Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition

In this work we introduce the forecasting model with which we participated in the NN5 forecasting competition (the forecasting of 111 time series representing daily cash withdrawal amounts at ATM machines). The main idea of this model is to utilize the concept of forecast combination, which has proven to be an effective methodology in the forecasting literature. In the proposed system we attempted to follow a principled approach, and make use of some of the guidelines and concepts that are known in the forecasting literature to lead to superior performance. For example, we considered various previous comparison studies and time series competitions as guidance in determining which individual forecasting models to test (for possible inclusion in the forecast combination system). The final model ended up consisting of neural networks, Gaussian process regression, and linear models, combined by simple average. We also paid extra attention to the seasonality aspect, decomposing the seasonality into weekly (which is the strongest one), day of the month, and month of the year seasonality.     

Sensitivity to autocorrelation in judgmental time series forecasting

How well can people use autocorrelation information when making judgmental forecasts? In Experiment 1, participants forecast from 12 series in which the autocorrelation varied within subjects. The participants showed a sensitivity to the degree of autocorrelation. However, their forecasts indicated that they implicitly assumed positive autocorrelation in uncorrelated time series. Experiments 2 and 2a used a one-shot single-trial between-subjects design and obtained similar results. Experiment 3 investigated the way in which the between-trials context influenced forecasting. The results showed that forecasts are affected by the characteristics of previous series, as well as those of the series from which forecasts are to be made. Our findings can be accommodated within an adaptive approach. Forecasters base their initial expectations of series characteristics on their past experience and modify these expectations in a pseudo-Bayesian manner on the basis of their analysis of those characteristics in the series to be forecast.     

The asymmetry of judgemental confidence intervals in time series forecasting

In forecasting a time series, one may be asked to communicate the likely distribution of the future actual value, often expressed as a confidence interval. Whilst the accuracy (calibration) of these intervals has dominated most studies to date, this paper is concerned with other possible characteristics of the intervals. It reports a study in which the prevalence and determinants of the symmetry of judgemental confidence intervals in time series forecasting was examined. Most prior work has assumed that this interval is symmetrically placed around the forecast. However, this study shows that people generally estimate asymmetric confidence intervals where the forecast is not the midpoint of the estimated interval. Many of these intervals are grossly asymmetric. Results indicate that the placement of the forecast in relation to the last actual value of a time series is a major determinant of the direction and size of the asymmetry.     

MLP ensembles improve long term prediction accuracy over single networks

This work describes an award winning approach for solving the NN3 Forecasting Competition problem, focusing on the sound experimental validation of its main innovative feature. The NN3 forecasting task consisted of predicting 18 future values of 111 short monthly time series. The main feature of the approach was the use of the median for combining the forecasts of an ensemble of 15 MLPs to predict each time series. Experimental comparison to a single MLP shows that the ensemble increases the performance accuracy for multiple-step ahead forecasting. This system performed well on the withheld data, having finished as the second best solution of the competition with an SMAPE of 16.17%.     

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.     

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.     

Kaggle forecasting competitions: An overlooked learning opportunity

We review the results of six forecasting competitions based on the online data science platform Kaggle, which have been largely overlooked by the forecasting community. In contrast to the M competitions, the competitions reviewed in this study feature daily and weekly time series with exogenous variables, business hierarchy information, or both. Furthermore, the Kaggle data sets all exhibit higher entropy than the M3 and M4 competitions, and they are intermittent.In this review, we confirm the conclusion of the M4 competition that ensemble models using cross-learning tend to outperform local time series models and that gradient boosted decision trees and neural networks are strong forecast methods. Moreover, we present insights regarding the use of external information and validation strategies, and discuss the impacts of data characteristics on the choice of statistics or machine learning methods. Based on these insights, we construct nine ex-ante hypotheses for the outcome of the M5 competition to allow empirical validation of our findings.     

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.     

The theta model: a decomposition approach to forecasting

This paper presents a new univariate forecasting method. The method is based on the concept of modifying the local curvature of the time-series through a coefficient ‘Theta’ (the Greek letter θ), that is applied directly to the second differences of the data. The resulting series that are created maintain the mean and the slope of the original data but not their curvatures. These new time series are named Theta-lines. Their primary qualitative characteristic is the improvement of the approximation of the long-term behavior of the data or the augmentation of the short-term features, depending on the value of the Theta coefficient. The proposed method decomposes the original time series into two or more different Theta-lines. These are extrapolated separately and the subsequent forecasts are combined. The simple combination of two Theta-lines, the Theta=0 (straight line) and Theta=2 (double local curves) was adopted in order to produce forecasts for the 3003 series of the M3 competition. The method performed well, particularly for monthly series and for microeconomic data.     

Consistent estimation of a general nonparametric regression function in time series

We propose an estimator of the conditional distribution of X_t|X_t−1,X_t−2,…, and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.     

