fETSmcs: Feature-based ETS model component selection

The well-developed ETS (ExponenTial Smoothing, or Error, Trend, Seasonality) method incorporates a family of exponential smoothing models in state space representation and is widely used for automatic forecasting. The existing ETS method uses information criteria for model selection by choosing an optimal model with the smallest information criterion among all models fitted to a given time series. The ETS method under such a model selection scheme suffers from computational complexity when applied to large-scale time series data. To tackle this issue, we propose an efficient approach to ETS model selection by training classifiers on simulated data to predict appropriate model component forms for a given time series. We provide a simulation study to show the model selection ability of the proposed approach on simulated data. We evaluate our approach on the widely used M4 forecasting competition dataset in terms of both point forecasts and prediction intervals. To demonstrate the practical value of our method, we showcase the performance improvements from our approach on a monthly hospital dataset.     

FFORMPP: Feature-based forecast model performance prediction

This paper introduces a novel meta-learning algorithm for time series forecast model performance prediction. We model the forecast error as a function of time series features calculated from historical time series with an efficient Bayesian multivariate surface regression approach. The minimum predicted forecast error is then used to identify an individual model or a combination of models to produce the final forecasts. It is well known that the performance of most meta-learning models depends on the representativeness of the reference dataset used for training. In such circumstances, we augment the reference dataset with a feature-based time series simulation approach, namely GRATIS, to generate a rich and representative time series collection. The proposed framework is tested using the M4 competition data and is compared against commonly used forecasting approaches. Our approach provides comparable performance to other model selection and combination approaches but at a lower computational cost and a higher degree of interpretability, which is important for supporting decisions. We also provide useful insights regarding which forecasting models are expected to work better for particular types of time series, the intrinsic mechanisms of the meta-learners, and how the forecasting performance is affected by various factors.     

Distributed ARIMA models for ultra-long time series

Providing forecasts for ultra-long time series plays a vital role in various activities, such as investment decisions, industrial production arrangements, and farm management. This paper develops a novel distributed forecasting framework to tackle the challenges of forecasting ultra-long time series using the industry-standard MapReduce framework. The proposed model combination approach retains the local time dependency. It utilizes a straightforward splitting across samples to facilitate distributed forecasting by combining the local estimators of time series models delivered from worker nodes and minimizing a global loss function. Instead of unrealistically assuming the data generating process (DGP) of an ultra-long time series stays invariant, we only make assumptions on the DGP of subseries spanning shorter time periods. We investigate the performance of the proposed approach with AutoRegressive Integrated Moving Average (ARIMA) models using the real data application as well as numerical simulations. Our approach improves forecasting accuracy and computational efficiency in point forecasts and prediction intervals, especially for longer forecast horizons, compared to directly fitting the whole data with ARIMA models. Moreover, we explore some potential factors that may affect the forecasting performance of our approach.     

Validation and forecasting accuracy in models of climate change

Forecasting researchers, with few exceptions, have ignored the current major forecasting controversy: global warming and the role of climate modelling in resolving this challenging topic. In this paper, we take a forecaster’s perspective in reviewing established principles for validating the atmospheric-ocean general circulation models (AOGCMs) used in most climate forecasting, and in particular by the Intergovernmental Panel on Climate Change (IPCC). Such models should reproduce the behaviours characterising key model outputs, such as global and regional temperature changes. We develop various time series models and compare them with forecasts based on one well-established AOGCM from the UK Hadley Centre. Time series models perform strongly, and structural deficiencies in the AOGCM forecasts are identified using encompassing tests. Regional forecasts from various GCMs had even more deficiencies. We conclude that combining standard time series methods with the structure of AOGCMs may result in a higher forecasting accuracy. The methodology described here has implications for improving AOGCMs and for the effectiveness of environmental control policies which are focussed on carbon dioxide emissions alone. Critically, the forecast accuracy in decadal prediction has important consequences for environmental planning, so its improvement through this multiple modelling approach should be a priority.     

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.     

When was the U.S. housing downturn predictable? A comparison of univariate forecasting methods

This paper uses three classes of univariate time series techniques (ARIMA type models, switching regression models, and state-space/structural time series models) to forecast, on an ex post basis, the downturn in U.S. housing prices starting around 2006. The performance of the techniques is compared within each class and across classes by out-of-sample forecasts for a number of different forecast points prior to and during the downturn. Most forecasting models are able to predict a downturn in future home prices by mid 2006. Some state-space models can predict an impending downturn as early as June 2005. State-space/structural time series models tend to produce the most accurate forecasts, although they are not necessarily the models with the best in-sample fit.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates

It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance. We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regime-switching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.     

