state-forecasting experiments suggest that large models with industrially disaggregated data tend to have higher predictive ability for industrially diversified states. For national-level data, we find that forecasting and aggregating state-level data can outperform a random walk but not an autoregression. We compare these real-time data experiments with forecasting experiments using final-vintage data and find very different results. Because these final-vintage results are obtained with revised data that would not have been available at the time the forecasts would have been made, we conclude that the use of real-time data is essential for drawing proper conclusions about state-level forecasting models.     

Robustness and the general dynamic factor model with infinite-dimensional space: Identification,estimation, and forecasting

General dynamic factor models have demonstrated their capacity to circumvent the curse of dimensionality in the analysis of high-dimensional time series and have been successfully considered in many economic and financial applications. As second-order models, however, they are sensitive to the presence of outliers—an issue that has not been analyzed so far in the general case of dynamic factors with possibly infinite-dimensional factor spaces (Forni et al. 2000, 2015, 2017). In this paper, we consider this robustness issue and study the impact of additive outliers on the identification, estimation, and forecasting performance of general dynamic factor models. Based on our findings, we propose robust versions of identification, estimation, and forecasting procedures. The finite-sample performance of our methods is evaluated via Monte Carlo experiments and successfully applied to a classical data set of 115 US macroeconomic and financial time series.     

Financial nowcasts and their usefulness in macroeconomic forecasting

Financial data often contain information that is helpful for macroeconomic forecasting, while multi-step forecast accuracy benefits from incorporating good nowcasts of macroeconomic variables. This paper considers the usefulness of financial nowcasts for making conditional forecasts of macroeconomic variables with quarterly Bayesian vector autoregressions (BVARs). When nowcasting quarterly financial variables’ values, we find that taking the average of the available daily data and a daily random walk forecast to complete the quarter typically outperforms other nowcasting approaches. Using real-time data, we find gains in out-of-sample forecast accuracy from the inclusion of financial nowcasts relative to unconditional forecasts, with further gains from the incorporation of nowcasts of macroeconomic variables. Conditional forecasts from quarterly BVARs augmented with financial nowcasts rival the forecast accuracy of mixed-frequency dynamic factor models and mixed-data sampling (MIDAS) models.     

The probability conflation: A reply to Tetlock et al.

We respond to Tetlock et al. (2022) showing (1) how expert judgment fails to reflect tail risk and (2) the lack of compatibility between forecasting tournaments and tail-risk assessment methods (such as extreme value theory). More importantly, we communicate a new result showing a greater gap between the properties of tail expectation and those of the corresponding probability.     

Transfer learning for hierarchical forecasting: Reducing computational efforts of M5 winning methods

The winning machine learning methods of the M5 Accuracy competition demonstrated high levels of forecast accuracy compared to the top-performing benchmarks in the history of the M-competitions. Yet, large-scale adoption is hampered due to the significant computational requirements to model, tune, and train these state-of-the-art algorithms. To overcome this major issue, we discuss the potential of transfer learning (TL) to reduce the computational effort in hierarchical forecasting and provide a proof of concept that TL can be applied on M5 top-performing methods. We demonstrate our easy-to-use TL framework on the recursive store-level LightGBM models of the M5 winning method and attain similar levels of forecast accuracy with roughly 25% less training time. Our findings provide evidence for a novel application of TL to facilitate the practical applicability of the M5 winning methods in large-scale settings with hierarchically structured data.     

Forecasting national activity using lots of international predictors: An application to New Zealand

We assess the marginal predictive content of a large international dataset for forecasting GDP in New Zealand, an archetypal small open economy. We apply “data-rich” factor and shrinkage methods to efficiently handle hundreds of predictor series from many countries. The methods covered are principal components, targeted predictors, weighted principal components, partial least squares, elastic net and ridge regression. We find that exploiting a large international dataset can improve forecasts relative to data-rich approaches based on a large national dataset only, and also relative to more traditional approaches based on small datasets. This is in spite of New Zealand’s business and consumer confidence and expectations data capturing a substantial proportion of the predictive information in the international data. The largest forecasting accuracy gains from including international predictors are at longer forecast horizons. The forecasting performance achievable with the data-rich methods differs widely, with shrinkage methods and partial least squares performing best in handling the international data.     

