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method [10,11] et al. In recent years, many researchers have used fuzzy **time** **series** **models** to handle **load** fore- casting problems [12-15]. Liu et al. proposed a **Time**- variant Slide Fuzzy **Time**-**series** Model (TVS) for short- term **load** **forecasting** [13], the TVS model only uses his- torical data to predict the **load** changes. Taking into ac- count the affect of season, temperature, and random fac- tors, a Weighted **Time**-variant Slide Fuzzy **Time**-**series** **Forecasting** Model (WTVS) is presented. The WTVS model is divided into three parts, including the data pre- processing, the trend training and the **load** **forecasting**. In the data preprocessing stage, the impact of random fac- tors will be weakened by smoothing the history data. In the trend training and **load** **forecasting** stage, the seasonal factor and the weight of history data are introduced into the TVS model. The WTVS model is tested on the **load** of the National Electric Power Company in Jordan. Re- sults show that the WTVS model achieves a significant improvement in **load** **forecasting** accuracy as compared to TVS **models**.

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The power system **load** is assumed to be **time** dependent evolving according to a probabilistic law. It is a common practice to employ a white noise sequences a(t) as input to a linear filter whose output y(t) is the power system **load**. This is an adequate model for predicting the **load** **time** **series**. The noise input is assumed normally distributed with zero mean and some variance σt. **Time** **series** **models** can use non weather as well as weather variables. These **models** are most widely used for **load** **forecasting**.

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During the last few decades, various methods for STLF have been proposed and imple- mented. These methods can be classified into two main types; traditional or conventional and computational intelligence approaches. **Time** **series** **models**, regression **models** and the Kalman filter are some of the conventional methods. Expert system **models**, pattern recog- nition **models** and neural network **models** are some of the computational intelligence based techniques. Hagan and Klein [4] were the first to use the periodic ARIMA model of Box and Jenkins for STLF. This is a univariate **time** **series** model, in which the **load** is mod- eled as a function of its past observed values, with daily and weekly cycles accounted for. Papalexopoulos and Hesterberg [5] used the regression model for STLF. The disadvantage of the regression model is that complex modeling techniques and heavy computational ef- forts are required to produce reasonably accurate results [6]. Other **time** **series** approaches are multiplicative autoregressive **models**, dynamic linear and nonlinear **models**, threshold autoregressive **models** and methods based on Kalman filtering.

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Finally, we examine the (in)stability of the (relative) **forecasting** performance of the C-RV model with its different copula specifications and the log-HAR model. Fr this purpose, panel (a) in Figure 6 shows the ratio of the MSPE of the volatility forecasts obtained from the C-RV model with the Gumbel and conditional Gumbel copula specifications over the MSPE of the forecasts obtained from the log-HAR model, computed for moving windows of 500 observations. The relative MSPEs are below one except for a short period with moving windows ending in 2004-5, indicating that these C-RV specifications outperform the log-HAR model quite consistently. To put this result into perspective, panel (b) of Figure 6 shows the MSPE of the forecasts obtained from the log-HAR model together with the mean and variance of the square root of the realized range, again computed for moving windows of 500 observations. This graph shows that during 2004-5, both the mean and variance of volatility were rapidly declining. The MSPE of the log-HAR model declines correspondingly. Apparently, the C-RV specifications adjust to this change in market conditions more slowly, such that they are temporarily outperformed by the log-HAR model. On the upside, the copula-based volatility forecasts are considerably more accurate when they matter most, that is, during turbulent times with high and volatile volatility.

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Abstract- **Forecasting** economic growth for developing countries is a problematic task, peculiarly because of particularities they face. The model identification process in this paper yielded a random walk model for the Gross Domestic Product (GDP) **series**. We applied ARIMA **models** to get empirical results and bring to a close that the **models** obtained are suitable for **forecasting** the economic output of Africa. The adequate **models** were used for each of 20 Africa's largest economies to forecast future **time** **series** values. Based on the estimation results, we concluded that from 1990 looking forward to 2030, there will be an increasing GDP growth where the average speed of the economy of Africa will be of 5.52%, and the GDP could achieve $2185.21 billion to $10186.18 billion.

