Energy **demand** **forecasting**, and specifically **electricity** **demand** **forecasting**, is a fun- damental feature in both industry and research. **Forecasting** techniques assist all **electricity** market participants in accurate planning, selling and purchasing decisions and strategies. Generation and distribution of **electricity** require appropriate, precise and accurate **forecasting** methods. Also accurate **forecasting** **models** assist producers, researchers and economists to make proper and beneficial future decisions. There are several research papers, which investigate this fundamental aspect and attempt var- ious statistical techniques. Although **weather** and economic effects have significant influences on **electricity** **demand**, in this study they are purposely eliminated from investigation. This research considers calendar-related effects such as months of the year, weekdays and holidays (that is, public holidays, the day before a public holiday, the day after a public holiday, school holidays, university holidays, Easter holidays and major religious holidays) and includes university exams, general election days, day after elections, and municipal elections in the analysis. Regression analysis, cate- gorical regression and auto-regression are used to illustrate the relationships between response variable and explanatory variables.

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Abstract. This paper presents a methodology for **short**-**term** load **forecasting** based on genetic algorithm feature selection and artiﬁcial neural network modeling. A feedforward artiﬁcial neural network is used to model the 24-h ahead load based on past consumption, **weather** and stock index data. A genetic algo‐ rithm is used in order to ﬁnd the best subset of variables for modeling. Three datasets of diﬀerent geographical locations, encompassing areas of diﬀerent dimensions with distinct load proﬁles are used in order to evaluate the method‐ ology. The developed approach was found to generate **models** achieving a minimum mean average percentage error under 2 %. The feature selection algo‐ rithm was able to signiﬁcantly reduce the number of used features and increase the accuracy of the **models**.

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Rouse (2006) defined fuzzy logic as a computing technique based on “degrees of truth” instead of the well-known Boolean logic “true or false” (1 or 0). Fuzzy logic is rather a generalisation of this Boolean logic on which modern computers are based. Ranaweera, Hubele and Karady (1996) described fuzzy logic **models** as a function that links a set of input variables to a set of output variables; these input variable values do not need to be numerical. They just need to be transcribed in a natural language. For example, a **weather** parameter such as the temperature may take on the “fuzzy” instances such as “low”, “medium” and “high”. The literature adds that very often fuzzy logic **models** incorporate a mapping of input and output values via a simple “IF THEN” logic statement. “IF the temperature is very low, THEN the load **demand** will be very high”, is an example of this logic statement given in the Ranaweera et al. (1996) paper. The authors further reiterated that this is a type of mapping and logic that allows a combination of the expert knowledge with fuzzy logic **models**. In many instances when precise outputs are needed, such as point estimates for forecast values, a reverse mapping called “defuzzification” process can be undertaken to produce those desirable outputs. Advantages of this method over traditional ones can be found in Gupta (2012). The drawbacks of the fuzzy logic **models** are that they are time consuming and lack of guarantees to obtain optimal fuzzy rules and membership functions since this process is based on trial and error.

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The paper presented an application of partially linear additive quantile regression **models** to **short** **term** **electricity** **demand** **forecasting** using South African data. The study focused on the peak hours of the day. Variable selection was done using Lasso via hierarchical pairwise interactions. **Models** for each hour were split into one with and one without pairwise interactions. **Models** of each hour were combined using an algorithm in which the average loss suffered was based on the pinball loss function. This resulted in three sets of forecasts for each hour. The best set of forecasts was selected based on probabilistic forecast error measures, pinball loss values, continuous ranked probability scores and the log scores. For instance, as shown in 2 the model without interactions has smaller pinball loss value as compared to the other two **models** considered for hour 18:00 and was found to be the best fitting model. while from hours 19:00 and 20:00 model with interactions and the combined model were the best fitting **models** respectively.

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Reference [4] developed a method of **forecasting** south- east Brazil's hourly **electricity** **demand** and compared the results against a benchmark model. The development of the forecast model involved treating each hour of the day as a separate time series. Each model is based on a two- step decomposition of the time series. The first step is comprised of Fourier series, dummy variables and a linear trend. The purpose of the first step is to integrate seasonality, day of the week and special event effects into the forecast model. The second step involved estimating linear autoregressive **models** by regression and NN. The benchmark model in this study was a modified version of the Seasonal Integrated Autoregressive Moving Average (SARIMA) model. It was found that their proposed model outperformed the benchmark model and that the second step NN estimation performed comparatively poorly at horizon **forecasting**.