An accurate and fully-automated ensemble model for weekly time series forecasting

Many businesses and industries require accurate forecasts for weekly time series nowadays. However, the forecasting literature does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task. We propose a forecasting method in this domain to fill this gap, leveraging state-of-the-art forecasting techniques, such as forecast combination, meta-learning, and global modelling. We consider different meta-learning architectures, algorithms, and base model pools. Based on all considered model variants, we propose to use a stacking approach with lasso regression which optimally combines the forecasts of four base models: a global Recurrent Neural Network (RNN) model, Theta, Trigonometric Box–Cox ARMA Trend Seasonal (TBATS), and Dynamic Harmonic Regression ARIMA (DHR-ARIMA), as it shows the overall best performance across seven experimental weekly datasets on four evaluation metrics. Our proposed method also consistently outperforms a set of benchmarks and state-of-the-art weekly forecasting models by a considerable margin with statistical significance. Our method can produce the most accurate forecasts, in terms of mean sMAPE, for the M4 weekly dataset among all benchmarks and all original competition participants.     

Online hierarchical forecasting for power consumption data

This paper proposes a three-step approach to forecasting time series of electricity consumption at different levels of household aggregation. These series are linked by hierarchical constraints—global consumption is the sum of regional consumption, for example. First, benchmark forecasts are generated for all series using generalized additive models. Second, for each series, the aggregation algorithm ML-Poly, introduced by Gaillard, Stoltz, and van Erven in 2014, finds an optimal linear combination of the benchmarks. Finally, the forecasts are projected onto a coherent subspace to ensure that the final forecasts satisfy the hierarchical constraints. By minimizing a regret criterion, we show that the aggregation and projection steps improve the root mean square error of the forecasts. Our approach is tested on household electricity consumption data; experimental results suggest that successive aggregation and projection steps improve the benchmark forecasts at different levels of household aggregation.     

A copula-based time series model for global horizontal irradiation

The increasing importance of solar power for electricity generation leads to increasing demand for probabilistic forecasting of local and aggregated photovoltaic (PV) yields. Based on publicly available irradiation data, this paper uses an indirect modeling approach for hourly medium to long-term local PV yields. We suggest a time series model for global horizontal irradiation that allows for multivariate probabilistic forecasts for arbitrary time horizons. It features several important stylized facts. Sharp time-dependent lower and upper bounds of global horizontal irradiations are estimated. The parameters of the beta distributed marginals of the transformed data are allowed to be time-dependent. A copula-based time series model is introduced for the hourly and daily dependence structure based on simple vine copulas with so-called tail dependence. Evaluation methods based on scoring rules are used to compare the model’s power for multivariate probabilistic forecasting with other models used in the literature showing that our model outperforms other models in many respects.     

Seasonal exponential smoothing with damped trends : An application for production planning

This paper reviews a spreadsheet-based forecasting approach which a process industry manufacturer developed and implemented to link annual corporate forecasts with its manufacturing/distribution operations. First, we consider how this forecasting system supports overall production planning and why it must be compatible with corporate forecasts. We then review the results of substantial testing of variations on the Winters three-parameter exponential smoothing model on 28 actual product family time series. In particular, we evaluate whether the use of damping parameters improves forecast accuracy. The paper concludes that a Winters four-parameter model (i.e. the standard Winters three-parameter model augmented by a fourth parameter to damp the trend) provides the most accurate forecasts of the models evaluated. Our application confirms the fact that there are situations where the use of damped trend parameters in short-run exponential smoothing based forecasting models is beneficial.     

Probabilistic electricity price forecasting with NARX networks: Combine point or probabilistic forecasts?

Recent electricity price forecasting studies have shown that decomposing a series of spot prices into a long-term trend-seasonal and a stochastic component, modeling them independently and then combining their forecasts, can yield more accurate point predictions than an approach in which the same regression or neural network model is calibrated to the prices themselves. Here, considering two novel extensions of this concept to probabilistic forecasting, we find that (i) efficiently calibrated non-linear autoregressive with exogenous variables (NARX) networks can outperform their autoregressive counterparts, even without combining forecasts from many runs, and that (ii) in terms of accuracy it is better to construct probabilistic forecasts directly from point predictions. However, if speed is a critical issue, running quantile regression on combined point forecasts (i.e., committee machines) may be an option worth considering. Finally, we confirm an earlier observation that averaging probabilities outperforms averaging quantiles when combining predictive distributions in electricity price forecasting.     

Combination of long term and short term forecasts, with application to tourism demand forecasting

Forecast combination is a well-established and well-tested approach for improving the forecasting accuracy. One beneficial strategy is to use constituent forecasts that have diverse information. In this paper we consider the idea of diversity being accomplished by using different time aggregations. For example, we could create a yearly time series from a monthly time series and produce forecasts for both, then combine the forecasts. These forecasts would each be tracking the dynamics of different time scales, and would therefore add diverse types of information. A comparison of several forecast combination methods, performed in the context of this setup, shows that this is indeed a beneficial strategy and generally provides a forecasting performance that is better than the performances of the individual forecasts that are combined.As a case study, we consider the problem of forecasting monthly tourism numbers for inbound tourism to Egypt. Specifically, we consider 33 individual source countries, as well as the aggregate. The novel combination strategy also produces a generally improved forecasting accuracy.     

