Loadforecasting is a process of predicting the future load demands. It is important for power system planners and demand controllers in ensuring that there would be enough generation to cope with the increasing demand. Accurate model for loadforecasting can lead to a better budget planning, maintenance scheduling and fuel management. This paper presents an attempt to forecast the maximum demand of electricity by ﬁnding an appropriate timeseries model. The methods considered in this study include the Naïve method, Exponential smoothing, Seasonal Holt-Winters, ARMA, ARAR algorithm, and Regression with ARMA Errors. The performance of these different methods was evaluated by using the forecasting accuracy criteria namely, the Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Relative Percentage Error (MARPE). Based on these three criteria the pure autoregressive model with an order 2, or AR (2) under ARMA family emerged as the best model for forecasting electricity demand.
method [10,11] et al. In recent years, many researchers have used fuzzy timeseriesmodels to handle load fore- casting problems [12-15]. Liu et al. proposed a Time- variant Slide Fuzzy Time-series Model (TVS) for short- term loadforecasting , 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-seriesForecasting Model (WTVS) is presented. The WTVS model is divided into three parts, including the data pre- processing, the trend training and the loadforecasting. In the data preprocessing stage, the impact of random fac- tors will be weakened by smoothing the history data. In the trend training and loadforecasting 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 loadforecasting accuracy as compared to TVS models.
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 loadtimeseries. The noise input is assumed normally distributed with zero mean and some variance σt. Timeseriesmodels can use non weather as well as weather variables. These models are most widely used for loadforecasting.
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. Timeseriesmodels, 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  were the first to use the periodic ARIMA model of Box and Jenkins for STLF. This is a univariate timeseries 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  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 . Other timeseries approaches are multiplicative autoregressive models, dynamic linear and nonlinear models, threshold autoregressive models and methods based on Kalman filtering.
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.
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 timeseries 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.
Abstract: Electrical loadforecasting 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 timeseries from previous historical load values. Autoregressive neural network timeseries along with triple exponential smoothing is used and run continuously to further predict from the previously forecasted values.
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 loadforecasting is done for the state of Assam using Simple Average, Moving Average and TimeSeries Regression(ARIMA) method and a comparative analysis is done for these methods. Also, a fuzzy logic controller has been designed for error minimization.
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.
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”.
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.
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 timeseries 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 timeseries. 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.
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.
Over the years, various timeseriesforecastingmodels have been developed in literature. The random walk, autoregressive (AR), moving average (MA), and ARIMA are some widely recognized statistical forecastingmodels which predict future observations of a timeseries 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  has rationally combined both ARIMA and ANN models in order to considerably increase the forecasting accuracy.
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.
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).