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with a long time period (2 years) for a specific store, Figure 11 shows the forecast in the case of historical 79. data with a short time period (3 days) for the same specific store[r]

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Abstract: Electrical **load** **forecasting** is a prime factor in planning of networks, saving costs and balancing supply and demand. As population increases, demand for consumer goods increases, all of which need electricity. While all possible ways are being found to generate electrical power, the ever increasing demand puts a strain on the resources. So a method to predict the **load** needs to be developed for cost effective supply, for planning networks, planning the generation and distribution. A method of **using** nonlinear autoregressive neural network model is used to predict the **load** values as a **time** **series** from previous historical **load** values. Autoregressive neural network **time** **series** along with triple exponential smoothing is used and run continuously to further predict from the previously forecasted values.

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ABSTRACT: An efficient forecast of power demand is a vital part of power system planning and operation. With the ever increasing demand for electrical energy in today’s world, it has become a challenging task to cope up with the demand. Hence a strong and efficient planning strategy is required to be adopted by power engineers that ensure both reliability and continuity of power supply to its consumers. In this paper **load** **forecasting** is done for the state of Assam **using** Simple Average, Moving Average and **Time** **Series** Regression(ARIMA) method and a comparative analysis is done for these methods. Also, a fuzzy logic controller has been designed for error minimization.

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Based on our findings, the in-sample model selection procedure favoured ARIMA (2,1,1)-GARCH (2,0)-std and ARIMA (1,1,0)-EGARCH (1,1)-std model while the out-of-sample model selection sufficed the choice of ARIMA (2,1,1)-EGARCH (1,1)-norm and ARIMA (1,1,0)-EGARCH (1,1)-norm **models** for the banks considered. Majorly, it is discovered that in each of the **models** se- lected through in-sample criteria are ill-conditioned. For instance, the constant term of the variance equation, ω of ARIMA (2,1,1)-GARCH (2,0)-std is zero which actually violates the constraint condition that requires ω > 0 . The impli- cation is that, this model is not suitable for **forecasting** long-run variance as it would collapse at zero. Again, in EGARCH (1,1)-std, the stationarity condition which requires ∑ p j β j < 1 , is violated. The implication is that, **forecasting** long-run variance **using** this model would not be realistic in that the variance Table 2. Diagnostic checking for heteroscedastic **models** of return **series** of diamond bank.

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In chapter 5, a new class of Bayesian forecasting model is developed which defines a conditional independence structure across the brand sales in a market and utilises any heuristic caus[r]

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In a supply chain, a demand (from a consumer) of a given component (produced by one manufacturer) generates a de- mand of parts (likely produced by several other manufactur- ers) that the component is composed of. This interdepen- dency among suppliers makes isolated **forecasting** by indi- vidual manufacturers less accurate. A cooperative forecast- ing is advantageous here as it benefits from knowledge and observations of all agents over their individual subdomains. Better **forecasting** will allow better planning and more cost- effective operation by all suppliers.

There are other approaches to embody the uncertainties of model parameters. Monte Carlo methods itself evoke the idea of **forecasting** combination and Ensemble Methods, as posed in Smith [ 2003 ], “In practice, ensemble **forecasting** is a Monte Carlo approach to estimating the probability density function (PDF) of future model states given uncertain initial conditions”. Forecast combination is not a new concept, see [ Clemen , 1989 ], and start from the idea to mix different sources to improve **forecasting**. This is sightly close to the concept of Ensemble Methods defined by Gneiting [ 2008 ] as “an ensemble prediction system consists of multiple runs of numerical weather prediction **models**, which differ in the initial conditions”. Also Leutbecher and Palmer [ 2008 ] states that “The ultimate goal of ensemble **forecasting** is to predict quantitatively the probability density of the state of the atmosphere at a future **time**”.

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From the combined forecasts of table 7, the contributions of the different economic variables to inflation according to the econometric model should be adjusted to obtain a precise explanation of the factors determining the final forecasts. Likewise, we will have to adjust the forecasts of the different price sub-indices by country and sector to provide a sector and geographic map of the estimated future values of inflation in the euro area. We thus obtain congruence between the geo-sectorial breakdown of inflation – which is necessary in any case to increase **forecasting** accuracy – and the contributions of the economic factors determining inflation forecasts. This is important, because the two sources of additional detail about future inflation are useful. The former informs of the nuclei (sectors through different countries) of more or less inflationist tension, and this is of interest for economic diagnosis and policy. The latter provides an estimation of the factors determining the inflation forecasts required by the authorities to design monetary policy and by economic agents to better assess inflation forecasts and, particularly, to form more accurate expectations related to changes in monetary policy.

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participants get to know the prices for all hours simultaneously – That means that it is not possible to forecast e.g. hour 10 by **using** information from hour 9, since the prices for hour 9 and 10 will be published together. Accordingly, every model that will be used in this work has to be refined in a way that only the realistically available data is considered in order to effectively simulate the **forecasting** process. To include this consideration into the econometric model, one could either use lags that are larger than the number of the currently estimated hour or it could be done by estimating each hour dependently and **using** lags of one, thereby referring to the day before. The second option which produces 24 independent **time** **series** has been used by Cuaresma et al. (2004) and, as it turns out, produced more precise forecasts than modelling the electricity prices as one single **time** **series**. This could be confirmed in preliminary datasets with this sample and additionally it has been found that the computation **time** decreases when only individual hours and autoregressive lags in the magnitude of 1 are estimated against the estimation of the complete sample and the respective lags in the magnitude of 24, which might also be due to the amount of exogenous variables that are included. While the estimation **time** on the used system, an Intel i7 processor with 2.7 GHz **using** STATA, is a few minutes for the individual hours, all hours taken together needed more than 60 Minutes estimation **time** for a similar model.

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The accuracy of the wind power forecasts can bring a lot of economic benefits. Wind can be described as a stochastic process, meaning that the power output from a wind power plant can vary substantially through **time**, and it is not controllable in the same way as that of conventional power plants. In many areas, the winds strength is too low to support a wind turbine and during these breaks, electricity demand must be supplied by other resources. So, the simplest benefit of an accurate wind forecast is that wind-generated energy can be planned and used by the utility, so that the utility avoids the need to consume fuel to produce electricity. Even more, researchers are addressing these problems by means of energy storage, which implies adding a battery or other types of storage devices to the overall system. The forecast improvement plays an important role in the area of storing of energy. By **using** energy storages the exceeded power could be used later when the consumption is greater than the need, this being a huge progress in the wind power field.

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Over the years, various **time** **series** **forecasting** **models** have been developed in literature. The random walk, autoregressive (AR), moving average (MA), and ARIMA are some widely recognized statistical **forecasting** **models** which predict future observations of a **time** **series** on the basis of some linear function of past values and white noise terms [1, 12]. As such, these **models** impose the inherent constraint of linearity on the data generating function. To overcome this, various nonlinear **models** have also been developed in literature. One widely popular among them is ANN that has many salient features [1, 13, 14]. Zhang [1] has rationally combined both ARIMA and ANN **models** in order to considerably increase the **forecasting** accuracy.

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To assess the prediction capacity of the two proposed **models**, different statistical measures are used. This capacity can be checked afterwards once the true market prices are available. For all three weeks under study, the average prediction error (in percentage) of the 24 h was computed for each day. Then, the average of the seven daily mean errors was computed and called mean week error (MWE). Also, the forecast mean-square error (FMSE) was computed for the 168 hours of each week. This parameter is the sum of the 168 square differences between the predicted prices and the actual ones. An index of uncertainty in a model is the variability of what is still unexplained after fitting the model that can be measured through the variance of the error term in (1) or (3). The smaller the more precise the prediction of prices. As the value of is unknown, an estimate is required. The standard deviation of the error terms, , can be used as such an estimate. This estimate is useful when true values of the **series** are not known.

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Finally , in section 8.4 of this chapter , one of the most popular methods in the econometric literature about multivariate time series modelling and forecasting , the so called BVAR Ba[r]

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The electricity spot price is not only dependent on the weekly and daily business cycles but also on other fundamental variables that can significantly alter this deterministic seasonal behavior. Recall, that the equilibrium between demand and supply defines the spot price. Both – demand and supply – are influenced by weather conditions, most notably air temperatures. In the short-term horizon, the variable cost of power generation is essentially just the cost of the fuel, consequently, the fuel price is another influential exogenous factor. Other factors like power plant availability (capacity) or grid traffic (for zonal and modal pricing) could also be considered. However, including all these factors would make the model not only cumbersome but also sensitive to the quality of the inputs and conditional on their availability at a given **time**. Instead we have decided to use only publicly available, high- frequency (hourly) information. In the California market of the late 1990s this includes system-wide loads and day-ahead CAISO **load** forecasts. In particular, the latter are important as they include the system operator‟s (and to some extent – the market‟s) expectations regarding weather, demand, generation and power grid conditions prevailing at the hour of delivery. The knowledge of these forecasts allows, in general, for more accurate spot price predictions. In the studied period (with some deviations in the volatile weeks 11-35), the logarithms of loads (or **load** forecasts) and the log-prices were approximately linearly dependent (the Pearson correlation was positive, ρ > 0.6, and highly significant with a p-value of approximately 0; null of no correlation).

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