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Selectively outputting relevant information from the current state allows the LSTM network to maintain useful, long-term dependencies to make predictions, both in current and future time-steps. LSTM has wide applications in classification, [5] [6] data processing, time series analysis tasks, [7] speech recognition, [8] [9] machine translation ...
For stationary time series, the ARMA model is used, while for non-stationary series, LSTM models are used to derive abstract features. The final value is obtained by reconstructing the predicted outcomes of each time series.
Recurrent neural networks (RNNs) are a class of artificial neural network commonly used for sequential data processing. Unlike feedforward neural networks, which process data in a single pass, RNNs process data across multiple time steps, making them well-adapted for modelling and processing text, speech, and time series.
A training data set is a data set of examples used during the learning process and is used to fit the parameters (e.g., weights) of, for example, a classifier. [9] [10]For classification tasks, a supervised learning algorithm looks at the training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model. [11]
According to Wold's decomposition theorem, [4] [5] [6] the ARMA model is sufficient to describe a regular (a.k.a. purely nondeterministic [6]) wide-sense stationary time series, so we are motivated to make such a non-stationary time series stationary, e.g., by using differencing, before we can use ARMA.
The time series included yearly, quarterly, monthly, daily, and other time series. In order to ensure that enough data was available to develop an accurate forecasting model, minimum thresholds were set for the number of observations: 14 for yearly series, 16 for quarterly series, 48 for monthly series, and 60 for other series.
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [1] [2] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.
Back_Propagation_Through_Time(a, y) // a[t] is the input at time t. y[t] is the output Unfold the network to contain k instances of f do until stopping criterion is met: x := the zero-magnitude vector // x is the current context for t from 0 to n − k do // t is time. n is the length of the training sequence Set the network inputs to x, a[t ...