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Yule-Walker-PCA Autoregressive Model (YWpcAR) to analyze and forecast many time-series individually with evolution of hidden components.
Overview
The Yule-Walker-PCA Autoregressive Model (YWpcAR) algorithm is developed to simultaneously analyze and forecast many time-series individually, assuming each time-series is influenced by evolution of "hidden components" (resulted from PCA). Here PCA standards for "principal components analysis". Different time-series is influenced by different sets of hidden components (PCs).
By applying objective data-driven constraints, the YWpcAR algorithm can estimate the influences of longer histories of the PCs. The algorithm accommodates wider ranges of values of model learning parameters. The wider ranges can further enhance the power of machine learning.
Current version of the YWpcAR algorithm estimates: (a) autoregressive coefficients of time-series, (b) filter coefficients to generate unobserved component (sum of PCs), (c) time-series of the unobserved component, and (d) forecasts of the observed time-series. Other estimates will be added in the future releases.
Highlights
- Introducing PCA into YW-AR modeling: 1. Applying principal components analysis (PCA) to sample variance-autocovariance matrix, C, in Yule-Walker (YW) equation of autoregressive (AR) model. 2. Replacing elements of the matrix C by PCA-based common components. 3. Replacing elements of the matrix and vector in the YW equation by the PCA-based common components of C. 4. Estimating AR model coefficients by the PCA-based YW equation. 5. In time-series forecast with the YW-PCA AR (YWpcAR) model, replacing observed time-series data by unobserved components associated with the PCs.
- Benefits of introducing PCA into YW-AR modeling: 1. Noise reduction due to dimension reduction when the number of PCs, m, smaller than the autoregressive order, p. 2. Avoiding over-fitting when estimating long-memory AR model of relatively larger value of order p.
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Dimension | Description | Cost/host/hour |
|---|---|---|
ml.m5.xlarge Inference (Batch) Recommended | Model inference on the ml.m5.xlarge instance type, batch mode | $0.10 |
ml.m5.xlarge Inference (Real-Time) Recommended | Model inference on the ml.m5.xlarge instance type, real-time mode | $0.10 |
ml.m5.xlarge Training Recommended | Algorithm training on the ml.m5.xlarge instance type | $0.10 |
ml.m4.4xlarge Inference (Batch) | Model inference on the ml.m4.4xlarge instance type, batch mode | $0.10 |
ml.g4dn.4xlarge Inference (Batch) | Model inference on the ml.g4dn.4xlarge instance type, batch mode | $0.10 |
ml.m5.4xlarge Inference (Batch) | Model inference on the ml.m5.4xlarge instance type, batch mode | $0.10 |
ml.m4.16xlarge Inference (Batch) | Model inference on the ml.m4.16xlarge instance type, batch mode | $0.10 |
ml.p3.16xlarge Inference (Batch) | Model inference on the ml.p3.16xlarge instance type, batch mode | $0.10 |
ml.m5.2xlarge Inference (Batch) | Model inference on the ml.m5.2xlarge instance type, batch mode | $0.10 |
ml.g4dn.2xlarge Inference (Batch) | Model inference on the ml.g4dn.2xlarge instance type, batch mode | $0.10 |
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Version release notes
The Yule-Walker-PCA Autoregressive Model (YWpcAR) algorithm is developed to simultaneously analyze and forecast many time-series individually, assuming each time-series is influenced by evolution of "hidden components" (resulted from PCA).
Current version of the YWpcAR algorithm estimates: (a) autoregressive coefficients of time-series, (b) filter coefficients to generate unobserved component (sum of PCs), (c) time-series of the unobserved component, and (d) forecasts of the observed time-series. Other estimates will be added in the future releases.
Additional details
Inputs
- Summary
The YWpcAR (Yule-Walker-PCA Autoregressive model) algorithm takes, as input data, multiple time-series data contained in a CSV (comma separated value) data table, in a format of a CSV text-string or a CSV text-file.
Each row of the data table is for values of an individual time-series (TS). Row header is the label or symbol of the time-series. Each column is for values of all time-series at a specific moment in time. Column header is the time-index or time-stamp of the moment.
- Input MIME type
- text/csv
https://github.com/i4cast/aws/blob/main/Yule-Walker-PCA_autoregressive_model/input/Weekly_VTS_6Yr.csv
https://github.com/i4cast/aws/blob/main/Yule-Walker-PCA_autoregressive_model/input/Weekly_VTS_6Yr.csv
Input data descriptions
The following table describes supported input data fields for real-time inference and batch transform.
Field name | Description | Constraints | Required |
|---|---|---|---|
Values of time stamp | Each row of the data table is for values of an individual time-series (TS). Row header is the label or symbol of the time-series. Each column is for values of all time-series at a specific moment in time. Column header is the time-index or time-stamp of the moment. The first data column is for the earliest time and the last column for the most recent time. The current version of YWpcAR requires equally spaced time-stamps. | Type: FreeText | Yes |
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For questions or call-back number, please send email to i4cast LLC at prod.i4cast@gmail.com .
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