Fast and accurate yearly time series forecasting with forecast combinations

It has long been known that combination forecasting strategies produce superior out-of-sample forecasting performances. In the M4 forecasting competition, a very simple forecast combination strategy achieved third place on yearly time series. An analysis of the ensemble model and its component models suggests that the competitive accuracy comes from avoiding poor forecasts, rather than from beating the best individual models. Moreover, the simple ensemble model can be fitted very quickly, can easily scale horizontally with additional CPU cores or a cluster of computers, and can be implemented by users very quickly and easily. This approach might be of particular interest to users who need accurate yearly forecasts without being able to spend significant time, resources, or expertise on tuning models. Users of the R statistical programming language can access this modeling approach using the “forecastHybrid” package.     

Bagged neural networks for forecasting Polish (low) inflation

Accurate inflation forecasts lie at the heart of effective monetary policy. This paper utilizes a thick modelling approach in order to investigate the quality of the out-of-sample short-term headline inflation forecasts generated by a combination of bagged single hidden-layer feed-forward artificial neural networks. The model’s accuracy rises during the period of consistently falling and persistently low inflation in the emerging economy of Poland, and it statistically outperforms some of the popular benchmarks more frequently, especially at longer horizons. However, dispensing with data preprocessing and bootstrap aggregation compromises its forecasting ability severely. Combining linear and non-linear univariate and multivariate approaches with diverse underlying model assumptions delivers further gains in predictive accuracy and statistically outperforms a panel of benchmarks in a number of cases. While the vague interpretability of the model poses a considerable hurdle for policy makers, its inclusion in the forecasting toolbox should increase the accuracy of the ensemble of models, especially in periods of structural change.     

Forecasting volatility via stock return,range, trading volume and spillover effects: The case of Brazil

For the purpose of developing alternative approach for forecasting volatility, we consider heterogeneous VAR (HVAR) model which accommodates the market effects of different horizons, namely, daily, weekly and monthly effects, and examine the interdependence of stock markets in Brazil and the US, based on information of daily return, range and trading volume. To compare with the new approach, we also work with the univariate and multivariate GARCH models with asymmetric effects, trading volumes and fat-tails. The heteroskedasticity-corrected Granger causality tests based on the HVAR show the strong evidence of such spillover effects. We assess the value-at-risk thresholds for Brazil, based on the out-of-sample forecasts of the HVAR model, finding the new approach works satisfactory for the periods including the global financial crisis, without assuming heavy-tailed conditional distributions.     

Subjective evaluation of composite econometric policy inputs

Studies have suggested that a composite forecast may be preferred to a single forecast. In addition, forecasting objectives are often conflicting. For example, one forecast may have the smallest sum of absolute forecast errors, while another has the smallest maximum absolute error. This paper examines the appropriateness of using multiple objective linear programming to determine weighted linear combinations of forecasts to be used as inputs for policy analysis. An example is presented where the methodology is used to combine the forecasts for several policy variables. The forecasts are selected from large econometric, consensus, and univariate time series models.     

Experience curve models in the electricity supply industry

There has been much controversy over the use of the Experience Curve for forecasting purposes. The Experience Curve model has been criticised both on theoretical grounds and because of the practical problems of using it. An alternative model of experience effects due to Towill has certain attractions from the standpoint of theory. However, a rather deeper question is whether experience curve type models produce superior forecasts to those derived using extrapolative techniques.This paper examines these questions in the context of three time series taken from the electricity supply industry, viz: average thermal efficiency; works costs; and price of electricity. The two latter series require price deflation. Both the implied GDP consumption deflator, and a wholesale price index for fuel and electricity were used for this purpose. It is argued that because of the absence of substitutes and of the effects of competition, along with the high quality of data available on the electricity supply industry, these three series provide a favourable test of the experience curve approach to forecasting. The two experience curves performed on the whole markedly worse than the simpler extrapolative methods on the two financial series examined. For the average thermal efficiency series the Towill model and the Experience Curve model marginally outperformed the extrapolative methods.Overall, there was little support for using either the Experience Curve or Towill models. These are obviously more difficult to use than simple univariate models and do not provide significantly better forecasts. Moreover, the Towill model gave rise to considerable estimation and specification problems with the data used here.     

Improving forecast stability using deep learning

In this paper, we define forecast (in)stability in terms of the variability in forecasts for a specific time period caused by updating the forecast for this time period when new observations become available, i.e., as time passes. We propose an extension to the state-of-the-art N-BEATS deep learning architecture for the univariate time series point forecasting problem. The extension allows us to optimize forecasts from both a traditional forecast accuracy perspective as well as a forecast stability perspective. We show that the proposed extension results in forecasts that are more stable without leading to a deterioration in forecast accuracy for the M3 and M4 data sets. Moreover, our experimental study shows that it is possible to improve both forecast accuracy and stability compared to the original N-BEATS architecture, indicating that including a forecast instability component in the loss function can be used as regularization mechanism.