Variance-covariance based weighing for neural network ensembles

Neural network (NN) is a popular artificial intelligence technique for solving complicated problems due to their inherent capabilities. However generalization in NN can be harmed by a number of factors including parameter's initialization, inappropriate network topology and setting parameters of the training process itself. Forecast combinations of NN models have the potential for improved generalization and lower training time. A weighted averaging based on Variance-Covariance method that assigns greater weight to the forecasts producing lower error, instead of equal weights is practiced in this paper. While implementing the method, combination of forecasts is done with all candidate models in one experiment and with the best selected models in another experiment. It is observed during the empirical analysis that forecasting accuracy is improved by combining the best individual NN models. Another finding of this study is that reducing the number of NN models increases the diversity and, hence, accuracy.

Learn from yesterday, live for today, hope for tomorrow : attempting to plan for coastal change in South West Victoria

Learn from yesterday, live for today hope for tomorrow. When Albert Einstein penned these opening words, the realm of planning was least on his mind despite the aptness of the thoughts. This paper, having regard to this quotation, questions whether demographic change in one coastal area is occurring at a faster rate than in non–coastal areas? The South West coastal area of Victoria, from 1981 onwards, has witnessed a dramatic increase in population and also major shifts in the social and economic characteristics of the region. What have been the historic demographic and employment characteristics of the area and has there been a shift in these characteristics leading to the rapid population growth? These questions are considered using the City of Warrnambool, the largest urban centre in South West Victoria, as a study vehicle. The impact of a growing population on the municipal landscape can be demanding in terms of land use planning, land supply and the urban design. This paper will review the population growth using a shift share analysis method compared against overall growth patterns in the Victorian state population and Australia overall. It will then examine government population forecasts for the City of Warrnambool and suggest those impacts upon the current City of Warrnambool landscape.

Short-term load and wind power forecasting using neural network-based prediction intervals

Electrical power systems are evolving from today's centralized bulk systems to more decentralized systems. Penetrations of renewable energies, such as wind and solar power, significantly increase the level of uncertainty in power systems. Accurate load forecasting becomes more complex, yet more important for management of power systems. Traditional methods for generating point forecasts of load demands cannot properly handle uncertainties in system operations. To quantify potential uncertainties associated with forecasts, this paper implements a neural network (NN)-based method for the construction of prediction intervals (PIs). A newly introduced method, called lower upper bound estimation (LUBE), is applied and extended to develop PIs using NN models. A new problem formulation is proposed, which translates the primary multiobjective problem into a constrained single-objective problem. Compared with the cost function, this new formulation is closer to the primary problem and has fewer parameters. Particle swarm optimization (PSO) integrated with the mutation operator is used to solve the problem. Electrical demands from Singapore and New South Wales (Australia), as well as wind power generation from Capital Wind Farm, are used to validate the PSO-based LUBE method. Comparative results show that the proposed method can construct higher quality PIs for load and wind power generation forecasts in a short time.

State dependent asymmetric loss and the consensus forecast of real U.S. GDP growth

It has been well documented that the consensus forecast from surveys of professional forecasters shows a bias that varies over time. In this paper, we examine whether this bias may be due to forecasters having an asymmetric loss function. In contrast to previous research, we account for the time variation in the bias by making the loss function depend on the state of the economy. The asymmetry parameter in the loss function is specified to depend on set state variables which may cause forecaster to intentionally bias their forecasts. We consider both the Lin–Ex and asymmetric power loss functions. For the commonly used Lin–Ex and Lin–Lin loss functions, we show the model can be easily estimated by least squares. We apply our methodology to the consensus forecast of real U.S. GDP growth from the Survey of Professional Forecasters. We find that forecast uncertainty has an asymmetric effect on the asymmetry parameter in the loss function dependent upon whether the economy is in expansion or contraction. When the economy is in expansion, forecaster uncertainty is related to an overprediction in the median forecast of real GDP growth. In contrast, when the economy is in contraction, forecaster uncertainty is related to an underprediction in the median forecast of real GDP growth. Our results are robust to the particular loss function that is employed in the analysis.