Forecasting the M4 competition weekly data: Forecast Pro’s winning approach

Forecast Pro forecasted the weekly series in the M4 competition more accurately than all other entrants. Our approach was to follow the same forecasting process that we recommend to our users. This approach involves determining the Key Performance Metric (KPI), establishing baseline forecasts using our automated expert selection algorithm, reviewing those baseline forecasts and customizing forecasts where needed. This article explores why this approach worked well for weekly data, discusses the applicability of the M4 competition to business forecasting and proposes some potential improvements for future competitions to make them more relevant to business forecasting.     

Damping seasonal factors: Shrinkage estimators for the X-12-ARIMA program

We examine the effect of damping X-12-ARIMA's estimated seasonal variation on the accuracy of its seasonal adjustments of time series. Two methods for damping seasonals are proposed. In a simulation experiment, we generated time series data for each of 90 distinct experimental conditions that, in aggregate, characterize the variety of monthly series in the M3-competition. X-12-ARIMA consistently overestimated the actual seasonal variation by an amount consistent with statistical theory. Damping seasonals reduced X-12-ARIMA's estimation error by as much as 79% and under no conditions was estimation error increased beyond a trivial amount. Improvement depended primarily on the degree to which random variation in a series dominated seasonal variation. When the multiplicative X-12-ARIMA model did not match the data-generating model, overestimation was less for trend series than for series with no trend; otherwise the presence of trend had no discernible effect. One of the proposed methods was somewhat more accurate and robust, but more complex, than the other. In an analysis of real data—the 1428 monthly series of the M3-competition-damping X-12-ARIMA seasonals prior to forecasting (1) reduced the average forecasting MAPE by 4.9–1.4% and (2) improved forecasting accuracy for 59–65% of the series, depending on the forecasting horizon. This research suggests that damping X-12-ARIMA seasonals leads to more accurate seasonal adjustments of time series, thus providing a more reliable basis for policy-making, forecasting, and the evaluation of forecasting methods by researchers.     

Out-of-sample forecasts of China's economic growth and inflation using rolling weighted least squares

Macroeconomic forecasting in China is essential for the government to take proper policy decisions on government expenditure and money supply, among other matters. The existing literature on forecasting Chinas macroeconomic variables is unclear on the crucial issue of how to choose an optimal window to estimate parameters with rolling out-of-sample forecasts. This study fills this gap in forecasting economic growth and inflation in China, by using the rolling weighted least squares (WLS) with the practically feasible cross-validation (CV) procedure of Hong et al. (2018) to choose an optimal estimation window. We undertake an empirical analysis of monthly data on up to 30 candidate indicators (mainly asset prices) for a span of 17 years (2000–2017). It is documented that the forecasting performance of rolling estimation is sensitive to the selection of rolling windows. The empirical analysis shows that the rolling WLS with the CV-based rolling window outperforms other rolling methods on univariate regressions in most cases. One possible explanation for this is that these macroeconomic variables often suffer from structural changes due to changes in institutional reforms, policies, crises, and other factors. Furthermore, we find that, in most cases, asset prices are key variables for forecasting macroeconomic variables, especially output growth rate.     

How useful are no-arbitrage restrictions for forecasting the term structure of interest rates?

We develop a general framework for analyzing the usefulness of imposing parameter restrictions on a forecasting model. We propose a measure of the usefulness of the restrictions that depends on the forecaster’s loss function and that could be time varying. We show how to conduct inference about this measure. The application of our methodology to analyzing the usefulness of no-arbitrage restrictions for forecasting the term structure of interest rates reveals that: (1) the restrictions have become less useful over time; (2) when using a statistical measure of accuracy, the restrictions are a useful way to reduce parameter estimation uncertainty, but are dominated by restrictions that do the same without using any theory; (3) when using an economic measure of accuracy, the no-arbitrage restrictions are no longer dominated by atheoretical restrictions, but for this to be true it is important that the restrictions incorporate a time-varying risk premium.     

DeepAR: Probabilistic forecasting with autoregressive recurrent networks

Probabilistic forecasting, i.e., estimating a time series’ future probability distribution given its past, is a key enabler for optimizing business processes. In retail businesses, for example, probabilistic demand forecasts are crucial for having the right inventory available at the right time and in the right place. This paper proposes DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an autoregressive recurrent neural network model on a large number of related time series. We demonstrate how the application of deep learning techniques to forecasting can overcome many of the challenges that are faced by widely-used classical approaches to the problem. By means of extensive empirical evaluations on several real-world forecasting datasets, we show that our methodology produces more accurate forecasts than other state-of-the-art methods, while requiring minimal manual work.