# Top PDF Load forecasting using time series models ### Load forecasting using time series models

Load forecasting 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 load forecasting 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 time series 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. ### Weighted Time Variant Slide Fuzzy Time Series Models for Short Term Load Forecasting

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 , 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. ### Study & Development of Short Term Load Forecasting Models Using Stochastic Time Series Analysis

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. ### Short Term Load Forecasting Using a Neural Network Based Time Series Approach

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  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  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 time series approaches are multiplicative autoregressive models, dynamic linear and nonlinear models, threshold autoregressive models and methods based on Kalman filtering. ### Forecasting Volatility with Copula-Based Time Series Models

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. ### Modeling and Forecasting Africa's GDP with Time Series Models

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. ### Machine Learning Models for Sales Time Series Forecasting

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] ### A Method of Hourly Load Forecasting by Time Series by Recycle of Predicted Values

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. ### Medium Term Load Forecasting using Time Series Regression and Fuzzy Logic for the State of Assam

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. ### Selection of Heteroscedastic Models: A Time Series Forecasting Approach

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. ### Bayesian graphical forecasting models for business time series

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] ### Multiagent Bayesian Forecasting of Time Series with Graphical Models

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. ### Scalable Models For Probabilistic Forecasting With Fuzzy Time Series

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”. ### Forecasting inflation in the euro area using monthly time series models and quarterly econometric models

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. ### Forecasting German day-ahead electricity prices using multivariate time series models

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. ### Wind power forecasting by nonparametric and parametric time series models

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. ### Time Series Forecasting Using Hybrid ARIMA and ANN Models Based on DWT Decomposition

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  has rationally combined both ARIMA and ANN models in order to considerably increase the forecasting accuracy. ### Forecasting Next-Day Electricity Prices by Time Series Models

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. ### Dynamic Bayesian models for vector time series analysis & forecasting

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] 