Construction of neural network-based prediction intervals for short-term electrical load forecasting

Short-term load forecasting (STLF) is of great importance for control and scheduling of electrical power systems. The uncertainty of power systems increases due to the random nature of climate and the penetration of the renewable energies such as wind and solar power. Traditional methods for generating point forecasts of load demands cannot properly handle uncertainties in datasets. To quantify these potential uncertainties associated with forecasts, this paper implements a neural network (NN)-based method for construction of prediction intervals (PIs). A newly proposed method, called lower upper bound estimation (LUBE), is applied to develop PIs using NN models. The primary multi-objective problem is firstly transformed into a constrained single-objective problem. This new problem formulation is closer to the original problem and has fewer parameters than the cost function. Particle swarm optimization (PSO) integrated with the mutation operator is used to solve the problem. Two case studies from Singapore and New South Wales (Australia) historical load datasets are used to validate the PSO-based LUBE method. Demonstrated results show that the proposed method can construct high quality PIs for load forecasting applications.

Flood forecasting in large rivers with data-driven models

Results from the application of adaptive neuro-fuzzy inference system (ANFIS) to forecast water levels at 3 stations along the mainstream of the Lower Mekong River are reported in this paper. The study investigated the effects of including water levels from upstream stations and tributaries, and rainfall as inputs to ANFIS models developed for the 3 stations. When upstream water levels in the mainstream were used as input, improvements to forecasts were realized only when the water levels from 1 or at most 2 upstream stations were included. This is because when there are significant contributions of flow from the tributaries, the correlation between the water levels in the upstream stations and stations of interest decreases, limiting the effectiveness of including water levels from upstream stations as inputs. In addition, only improvements at short lead times were achieved. Including the water level from the tributaries did not significantly improve forecast results. This is attributed mainly to the fact that the flow contributions represented by the tributaries may not be significant enough, given that there could be large volume of flow discharging directly from the catchments which are ungauged, into the mainstream. The largest improvement for 1-day forecasts was obtained for Kratie station where lateral flow contribution was 17 %, the highest for the 3 stations considered. The inclusion of rainfall as input resulted in significant improvements to long-term forecasts. For Thakhek, where rainfall is most significant, the persistence index and coefficient of efficiency for 5-lead-day forecasts improved from 0.17 to 0.44 and 0.89 to 0.93, respectively, whereas the root mean square error decreased from 0.83 to 0.69 m.

Prediction interval-based neural network modelling of polystyrene polymerization reactor - a new perspective of data-based modelling

In this paper, prediction interval (PI)-based modelling techniques are introduced and applied to capture the nonlinear dynamics of a polystyrene batch reactor system. Traditional NN models are developed using experimental datasets with and without disturbances. Simulation results indicate that traditional NNs cannot properly handle disturbances in reactor data and demonstrate a poor forecasting performance, with an average MAPE of 22% in the presence of disturbances. The lower upper bound estimation (LUBE) method is applied for the construction of PIs to quantify uncertainties associated with forecasts. The simulated annealing optimization technique is employed to adjust NN parameters for minimization of an innovative PI-based cost function. The simulation results reveal that the LUBE method generates quality PIs without requiring prohibitive computations. As both calibration and sharpness of PIs are practically and theoretically satisfactory, the constructed PIs can be used as part of the decision-making and control process of polymerization reactors. © 2014 The Institution of Chemical Engineers.

Effects of type reduction algorithms on forecasting accuracy of IT2FLS models

Type reduction (TR) is one of the key components of interval type-2 fuzzy logic systems (IT2FLSs). Minimizing the computational requirements has been one of the key design criteria for developing TR algorithms. Often researchers give more rewards to computationally less expensive TR algorithms. This paper evaluates and compares five frequently used TR algorithms based on their contribution to the forecasting performance of IT2FLS models. Algorithms are judged based on the generalization power of IT2FLS models developed using them. Synthetic and real world case studies with different levels of uncertainty are considered to examine effects of TR algorithms on forecasts' accuracies. As per obtained results, Coupland-Jonh TR algorithm leads to models with a higher and more stable forecasting performance. However, there is no obvious and consistent relationship between the widths of the type reduced set and the TR algorithm. © 2013 Elsevier B.V.

