One method of establishing the underlying trend (smoothing out peaks and troughs) in a set of data is using the moving averages technique. The trend and seasonal variations can be used to help make predictions about the future – and as such can be very useful when budgeting and forecasting. This could be a weekly variation with certain days traditionally experiencing higher or lower sales than other days, or it could be monthly or quarterly variations. The seasonal variation refers to the regular variations which exist within the data.
The trend refers to the general direction the data is heading in and can be upward or downward.
Time series analysis can be used to analyse historic data and establish any underlying trend and seasonal variations within the data.
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Virtual classroom support for learning partners.Becoming an ACCA Approved Learning Partner.A search of the candidate sinusoids is conducted until a given mean-square criterion is satisfied. The relevant frequencies are estimated by an orthogonal search procedure. In the case of time-series analysis, a non-Fourier sinusoidal series approach is stressed. The model is constructed by adding parallel paths (each consisting of the cascade of dynamic linear and static nonlinear systems). In the case of nonlinear systems modeling, discrete-time Volterra series is stressed, or rather a more efficient parallel-cascade approach. A suboptimal, recursive, pairwise search of the orthogonal candidate data records is conducted, until a given least-squares criterion is satisfied. The ARMA identification algorithm presented does not require a priori knowledge of, or assumptions about, the order of the system to be identified or signal to be modeled. Sufficient detail and references are furnished to enable ready implementation, and examples are provided to demonstrate superiority over established classical techniques. Some recent, efficient approaches to nonlinear system identification, ARMA modeling, and time-series analysis are described and illustrated. The acoustic signal decomposition and its reconstruction from a reduced set of frequency domain samples is demonstrated on examples. Since the signal components can be considered as sparse in the dual polynomial Fourier transform domain, these samples can be omitted and reconstructed using the compressive sensing methods. Common form of disturbances are the sinusoidal signals, making some of the frequency domain signal samples unreliable. In real-world signals, some disturbances are introduced during the transmission. In this paper, we present a method for decomposition of multicomponent acoustic signals using the dual polynomial Fourier transform and time-frequency methods. Commonly, several components with different paths are received. Even if a simple signal is transmitted, it can change its characteristics (phase and frequency) during the transmission through an underwater acoustic dispersive communication channel. A signal which is transmitted through a dispersive channel is usually non-stationary. The acoustic waves transmitted through a dispersive environments can be quite complex for decomposition and localization. Both case-studies exhibit the superior performance of the proposed model when compared to state-of-the-art and traditional load forecasting schemes. The proposed model is designed to predict the hourly load for the next seven days and its effectiveness is evaluated in two different case studies namely the Hellenic interconnected power system and the isolated power system of Crete. Both RBFNNs and CNNs are trained with the Adam optimization algorithm within the Tensorflow deep learning framework. Thus, a neural network is formed consisting of a radial basis function (RBF), a convolutional, a pooling and two fully-connected layers. Then, a convolutional neural network (CNN) is deployed receiving as input the latter dataset. Following a two-stage approach, initially, a radial basis function neural network (RBFNN) is trained using three-fold cross-validation and the hidden layers of the best three RBFNNs are used to transform the input data to a four dimensional dataset.
For each cluster created, a new regression approach is applied to model locally the load forecasting problem. The proposed model initially clusters the input data using a novel fuzzy clustering method for creating an ensemble prediction. The proposed implementation combines attributes from ensemble forecasting, artificial neural networks and deep learning architectures. It is the energy market evolution that compels its participants to require load predictions whose accuracy cannot be provided by traditional means. A novel, hybrid structure for week-ahead load forecasting is presented.