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is a complicated function of a large number of interacting variables. In this paper, several fuzzy and neuro-fuzzy **models** are presented and their results for **short**-**term** water **demand** **forecasting** in Tehran are compared. **Weather** data from three Tehran **weather** stations is weighted with the Thissen method and effective input data parameters are selected with regression of weighted effective **weather** and consumption data. The effective parameters include daily average temperature, relative humidity percent and last day, last week and last year water consumption. Consumption of all days between last day and the last week were also used. For the construction of fuzzy **models** a fuzzy rule-based approach is applied. The working rules are formulated from a set of past observations such as the relation between the parameters and the given input/output data sets. For neuro fuzzy modeling the toolbox function of Adaptive Neuro-Fuzzy Inference System (ANFIS) constructs a Sugeno Inference System (SFIS). The membership function parameters are adjusted using a back propagation algorithm in combination with a least squares method. Outputs of the fuzzy and the neuro fuzzy **models** demonstrate that the results of fuzzy **models** do not show high accuracy, but neuro fuzzy **models** produce better results. Besides, outputs of the neuro fuzzy **models** with just water consumption inputs have high accuracy. A comparison of outputs with the results of the Artificial Neural Networks (ANN) approach shows the capability of the ANFIS model to predict Tehran water consumption.

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The natures of long-**term** and **short**-**term** **demand** forecasts are quite different. For **short**-**term** **forecasting**, we are often interested in point forecasts (i.e., forecasts of the mean or median of the future **demand** distribution). For long-**term** **forecasting**, point forecasts are of limited interest as they cannot be used to evaluate and hedge the financial risk accrued by **demand** variability and **forecasting** uncertainty. Instead, density forecasts (providing estimates of the full probability distributions of the possible future values of the **demand**) are more helpful and necessary for long-**term** planning. For example, the National **Electricity** Market (NEM) of Australia asks for different levels of the Probability of Exceedance (POE) to be provided with **forecasting** (Power Systems Planning and Development, 2005). Another difference between **short**-**term** and long-**term** **demand** **forecasting** is in their use of meteorological information. It is well known that meteorological variables are the key inputs for most **demand** **models**. For **short**-**term** forecasts (up to one week ahead), such information can be obtained from **weather** services; but it is unavailable for long-**term** forecasts and so we require a feasible method to generate realistic future temperatures.

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There is rich literature providing references about **short**-**term** load **forecasting** with ANN [7-11]. Of many structures of ANNs, two structures are commonly used: the MultiLayer Perceptron (MLP) and the Kohonen network. Bakirtzis et al. [7] used a MLP ANN model for the electric power prediction using **weather** parameters and concluded that the prediction model has better accuracy than the statistical **models**. Khotanzad, et al. [9] also used the ANN model to predict the **short** **term** electric load. The availability of historical load data on the utility databases makes this area highly suitable for ANN implementation. ANNs are able to learn the relationship between the past, present, and the future **weather** variables and loads, combining both time series and regressional approaches. As is the case with time series approach, the ANN traces previous load patterns and predicts (i.e., extrapolates) a load pattern using recent load data. It can also use **weather** information for modeling. The ANN is able to perform non-linear modeling and adaptation. It does not need assumption of any functional relationships between load and **weather** variables in advance. We can adapt the ANN by exposing it to new data. Their ability to outperform traditional methods, especially during rapidly changing **weather** conditions and the **short** time required to their development, has made ANN based load **forecasting** **models** very attractive alternative for on-line implementation in energy control centers [2].

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Perfect knowledge of the **weather** variables over the forecast horizon (1 week) is assumed. **Forecasting** accuracy was compared between the ARIMA model, the TF model and the ANN model. Thirty forecast of one week each were generated, starting at midnight, for 30 consecutive days covering the period from the last week of May until the last week of June 2011. Table 3 presents the **forecasting** accuracy (MAPE) for the three **models** averaged over each of three different forecast horizons: first 24 hours (1:24), first 48 hours (1:48) and the full week (1:168). For the ANN model, due to large number of parameters to be identified, the non-convex nature of the estimation problem and the random starting parameters utilized for the training, each run produced slightly different results. The ANN model with best performing cross- validation after 10 runs was used for comparison to ARIMA and TF.