Uncertainty handling using neural network-based prediction intervals for electrical load forecasting

The complexity and level of uncertainty present in operation of power systems have significantly grown due to penetration of renewable resources. These complexities warrant the need for advanced methods for load forecasting and quantifying uncertainties associated with forecasts. The objective of this study is to develop a framework for probabilistic forecasting of electricity load demands. The proposed probabilistic framework allows the analyst to construct PIs (prediction intervals) for uncertainty quantification. A newly introduced method, called LUBE (lower upper bound estimation), is applied and extended to develop PIs using NN (neural network) models. The primary problem for construction of intervals is firstly formulated as a constrained single-objective problem. The sharpness of PIs is treated as the key objective and their calibration is considered as the constraint. PSO (particle swarm optimization) enhanced by the mutation operator is then used to optimally tune NN parameters subject to constraints set on the quality of PIs. Historical load datasets from Singapore, Ottawa (Canada) and Texas (USA) are used to examine performance of the proposed PSO-based LUBE method. According to obtained results, the proposed probabilistic forecasting method generates well-calibrated and informative PIs. Furthermore, comparative results demonstrate that the proposed PI construction method greatly outperforms three widely used benchmark methods. © 2014 Elsevier Ltd.

Electricity load and price forecasting with influential factors in a deregulated power industry

With the emergence of smart power grid and distributed generation technologies in recent years, there is need to introduce new advanced models for forecasting. Electricity load and price forecasts are two primary factors needed in a deregulated power industry. The performances of the demand response programs are likely to be deteriorated in the absence of accurate load and price forecasting. Electricity generation companies, system operators, and consumers are highly reliant on the accuracy of the forecasting models. However, historical prices from the financial market, weekly price/load information, historical loads and day type are some of the explanatory factors that affect the accuracy of the forecasting. In this paper, a neural network (NN) model that considers different influential factors as feedback to the model is presented. This model is implemented with historical data from the ISO New England. It is observed during experiments that price forecasting is more complicated and hence less accurate than the load forecasting.

Predicting the likely response of data-poor ecosystems to climate change using space-for-time substitution across domains

Predicting ecological response to climate change is often limited by a lack of relevant local data from which directly applicable mechanistic models can be developed. This limits predictions to qualitative assessments or simplistic rules of thumb in data-poor regions, making management of the relevant systems difficult. We demonstrate a method for developing quantitative predictions of ecological response in data-poor ecosystems based on a space-for-time substitution, using distant, well-studied systems across an inherent climatic gradient to predict ecological response. Changes in biophysical data across the spatial gradient are used to generate quantitative hypotheses of temporal ecological responses that are then tested in a target region. Transferability of predictions among distant locations, the novel outcome of this method, is demonstrated via simple quantitative relationships that identify direct and indirect impacts of climate change on physical, chemical and ecological variables using commonly available data sources. Based on a limited subset of data, these relationships were demonstrably plausible in similar yet distant (>2000 km) ecosystems. Quantitative forecasts of ecological change based on climate-ecosystem relationships from distant regions provides a basis for research planning and informed management decisions, especially in the many ecosystems for which there are few data. This application of gradient studies across domains - to investigate ecological response to climate change - allows for the quantification of effects on potentially numerous, interacting and complex ecosystem components and how they may vary, especially over long time periods (e.g. decades). These quantitative and integrated long-term predictions will be of significant value to natural resource practitioners attempting to manage data-poor ecosystems to prevent or limit the loss of ecological value. The method is likely to be applicable to many ecosystem types, providing a robust scientific basis for estimating likely impacts of future climate change in ecosystems where no such method currently exists.

Least squares learning and the US Treasury bill rate

Understanding how agents formulate their expectations about Fed behavior is important for market participants because they can potentially use this information to make more accurate estimates of stock and bond prices. Although it is commonly assumed that agents learn over time, there is scant empirical evidence in support of this assumption. Thus, in this paper we test if the forecast of the three month T-bill rate in the Survey of Professional Forecasters (SPF) is consistent with least squares learning when there are discrete shifts in monetary policy. We first derive the mean, variance and autocovariances of the forecast errors from a recursive least squares learning algorithm when there are breaks in the structure of the model. We then apply the Bai and Perron (1998) test for structural change to a forecasting model for the three month T-bill rate in order to identify changes in monetary policy. Having identified the policy regimes, we then estimate the implied biases in the interest rate forecasts within each regime. We find that when the forecast errors from the SPF are corrected for the biases due to shifts in policy, the forecasts are consistent with least squares learning. © 2014 Elsevier B.V.

The influence of non-climate predictors at local and landscape resolutions depends on the autecology of the species

Species distribution models have come under criticism for being too simplistic for making robust future forecasts, partly because they assume that climate is the main determinant of geographical range at large spatial extents and coarse resolutions, with non-climate predictors being important only at finer scales. We suggest that this paradigm might be obscured by species movement patterns. To explore this we used contrasting kangaroo (family Macropodidae) case studies: two species with relatively small, stable home ranges (Macropus giganteus and M.robustus) and three species with more extensive, adaptive ranging behaviour (M.antilopinus, M.fuliginosus and M.rufus). We predicted that non-climate predictors will be most influential to model fit and predictive performance at local spatial resolution for the former species and at landscape resolution for the latter species. We compared residuals autocovariate - boosted regression tree (RAC-BRT) model statistics with and without species-specific non-climate predictors (habitat, soil, fire, water and topography), at local- and landscape-level spatial resolutions (5 and 50km). As predicted, the influence of non-climate predictors on model fit and predictive performance (compared with climate-only models) was greater at 50 compared with 5km resolution for M.rufus and M.fuliginosus and the opposite trend was observed for M.giganteus. The results for M.robustus and M.antilopinus were inconclusive. Also notable was the difference in inter-scale importance of climate predictors in the presence of non-climate predictors. In conclusion, differences in autecology, particularly relating to space use, may contribute to the importance of non-climate predictors at a given scale, not model scale per se. Further exploration of this concept across a range of species is encouraged and findings may contribute to more effective conservation and management of species at ecologically meaningful scales. © 2014 Ecological Society of Australia.

Aggregation of Pi-based forecast to enhance prediction accuracy

In contrast to point forecast, prediction interval-based neural network offers itself as an effective tool to quantify the uncertainty and disturbances that associated with process data. However, single best neural network (NN) does not always guarantee to predict better quality of forecast for different data sets or a whole range of data set. Literature reported that ensemble of NNs using forecast combination produces stable and consistence forecast than single best NN. In this work, a NNs ensemble procedure is introduced to construct better quality of Pis. Weighted averaging forecasts combination mechanism is employed to combine the Pi-based forecast. As the key contribution of this paper, a new Pi-based cost function is proposed to optimize the individual weights for NN in combination process. An optimization algorithm, named simulated annealing (SA) is used to minimize the PI-based cost function. Finally, the proposed method is examined in two different case studies and compared the results with the individual best NNs and available simple averaging Pis aggregating method. Simulation results demonstrated that the proposed method improved the quality of Pis than individual best NNs and simple averaging ensemble method.

Is carbon emissions trading profitable?

The European Carbon Emissions Trading Scheme introduced in 2005 has led to both spot and futures market trading of carbon emissions. However, despite seven years of trading, we have no knowledge on how profitable carbon emissions trading is. In this paper, we first test whether carbon forward returns predict carbon spot returns. We find strong evidence on both in-sample and out-of-sample predictability. Based on this evidence, we forecast carbon spot returns using both carbon forward returns and a constant. We consider a mean-variance investor and a CRRA investor, and show that they have higher utility and can make more statistically significant profits by following forecasts generated from the forward returns model than from a constant returns model.