Autoregressive-Moving-Average (ARMA) Training Algorithm
An Autoregressive-Moving-Average (ARMA) Training Algorithm is a model-based time series fitting model that provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the auto-regression and the second for the moving average.
- Context:
- It can be an input to an ARMA Model Fitting Algorithm.
- See: AR Model, MA Model, ARIMA Model, Autoregressive Model.
References
2018
- https://machinelearningmastery.com/time-series-forecasting-methods-in-python-cheat-sheet/
- QUOTE: The Autoregressive Moving Average (ARMA) method models the next step in the sequence as a linear function of the observations and resiudal errors at prior time steps. It combines both Autoregression (AR) and Moving Average (MA) models. The notation for the model involves specifying the order for the AR(p) and MA(q) models as parameters to an ARMA function, e.g. ARMA(p, q). An ARIMA model can be used to develop AR or MA models.
The method is suitable for univariate time series without trend and seasonal components.
- QUOTE: The Autoregressive Moving Average (ARMA) method models the next step in the sequence as a linear function of the observations and resiudal errors at prior time steps. It combines both Autoregression (AR) and Moving Average (MA) models. The notation for the model involves specifying the order for the AR(p) and MA(q) models as parameters to an ARMA function, e.g. ARMA(p, q). An ARIMA model can be used to develop AR or MA models.
Python Code # ARMA example from statsmodels.tsa.arima_model import ARMA from random import random # contrived dataset data = [random() for x in range(1, 100)] # fit model model = ARMA(data, order=(2, 1)) model_fit = model.fit(disp=False) # make prediction that = model_fit.predict(len(data), len(data)) print(yhat)
2016
- (Wikipedia, 2016) ⇒ http://wikipedia.org/wiki/Autoregressive–moving-average_model Retrieved:2016-4-13.
- In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the auto-regression and the second for the moving average. The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1971 book by George E. P. Box and Gwilym Jenkins.
Given a time series of data Xt, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The model is usually then referred to as the ARMA(p,q) model where p is the order of the autoregressive part and q is the order of the moving average part (as defined below).
- In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the auto-regression and the second for the moving average. The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1971 book by George E. P. Box and Gwilym Jenkins.
2015
- http://www.mathworks.com/help/econ/arma-model.html
- QUOTE: An ARMA model expresses the conditional mean of yt as a function of both past observations, yt−1,…,yt−p, and past innovations, εt−1,…,εt−q. The number of past observations that yt depends on, p, is the AR degree. The number of past innovations that yt depends on, q, is the MA degree. In general, these models are denoted by ARMA(p,q).
2014
- (Gupta et al., 2014a) ