The energy output a photo voltaic(PV) panel is a function of solar irradiation and weather parameters like temperature and wind speed etc. A general measure for solar irradiation called Global Horizontal Irradiance (GHI), customarily reported in Watt meter @math , is a generic indicator for this intermittent energy resource. An accurate prediction of GHI is necessary for reliable grid integration of the renewable as well as for power market trading. While some machine learning techniques are well introduced along with the traditional time-series forecasting techniques, deep-learning techniques remains less explored for the task at hand. In this paper we give deep learning models suitable for sequence to sequence prediction of GHI. The deep learning models are reported for short-term forecasting @math hour along with the state-of-the art techniques like Gradient Boosted Regression Trees(GBRT) and Feed Forward Neural Networks(FFNN). We have checked that spatio-temporal features like wind direction, wind speed and GHI of neighboring location improves the prediction accuracy of the deep learning models significantly. Among the various sequence-to-sequence encoder-decoder models LSTM performed superior, handling short-comings of the state-of-the-art techniques.
Traditionally time series forecasting was under the scope of statistics and models like Auto Regression Integrated Moving Average (ARIMA), Seasonal ARIMA were extensively used linear models @cite_2 . But due to possible non-linearity in the data Artifical Neural Networks @cite_6 were introduced and subsequently hybrid ARIMA models were used @cite_20 @cite_8 . Random Forest based methods were reported used in forecasting. @cite_12 , however the above were outperformed by Gradient Boosted Regression Tree (GBRT) while used for forecasting problem in Global Energy Forecasting Competition 2014 @cite_16 . A summary of related PV power forecasting models is available in @cite_10 .
@cite_8 @cite_6 @cite_2 @cite_16 @cite_10 @cite_12 @cite_20
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A suitable combination of linear and nonlinear models provides a more accurate prediction model than an individual linear or nonlinear model for forecasting time series data originating from various applications. The linear autoregressive integrated moving average (ARIMA) and nonlinear artificial neural network (ANN) models are explored in this paper to devise a new hybrid ARIMA-ANN model for the prediction of time series data. Many of the hybrid ARIMA-ANN models which exist in the literature apply an ARIMA model to given time series data, consider the error between the original and the ARIMA-predicted data as a nonlinear component, and model it using an ANN in different ways. Though these models give predictions with higher accuracy than the individual models, there is scope for further improvement in the accuracy if the nature of the given time series is taken into account before applying the models. In the work described in this paper, the nature of volatility was explored using a moving-average filter, and then an ARIMA and an ANN model were suitably applied. Using a simulated data set and experimental data sets such as sunspot data, electricity price data, and stock market data, the proposed hybrid ARIMA-ANN model was applied along with individual ARIMA and ANN models and some existing hybrid ARIMA-ANN models. The results obtained from all of these data sets show that for both one-step-ahead and multistep-ahead forecasts, the proposed hybrid model has higher prediction accuracy. This paper considers univariate online electricity demand forecasting for lead times from a half-hour-ahead to a day-ahead. A time series of demand recorded at half-hourly intervals contains more than one seasonal pattern. A within-day seasonal cycle is apparent from the similarity of the demand profile from one day to the next, and a within-week seasonal cycle is evident when one compares the demand on the corresponding day of adjacent weeks. There is strong appeal in using a forecasting method that is able to capture both seasonalities. The multiplicative seasonal ARIMA model has been adapted for this purpose. In this paper, we adapt the Holt-Winters exponential smoothing formulation so that it can accommodate two seasonalities. We correct for residual autocorrelation using a simple autoregressive model. The forecasts produced by the new double seasonal Holt-Winters method outperform those from traditional Holt-Winters and from a well-specified multiplicative double seasonal ARIMA model. Abstract Autoregressive integrated moving average (ARIMA) is one of the popular linear models in time series forecasting during the past three decades. Recent research activities in forecasting with artificial neural networks (ANNs) suggest that ANNs can be a promising alternative to the traditional linear methods. ARIMA models and ANNs are often compared with mixed conclusions in terms of the superiority in forecasting performance. In this paper, a hybrid methodology that combines both ARIMA and ANN models is proposed to take advantage of the unique strength of ARIMA and ANN models in linear and nonlinear modeling. Experimental results with real data sets indicate that the combined model can be an effective way to improve forecasting accuracy achieved by either of the models used separately. Abstract A feedforward neural network which can account for nonlinear relationships was used to compare ARIMA and neural network price forecasting performance. Data used was monthly live cattle and wheat prices from 1950 through 1990. The experiment was repeated seven times for successive three year periods. This involved using a walk forward or sliding window approach from 1970 through 1990 which generated out of sample results. The neural network models achieved a 27 percent and 56 percent lower mean squared error than ARIMA model. The absolute mean error and mean absolute percent error were also lower for the neural network models. The neural network models were able to capture a significant number of turning points for both wheat and cattle, while the ARIMA model was only able to do so for wheat. Since this forecasting method is not problem specific and uses only past prices, it can be applied to other forecasting problems such as stocks and other financial prices. Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package. Financial time series forecasting has become a challenge because it is noisy, non-stationary and chaotic. Most of the existing forecasting models for this problem do not take market sentiment into consideration. To overcome this limitation, motivated by the fact that market sentiment contains some useful forecasting information, this paper uses textual information to aid the financial time series forecasting and presents a novel text mining approach via combining ARIMA and SVR (Support Vector Regression) to forecasting. The approach contains three steps: representing textual data as feature vectors, using ARIMA to analyze the linear part and developing a SVR model based only on textual feature vector to model the nonlinear part. To verify the effectiveness of the proposed approach, quarterly ROEs (Return of Equity) of six security companies are chosen as the forecasting targets. Comparing with some existing state-of-the-art models, the proposed approach gives superior results. It indicates that the proposed model that uses additional market sentiment provides a promising alternative to financial time series prediction. In this paper, we tackle the problem of power prediction of several photovoltaic (PV) plants spread over an extended geographic area and connected to a power grid. The paper is intended to be a comprehensive study of one-day ahead forecast of PV energy production along several dimensions of analysis: 1) The consideration of the spatio-temporal autocorrelation, which characterizes geophysical phenomena, to obtain more accurate predictions. 2) The learning setting to be considered, i.e., using simple output prediction for each hour or structured output prediction for each day. 3) The learning algorithms: We compare artificial neural networks, most often used for PV prediction forecast, and regression trees for learning adaptive models. The results obtained on two PV power plant datasets show that: taking into account spatio temporal autocorrelation is beneficial; the structured output prediction setting significantly outperforms the nonstructured output prediction setting; and regression trees provide better models than artificial neural networks. We evaluate and compare two common methods, artificial neural networks (ANN) and support vector regression (SVR), for predicting energy productions from a solar photovoltaic (PV) system in Florida 15 min, 1 h and 24 h ahead of time. A hierarchical approach is proposed based on the machine learning algorithms tested. The production data used in this work corresponds to 15 min averaged power measurements collected from 2014. The accuracy of the model is determined using computing error statistics such as mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), relative MBE (rMBE), mean percentage error (MPE) and relative RMSE (rRMSE). This work provides findings on how forecasts from individual inverters will improve the total solar power generation forecast of the PV system. Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online. Abstract This paper provides a technique based on stochastic programming to optimally solve the wind power problem faced by the uncertainty. Uncertainties regarding the wind availability, market prices, and balancing energy needs are considered throughout the paper. The objective of this paper is to derive the best offering strategy for a wind power producer in a Short-Term electricity market, while limiting the risk of expected profit and required reserve due to wind speed forecast volatility. Risk aversion is explicitly modeled using the conditional value-at-risk methodology. ARIMA techniques are used to predict next-day electricity prices and wind speed forecast. For more performance the probability distribution function of the error between forecasted value and realized value to scenario generation is used. A realistic of numerical case studies demonstrates the interest and the effectiveness. We investigate the probabilistic forecasting of solar and wind power generation in connection with the Global Energy Forecasting Competition 2014. We use a voted ensemble of a quantile regression forest model and a stacked random forest–gradient boosting decision tree model to predict the probability distribution. The raw probabilities thus obtained need to be post-processed using isotonic regression in order to conform to the monotonic-increase attribute of probability distributions. The results show a great performance in terms of the weighted pinball loss, with the model achieving second place on the final competition leaderboard. Autoregressive moving average (ARMA) method is applied to modeling the time series of position changes of GPS sites, obtained by the Geographical Survey Institute (GSI) of Japan during the period from April 1996 to March 1998. The present application is focused on denoising of the GPS time series data where only white noise is considered, and detection of data discontinuities and outliers in