Holt’s exponential smoothing and neural network models for forecasting interval-valued time series

Interval-valued time series are interval-valued data that are collected in a chronological sequence over time. This paper introduces three approaches to forecasting interval-valued time series. The first two approaches are based on multilayer perceptron (MLP) neural networks and Holt’s exponential smoothing methods, respectively. In Holt’s method for interval-valued time series, the smoothing parameters are estimated by using techniques for non-linear optimization problems with bound constraints. The third approach is based on a hybrid methodology that combines the MLP and Holt models. The practicality of the methods is demonstrated through simulation studies and applications using real interval-valued stock market time series.     

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.     

FFORMA: Feature-based forecast model averaging

We propose an automated method for obtaining weighted forecast combinations using time series features. The proposed approach involves two phases. First, we use a collection of time series to train a meta-model for assigning weights to various possible forecasting methods with the goal of minimizing the average forecasting loss obtained from a weighted forecast combination. The inputs to the meta-model are features that are extracted from each series. Then, in the second phase, we forecast new series using a weighted forecast combination, where the weights are obtained from our previously trained meta-model. Our method outperforms a simple forecast combination, as well as all of the most popular individual methods in the time series forecasting literature. The approach achieved second position in the M4 competition.     

Mixture of MLP-experts for trend forecasting of time series: A case study of the Tehran stock exchange

A new method for forecasting the trend of time series, based on mixture of MLP experts, is presented. In this paper, three neural network combining methods and an Adaptive Network-Based Fuzzy Inference System (ANFIS) are applied to trend forecasting in the Tehran stock exchange. There are two experiments in this study. In experiment I, the time series data are the Kharg petrochemical company’s daily closing prices on the Tehran stock exchange. In this case study, which considers different schemes for forecasting the trend of the time series, the recognition rates are 75.97%, 77.13% and 81.64% for stacked generalization, modified stacked generalization and ANFIS, respectively. Using the mixture of MLP experts (ME) scheme, the recognition rate is strongly increased to 86.35%. A gain and loss analysis is also used, showing the relative forecasting success of the ME method with and without rejection criteria, compared to a simple buy and hold approach. In experiment II, the time series data are the daily closing prices of 37 companies on the Tehran stock exchange. This experiment is conducted to verify the results of experiment I and to show the efficiency of the ME method compared to stacked generalization, modified stacked generalization and ANFIS.     

Forecasting the NN5 time series with hybrid models

We propose a simple way of predicting time series with recurring seasonal periods. Missing values of the time series are estimated and interpolated in a preprocessing step. We combine several forecasting methods by taking the weighted mean of forecasts that were generated with time-domain models which were validated on left-out parts of the time series. The hybrid model is a combination of a neural network ensemble, an ensemble of nearest trajectory models and a model for the 7-day cycle. We apply this approach to the NN5 time series competition data set.     

Are low-frequency data really uninformative? A forecasting combination perspective

In this study, we investigate whether low-frequency data improve volatility forecasting when high-frequency data are available. To answer this question, we utilize four forecast combination strategies that combine low-frequency and high-frequency volatility models and employ a rolling window and a range of loss functions in the framework of the novel Model Confidence Set test. Out-of-sample results show that combination forecasts with GARCH-class models can achieve high forecast accuracy. However, the combination forecast methods appear not to significantly outperform individual high-frequency volatility models. Furthermore, we find that models that combine low-frequency and high-frequency volatility yield significantly better performance than other models and combination forecast strategies in both a statistical and economic sense.     

Advances in forecasting with neural networks? Empirical evidence from the NN3 competition on time series prediction

This paper reports the results of the NN3 competition, which is a replication of the M3 competition with an extension of the competition towards neural network (NN) and computational intelligence (CI) methods, in order to assess what progress has been made in the 10 years since the M3 competition. Two masked subsets of the M3 monthly industry data, containing 111 and 11 empirical time series respectively, were chosen, controlling for multiple data conditions of time series length (short/long), data patterns (seasonal/non-seasonal) and forecasting horizons (short/medium/long). The relative forecasting accuracy was assessed using the metrics from the M3, together with later extensions of scaled measures, and non-parametric statistical tests. The NN3 competition attracted 59 submissions from NN, CI and statistics, making it the largest CI competition on time series data. Its main findings include: (a) only one NN outperformed the damped trend using the sMAPE, but more contenders outperformed the AutomatANN of the M3; (b) ensembles of CI approaches performed very well, better than combinations of statistical methods; (c) a novel, complex statistical method outperformed all statistical and CI benchmarks; and (d) for the most difficult subset of short and seasonal series, a methodology employing echo state neural networks outperformed all others. The NN3 results highlight the ability of NN to handle complex data, including short and seasonal time series, beyond prior expectations, and thus identify multiple avenues for future research.     

Correlated daily time series and forecasting in the M4 competition

We participated in the M4 competition for time series forecasting and here describe our methods for forecasting daily time series. We used an ensemble of five statistical forecasting methods and a method that we refer to as the correlator. Our retrospective analysis using the ground truth values published by the M4 organisers after the competition demonstrates that the correlator was responsible for most of our gains over the naïve constant forecasting method. We identify data leakage as one reason for its success, due partly to test data selected from different time intervals, and partly to quality issues with the original time series. We suggest that future forecasting competitions should provide actual dates for the time series so that some of these leakages could be avoided by participants.     