Model selection in univariate time series forecasting using discriminant analysis

When a large number of time series are to be forecast on a regular basis, as in large scale inventory management or production control, the appropriate choice of a forecast model is important as it has the potential for large cost savings through improved accuracy. A possible solution to this problem is to select one best forecast model for all the series in the dataset. Alternatively one may develop a rule that will select the best model for each series. Fildes (1989) calls the former an aggregate selection rule and the latter an individual selection rule. In this paper we develop an individual selection rule using discriminant analysis and compare its performance to aggregate selection for the quarterly series of the M-Competition data. A number of forecast accuracy measures are used for the evaluation and confidence intervals for them are constructed using bootstrapping. The results indicate that the individual selection rule based on discriminant scores is more accurate, and sometimes significantly so, than any aggregate selection method.     

U-Convolutional model for spatio-temporal wind speed forecasting

The increasing penetration of intermittent renewable energy in power systems brings operational challenges. One way of supporting them is by enhancing the predictability of renewables through accurate forecasting. Convolutional Neural Networks (Convnets) provide a successful technique for processing space-structured multi-dimensional data. In our work, we propose the U-Convolutional model to predict hourly wind speeds for a single location using spatio-temporal data with multiple explanatory variables as an input. The U-Convolutional model is composed of a U-Net part, which synthesizes input information, and a Convnet part, which maps the synthesized data into a single-site wind prediction. We compare our approach with advanced Convnets, a fully connected neural network, and univariate models. We use time series from the Climate Forecast System Reanalysis as datasets and select temperature and u- and v-components of wind as explanatory variables. The proposed models are evaluated at multiple locations (totaling 181 target series) and multiple forecasting horizons. The results indicate that our proposal is promising for spatio-temporal wind speed prediction, with results that show competitive performance on both time horizons for all datasets.     

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.     

Are forecasting competitions data representative of the reality?

Forecasters typically evaluate the performances of new forecasting methods by exploiting data from past forecasting competitions. Over the years, numerous studies have based their conclusions on such datasets, with mis-performing methods being unlikely to receive any further attention. However, it has been reported that these datasets might not be indicative, as they display many limitations. Since forecasting research is driven somewhat by data from forecasting competitions, it becomes vital to determine whether they are indeed representative of the reality or whether forecasters tend to over-fit their methods on a random sample of series. This paper uses the data from M4 as proportionate to the real world and compares its properties with those of past datasets commonly used in the literature as benchmarks in order to provide evidence on that question. The results show that many popular benchmarks of the past may indeed deviate from reality, and ways forward are discussed in response.     

Expectation-based scan statistics for monitoring spatial time series data

We consider the simultaneous monitoring of a large number of spatially localized time series in order to detect emerging spatial patterns. For example, in disease surveillance, we detect emerging outbreaks by monitoring electronically available public health data, e.g. aggregate daily counts of Emergency Department visits. We propose a two-step approach based on the expectation-based scan statistic: we first compute the expected count for each recent day for each spatial location, then find spatial regions (groups of nearby locations) where the recent counts are significantly higher than expected. By aggregating information across multiple time series rather than monitoring each series separately, we can improve the timeliness, accuracy, and spatial resolution of detection. We evaluate several variants of the expectation-based scan statistic on the disease surveillance task (using synthetic outbreaks injected into real-world hospital Emergency Department data), and draw conclusions about which models and methods are most appropriate for which surveillance tasks.     

Forecasting monthly and quarterly time series using STL decomposition

This paper is a re-examination of the benefits and limitations of decomposition and combination techniques in the area of forecasting, and also a contribution to the field, offering a new forecasting method. The new method is based on the disaggregation of time series components through the STL decomposition procedure, the extrapolation of linear combinations of the disaggregated sub-series, and the reaggregation of the extrapolations to obtain estimates for the global series. Applying the forecasting method to data from the NN3 and M1 Competition series, the results suggest that it can perform well relative to four other standard statistical techniques from the literature, namely the ARIMA, Theta, Holt-Winters’ and Holt’s Damped Trend methods. The relative advantages of the new method are then investigated further relative to a simple combination of the four statistical methods and a Classical Decomposition forecasting method. The strength of the method lies in its ability to predict long lead times with relatively high levels of accuracy, and to perform consistently well for a wide range of time series, irrespective of the characteristics, underlying structure and level of noise of the data.     

Kernel-weighted GMM estimators for linear time series models

This paper analyzes the higher-order asymptotic properties of generalized method of moments (GMM) estimators for linear time series models using many lags as instruments. A data-dependent moment selection method based on minimizing the approximate mean squared error is developed. In addition, a new version of the GMM estimator based on kernel-weighted moment conditions is proposed. It is shown that kernel-weighted GMM estimators can reduce the asymptotic bias compared to standard GMM estimators. Kernel weighting also helps to simplify the problem of selecting the optimal number of instruments. A feasible procedure similar to optimal bandwidth selection is proposed for the kernel-weighted GMM estimator.