order to obtain time-averaged velocity and strain fields in central Japan. The data discontinuities are detected by a typical Kalman filter algorithm. The outliers are eliminated by using robust estimation techniques during the ARMA process. The averaged strain field, calculated by the least-squares collocation method from the improved two-year time series data, distinguishes clearly between the tectonically active and inactive regions. Higher maximum shear strain rates were detected in the southern area of the Kanto district. In the areas with very high seismicities, however, the difference between the maximum shear strain rates, that were estimated from the raw time series data and the ARMA-analyzed data, amounted to about 0.2 microstrain yr. This indicates that the existence of noise and discontinuities can lead to an over-prediction of the strain field. textabstractForecasting financial time series using past observations has been a significant topic of interest. While temporal relationships in the data exist, they are difficult to analyze and predict accurately due to the non-linear trends and noise present in the series. We propose to learn these dependencies by a convolutional neural network. In particular the focus is on multivariate time series forecasting. Effectively, we use multiple financial time series as input in the neural network, thus conditioning the forecast of a time series x(t) on both its own history as well as that of a second (or third) time series y(t). Training a model on multiple stock series allows the network to exploit the correlation structure between these series so that the network can learn the market dynamics in shorter sequences of data. We show that long-term temporal dependencies in and between financial time series can be learned by means of a deep convolutional neural network based on the WaveNet model [2]. The network makes use of dilated convolutions applied to multiple time series so that the receptive field of the network is wide enough to learn both short and long-term dependencies. The architecture includes batch normalization and uses a 1 × k convolution with parametrized skip connections from the input time series as well as the time series we condition on, in this way learning long-term interdependencies in an efficient manner [1]. This improves the forecast, while at the same time limiting the requirement for a long historical price series and reducing the noise. Knowing the strong performance of CNNs on classification problems we show that they can be applied successfully to forecasting financial time series, without the need of large samples of data. We compare the performance of the WaveNet model to a state-of-the-art fully convolutional network (FCN), and an autoregressive model popular in econometrics and show that our model is much better able to learn important dependencies in between financial time series resulting in a more robust and accurate forecast. From the Publisher: This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods. Graphical abstractDisplay Omitted HighlightsWe predict maximum and minimum day stock prices of power companies.The methodology is based on attribute selection and time series prediction.The most relevant attributes are determined by correlation analysis.The actual time series prediction is carried out by neural networks.The proposed methodology provides very good results. Time series forecasting has been widely used to determine future prices of stocks, and the analysis and modeling of finance time series is an important task for guiding investors' decisions and trades. Nonetheless, the prediction of prices by means of a time series is not trivial and it requires a thorough analysis of indexes, variables and other data. In addition, in a dynamic environment such as the stock market, the non-linearity of the time series is a pronounced characteristic, and this immediately affects the efficacy of stock price forecasts. Thus, this paper aims at proposing a methodology that forecasts the maximum and minimum day stock prices of three Brazilian power distribution companies, which are traded in the Sao Paulo Stock Exchange BM&FBovespa. When compared to the other papers already published in the literature, one of the main contributions and novelty of this paper is the forecast of the range of closing prices of Brazilian power distribution companies' stocks. As a result of its application, investors may be able to define threshold values for their stock trades. Moreover, such a methodology may be of great interest to home brokers who do not possess ample knowledge to invest in such companies. The proposed methodology is based on the calculation of distinct features to be analysed by means of attribute selection, defining the most relevant attributes to predict the maximum and minimum day stock prices of each company. Then, the actual prediction was carried out by Artificial Neural Networks (ANNs), which had their performances evaluated by means of Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) calculations. The proposed methodology for addressing the problem of prediction of maximum and minimum day stock prices for Brazilian distribution companies is effective. In addition, these results were only possible to be achieved due to the combined use of attribute selection by correlation analysis and ANNs. Abstract This paper proposes a stochastic and dynamic mixed-integer linear program (SD-MILP) for optimal coordinated bidding of a risk-averse profit-maximizing hydropower producer. The day-ahead, intra-day, and real-time markets are considered. To model and predict day-ahead, intra-day, and real-time prices, the Holt–Winter (HW) and the Generalized Autoregressive Conditional Heteroscedastic (GARCH) predictors are combined using a proposed Markov switch. The discrete behavior of intra-day and real-time prices is modeled as different Markov states. The proposed Markov-based HW–GARCH model with a standard scenario generation-reduction technique is used to capture the uncertainty in day-ahead, intra-day, and real-time prices. The time-dependent conditional value at risk (T-CVaR) is proposed to model the risk of trading in different considered markets. The convex combination of the expected profit and T-CVaR is used as the objective of SD-MILP. The Markov-based HW–GARCH is modeled in Matlab and the SD-MILP is coded in GAMS. The Markov-based HW–GARCH predictor and the SD-MILP are used to develop the bidding curve of a three-reservoir hydropower producer using the electricity prices from the Nordic power market. To further examine the developed models a seven-reservoir hydropower producer is also studied. For these two cases, the coordinated bidding curves are derived and discussed. Both linear and nonlinear models have been proposed for forecasting the power output of photovoltaic systems. Linear models are simple to implement but less flexible. Due to the stochastic nature of the power output of PV systems, nonlinear models tend to provide better forecast than linear models. Motivated by this, this paper suggests a fairly simple nonlinear regression model known as multivariate adaptive regression splines (MARS), as an alternative to forecasting of solar power output. The MARS model is a data-driven modeling approach without any assumption about the relationship between the power output and predictors. It maintains simplicity of the classical multiple linear regression (MLR) model while possessing the capability of handling nonlinearity. It is simpler in format than other nonlinear models such as ANN, k-nearest neighbors (KNN), classification and regression tree (CART), and support vector machine (SVM). The MARS model was applied on the daily output of a grid-connected 2.1kW PV system to provide the 1-day-ahead mean daily forecast of the power output. The comparisons with a wide variety of forecast models show that the MARS model is able to provide reliable forecast performance. We propose a wavelet multiscale decomposition-based autoregressive approach for the prediction of 1-h ahead load based on historical electricity load data. This approach is based on a multiple resolution decomposition of the signal using the non-decimated or redundant Haar a trous wavelet transform whose advantage is taking into account the asymmetric nature of the time-varying data. There is an additional computational advantage in that there is no need to recompute the wavelet transform (wavelet coefficients) of the full signal if the electricity data (time series) is regularly updated. We assess results produced by this multiscale autoregressive (MAR) method, in both linear and non-linear variants, with single resolution autoregression (AR), multilayer perceptron (MLP), Elman recurrent neural network (ERN) and the general regression neural network (GRNN) models. Results are based on the New South Wales (Australia) electricity load data that is provided by the National Electricity Market Management Company (NEMMCO). We consider the problem of forecasting the aggregate demand of a pool of price-responsive consumers of electricity. The response of the aggregate load to price is modeled by an optimization problem that is characterized by a set of marginal utility curves and minimum and maximum power consumption limits. The task of estimating these parameters is addressed using a generalized inverse optimization scheme that, in turn, requires solving a nonconvex mathematical program. We introduce a solution method that overcomes the nonconvexities by solving instead two linear problems with a penalty term, which is statistically adjusted by using a cross-validation algorithm. The proposed methodology is data-driven and leverages information from regressors, such as time and weather variables, to account for changes in the parameter estimates. The power load of a group of heating, ventilation, and air conditioning systems in buildings is simulated, and the results show that the aggregate demand of the group can be successfully captured by the proposed model, making it suitable for short-term forecasting purposes. This paper proposes a method for selecting explanatory variables for global solar radiation forecasting. The weather conditions affect generation output of renewable energy significantly. As a result, smart grids increase the uncertainties caused by the power injections of photovoltaic (PV) and or wind power generation. To smooth smart grid operation, it is necessary to select the predicted input variables for the forecasting model. In this paper, how to select explanatory variables in the forecasting model of PV generation is discussed because Japan gives much higher priority to PV generation in the framework of future energy policy. The global solar radiation is one of the most important variables in dealing with PV generation output forecasting. This paper focuses on the relationship between the global solar radiation and its explanatory variables. The proposed method makes use of the CART (Classification and Regression Trees) algorithm of data mining method to select the explanatory or input variables in the forecasting model of global solar radiation. CART has the function to give priority to explanatory variables through an index called Variable Importance. The proposed method was applied to real data of global solar radiation in Tokyo, Japan.