Improving forecasting by estimating time series structural components across multiple frequencies

Identifying the most appropriate time series model to achieve a good forecasting accuracy is a challenging task. We propose a novel algorithm that aims to mitigate the importance of model selection, while increasing the accuracy. Multiple time series are constructed from the original time series, using temporal aggregation. These derivative series highlight different aspects of the original data, as temporal aggregation helps in strengthening or attenuating the signals of different time series components. In each series, the appropriate exponential smoothing method is fitted and its respective time series components are forecast. Subsequently, the time series components from each aggregation level are combined, then used to construct the final forecast. This approach achieves a better estimation of the different time series components, through temporal aggregation, and reduces the importance of model selection through forecast combination. An empirical evaluation of the proposed framework demonstrates significant improvements in forecasting accuracy, especially for long-term forecasts.     

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.     

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.     

Tracking world trade and GDP in real time

This paper proposes a simple procedure for obtaining monthly assessments of short-run perspectives for quarterly world GDP and trade. It combines high-frequency information from emerging and advanced countries so as to explain quarterly national accounts variables through bridge models. The union of all bridge equations leads to our world bridge model (WBM). The WBM approach of this paper is new for two reasons: its equations combine traditional short-run bridging with theoretical level-relationships, and it is the first time that forecasts of world GDP and trade have been computed for both advanced and emerging countries on the basis of a real-time database of approximately 7000 time series. Although the performances of the equations that are searched automatically should be taken as a lower bound, our results show that the forecasting ability of the WBM is superior to the benchmark. Finally, our results confirm that the use of revised data leads to models’ forecasting performances being overstated significantly.     

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.     

Automatic feature identification and graphical support in rule-based forecasting: a comparison

We examined automatic feature identification and graphical support in rule-based expert systems for forecasting. The rule-based expert forecasting system (RBEFS) includes predefined rules to automatically identify features of a time series and selects the extrapolation method to be used. The system can also integrate managerial judgment using a graphical interface that allows a user to view alternate extrapolation methods two at a time. The use of the RBEFS led to a significant improvement in accuracy compared to equal-weight combinations of forecasts. Further improvement were achieved with the user interface. For 6-year ahead ex ante forecasts, the rule-based expert forecasting system has a median absolute percentage error (MdAPE) 15% less than that of equally weighted combined forecasts and a 33% improvement over the random walk. The user adjusted forecasts had a MdAPE 20% less than that of the expert system. The results of the system are also compared to those of an earlier rule-based expert system which required human judgments about some features of the time series data. The results of the comparison of the two rule-based expert systems showed no significant differences between them.     

Predicting relative forecasting performance: An empirical investigation

The relative performances of forecasting models change over time. This empirical observation raises two questions. First, is the relative performance itself predictable? Second, if so, can it be exploited in order to improve the forecast accuracy? We address these questions by evaluating the predictive abilities of a wide range of economic variables for two key US macroeconomic aggregates, namely industrial production and inflation, relative to simple benchmarks. We find that business cycle indicators, financial conditions, uncertainty and measures of past relative performances are generally useful for explaining the models’ relative forecasting performances. In addition, we conduct a pseudo-real-time forecasting exercise, where we use the information about the conditional performance for model selection and model averaging. The newly proposed strategies deliver sizable improvements over competitive benchmark models and commonly-used combination schemes. The gains are larger when model selection and averaging are based on both financial conditions and past performances measured at the forecast origin date.     

Forecasting small area populations with long short-term memory networks

Local and state governments depend on small area population forecasts to make important decisions concerning the development of local infrastructure and services. Despite their importance, current methods often produce highly inaccurate forecasts. Recent years have witnessed promising developments in time series forecasting using Machine Learning across a wide range of social and economic variables. However, limited work has been undertaken to investigate the potential application of Machine Learning methods in demography, particularly for small area population forecasting. In this paper we describe the development of two Long-Short Term Memory network architectures for small area populations. We employ the Keras Tuner to select layer unit numbers, vary the window width of input data, and apply a double training and validation regime which supports work with short time series and prioritises later sequence values for forecasts. These methods are transferable and can be applied to other data sets. Retrospective small area population forecasts for Australia were created for the periods 2006–16 and 2011–16. Model performance was evaluated against actual data and two benchmark methods (LIN/EXP and CSP-VSG). We also evaluated the impact of constraining small area population forecasts to an independent national forecast. Forecast accuracy was influenced by jump-off year, constraining, area size, and remoteness. The LIN/EXP model was the best performing method for the 2011-based forecasts whilst deep learning methods performed best for the 2006-based forecasts, including significant improvements in the accuracy of 10 year forecasts. However, benchmark methods were consistently more accurate for more remote areas and for those with populations <5000.     

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.     

Beyond point forecasting: Evaluation of alternative prediction intervals for tourist arrivals

This paper evaluates the performances of prediction intervals generated from alternative time series models, in the context of tourism forecasting. The forecasting methods considered include the autoregressive (AR) model, the AR model using the bias-corrected bootstrap, seasonal ARIMA models, innovations state space models for exponential smoothing, and Harvey’s structural time series models. We use thirteen monthly time series for the number of tourist arrivals to Hong Kong and Australia. The mean coverage rates and widths of the alternative prediction intervals are evaluated in an empirical setting. It is found that all models produce satisfactory prediction intervals, except for the autoregressive model. In particular, those based on the bias-corrected bootstrap perform best in general, providing tight intervals with accurate coverage rates, especially when the forecast horizon is long.