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needed since it can help to make right decision in expansion planning of **electricity** system and has big impact to profits [3,4]. Besides, it can reduce costs of operation and maintenance, and enhance continuity level of power supply [3]. With regards to this, one of the main methods that has been used successfully is fuzzy approach. Related to uncertainties of load characteristics and ability of fuzzy method to include human knowledge or experience in model such as in selecting input variables, and also to make smaller rule set when we have a lot of data caused fuzzy approach is suitable and interesting for load **forecasting** application [7,8]. Concerning its applications, paper of [2] proposeda fuzzy linear regression model for STLF which is composed for summer and winter seasons using **weather** parameters. In [8], the authors presented **forecasting** study for power system in India. In their case, fuzzy based STLF which implemented for peak, medium, and off-peak **demand** seasons gives better result than conventional method. Time and temperature variables are used as inputsfor the model. Meanwhile in the paper of [7], the authors conducted STLF study for Jordan context. A fuzzy inference model is presented with input namely last day and last week consumptions, last day and forecasted temperatures, **weather**, and type of day. Recently, **short**-**term** **forecasting** for **electricity** **demand** in Turkey using fuzzy logic and ANFIS is presented in [1]. Four day type **models** for each method are composed that is Monday, Weekday, Saturday, and Sunday **models**. Historical load **demand**, difference of temperature, and season data are inputs in their **models**.

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The first statistical regression model used in the building engineering field for energy consumption was introduced by Fels in 1986 [29]. The Princeton Scorekeeping Method (PRISM) is a univariate linear regression model linking the building energy consumption to the daily average outdoor air temperature. In the PRISM method, the building energy consumption is correlated to one **weather** regressor, the outdoor dry bulb temperature. These specific **models** are also called energy signatures. Other regressors characterizing the climate conditions are added to the temperature in statistical regression **models**, such as the relative humidity or the solar radiations when available. They have showed a better performance, at estimating the value of the heat loss coefficient of the building for instance [30]. The inclusion of time factors, such as day-type index, as a regressor of statistical regression **models** improved their performance [31]. A nonlinear relationship between the building energy consumption and the regressors can be described by polynomial regression **models**. The polynomial **models** are still considered as a linear regression in terms of the unknown parameters (coefficient of regression) which are estimated based on the measurements.

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Chapter2. Project Research ‐ 15 ‐ may need **forecasting** as well. Therefore, the selection of a suitable **forecasting** technique with proper input factors is vitally important for accurately **forecasting** **electricity** prices. In this thesis, the influential factors are not taken into account when **forecasting** the **short**- **term** **electricity** prices. The reasons for doing this are as follows. First of all, such influential factors, such as the amount of different types of reserve, power import and predicted power shortfall do not improve the forecast at all [53]. Secondly, the effect of temperature is incorporated with the load **demand**. According to ref. [54], considering the historical load **demand** as the input factor does not significantly improve the predictions of ANN and SVM **models**, which are adopted for our forecast. Finally, the extremely high prices are considered as the consequence of bidding strategies by the market players. Those speculative behaviors are unpredictable. Therefore, only the publicly historical price data are used to forecast the future prices in this thesis, as the natural correlation between the historical and future price data are believed.

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This study applies various methodologies to estimate **models** of water **demand** in El Paso, Texas, and compares the **short**-run **forecasting** accuracy of each model. The LTF ARIMA parameter estimates indicate that a 10 % rate increase will lead to a 3.2 % decline in water **demand** after a lag of three months. Impulse response functions generated using the VAR model also suggests that prices negatively impact **demand** after a multi-month lag. These outcomes imply that price increases can serve as an instrument for controlling the growth of water consumption in El Paso. However, the results also indicate that the full effect of rate changes may not be felt immediately as price information is typically gleaned from bills for water already consumed. Furthermore, consumers in El Paso appear to react rather quickly, within one month, to changing **weather** conditions. Thus, in the event of a severe drought, it is likely that non-price conservation measures such as public information campaigns will be needed in addition to appropriate price signals in order to rapidly curtail water use.

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This section reports the **forecasting** results for both the TLSAR and DASARIMA **models**. One of the most used measure of **forecasting** accuracy in the load fore- casting literature is the Mean Absolute Percentage Error (MAPE) (see [39] and [35]), which measures the pro- portionality between the error and the observed load. An important point deserves attention. Several authors (see, for example, [39]) achieve MAPEs as low as 2% when predicting the total daily load, but results of different **models** cannot be compared on different datasets because of the differences among load curves in different countries. For example, a load profile of a country with tropical **weather**, such as Brazil, is distinct from one like USA or United Kingdom. Hence, if different datasets are used, the same model(s) must be used, and the comparison should be made among data sets and not **models**. If the researcher wants to compare the performance of different **models**, the same data with the same **forecasting** period must be used.

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Literature on **short**-**term** load forecast show numerous experiments using sta- tistical and computational intelligence methods. These methods may be applied to uni- variate **models**, in which the load is written as a linear function of the past loads and usually forecast by time series techniques [2], or multivariate, which also consider the effects of so called exogenous variables, such as social, economic and, mainly, **weather**- related (air temperature, wind speed, cloud covers, for example).

