Abstract: By the abovementioned technical solutions, the present disclosure provides optimizing a vector autoregressive model conforming to structural constraints of sparsity and acyclicity. A regularization term is introduced to the model to impose the sparsity structural constraint such that most off-diagonal coefficients of an autoregressive coefficient matrix are forced to zero values. One or more penalty terms are introduced to the model to impose the acyclicity structural constraint such that coefficients of the main diagonal are not causally self-related. The resulting model is then reformulated for computation as an augmented Lagrangian function, and further computed for different parameters in alternating iterations to make the computations tractable and within magnitude and precision limits of digital computers.

Abstract: Time series decomposition method and system are provided. Time series data including at least a seasonality component is received. A noise removal filter may be applied to the time series data. Furthermore, a trend component and the seasonality component are extracted from the time series data. A residual component may subsequently be extracted from the time series data based on the trend component and the seasonality component. Anomaly detection may then be performed on the trend component or the residual component to determine whether an anomaly exists in the time series data.

Abstract: Input time series data of a particular time length may be received, and pre-processed to obtain processed time series data. The processed time series data may then be decomposed into a plurality of pieces of time series data of the particular time length at different levels, and a detection of whether a piece of time series data at a particular level includes a periodic component candidate in a frequency domain may be performed. In response to detecting that the piece of time series data at the particular level includes the periodic component candidate in the frequency domain, a validation may be performed to determine whether the periodic component candidate in the piece of time series data at the particular level is a true periodic component of the input time series data in a time domain.

Abstract: By the abovementioned technical solutions, the present disclosure provides optimizing a vector autoregressive model conforming to structural constraints of sparsity and acyclicity. A regularization term is introduced to the model to impose the sparsity structural constraint such that most off-diagonal coefficients of an autoregressive coefficient matrix are forced to zero values. One or more penalty terms are introduced to the model to impose the acyclicity structural constraint such that coefficients of the main diagonal are not causally self-related. The resulting model is then reformulated for computation as an augmented Lagrangian function, and further computed for different parameters in alternating iterations to make the computations tractable and within magnitude and precision limits of digital computers.

Abstract: Input time series data of a particular time length may be received, and pre-processed to obtain processed time series data. The processed time series data may then be decomposed into a plurality of pieces of time series data of the particular time length at different levels, and a detection of whether a piece of time series data at a particular level includes a periodic component candidate in a frequency domain may be performed. In response to detecting that the piece of time series data at the particular level includes the periodic component candidate in the frequency domain, a validation may be performed to determine whether the periodic component candidate in the piece of time series data at the particular level is a true periodic component of the input time series data in a time domain.

Abstract: Time series decomposition method and system are provided. Time series data including at least a seasonality component is received. A noise removal filter may be applied to the time series data. Furthermore, a trend component and the seasonality component are extracted from the time series data. A residual component may subsequently be extracted from the time series data based on the trend component and the seasonality component. Anomaly detection may then be performed on the trend component or the residual component to determine whether an anomaly exists in the time series data.