A day ahead **demand** **forecasting** is essential for the efficient operation of **electricity** companies in the competitive **electricity** markets. Both the power producers and consumer needs single compact and robust **demand** **forecasting** tool for the efficient power system planning and execution. This research work proposes a day ahead **short** **term** **demand** **forecasting** for the competitive **electricity** markets using Artificial Neural Networks (ANNs). Historical **demand** data are collected for the month of January 2014 from PJM **electricity** markets. The work proposes the approach to reduce prediction error for **electricity** demands and aims to enhance the accuracy of next day **electricity** **demand** **forecasting**. Two types of **demand** **forecasting** **models**: classical **forecasting** and correlation **forecasting** **models** are proposed, explained and checked against each other. Proposed **models** are applied on real world case, PJM **electricity** markets for **forecasting** the **demand** on weekly working day, weekly off day and weekly middle day. The Mean Absolute Percentage Error (MAPE) for the two proposed **models** in the three respective cases is evaluated and analyzed. Results present that with all respects a day ahead **demand** **forecasting** through the correlation model are best and suitable for PJM **electricity** markets and produce less error with comparison of other classical **models**.

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Abstract: This paper presents novel intraday session **models** for price forecasts (ISMPF **models**) for hourly price **forecasting** in the six intraday sessions of the Iberian **electricity** market (MIBEL) and the analysis of mean absolute percentage errors (MAPEs) obtained with suitable combinations of their input variables in order to find the best ISMPF **models**. Comparisons of errors from different ISMPF **models** identified the most important variables for **forecasting** purposes. Similar analyses were applied to determine the best daily session **models** for price forecasts (DSMPF **models**) for the day-ahead price **forecasting** in the daily session of the MIBEL, considering as input variables extensive hourly time series records of recent prices, power demands and power generations in the previous day, forecasts of **demand**, wind power generation and **weather** for the day-ahead, and chronological variables. ISMPF **models** include the input variables of DSMPF **models** as well as the daily session prices and prices of preceding intraday sessions. The best ISMPF **models** achieved lower MAPEs for most of the intraday sessions compared to the error of the best DSMPF model; furthermore, such DSMPF error was very close to the lowest limit error for the daily session. The best ISMPF **models** can be useful for MIBEL agents of the **electricity** intraday market and the electric energy industry.

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Expert systems are new techniques that have emerged as a result of advances in the field of artificial intelligence. An expert system is a computer program that has the ability to reason, explain and have its knowledge base expanded as new information becomes available to it. To build the model, the ‘knowledge engineer’ extracts load **forecasting** knowledge from an expert in the field by what is called the knowledge base component of the expert system. This knowledge is represented as facts and IF-THEN rules, and consists of the set of relationships. Between the changes in the system load and changes in natural and forced condition factors that affect the use of **electricity** this rule base is used daily to generate the forecasts. Some of the rules do not change over time, while others have to be updated continually. The logical and syntactical relationships between **weather** load and the prevailing daily load shapes have been widely examined to develop different rules for different approaches. The typical variables in the process are the season under consideration, day of the week, the temperature and the change in this temperature. Illustrations of this method can be found in Rahman [31, 73] and Ho [63]. The algorithms of Rahman and Hazim [73] combine features from knowledge-based and statistical techniques, using the pairwise comparison technique to prioritize categorical variables. Brown [74] used a knowledge based load-**forecasting** approach that combines existing system knowledge, load growth patterns, and horizon year data to develop multiple load growth scenarios.

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We evaluate the **forecasting** performance of six different **models** for **short**-**term** **forecasting** of Macedonian GDP: 1) ARIMA model; 2) AR model estimated by the Kalman filter; 3) model that explains Macedonian GDP as a function of the foreign **demand**; 4) small structural model that links GDP components to a small set of explanatory variables; 5) static factor model that links GDP to the current values of several principal components obtained from a set of high-frequency indicators; 6) FAVAR model that explains GDP through its own lags and lags of the principal components. The comparison is done on the grounds of the Root Mean Squared Error and the Mean Absolute Error of the one-quarter- ahead forecasts. Results indicate that the static factor model outperforms the other **models**, providing evidence that information from large dataset can indeed improve the forecasts and suggesting that future efforts should be directed towards developing a state-of-the-art dynamic factor model. The simple model that links domestic GDP to foreign **demand** comes second, showing that simplicity must not be dismissed. The small structural model that explains every GDP component as a function of economic determinants comes third, “reviving” the interest in these old-school **models**, at least for the case of Macedonia.

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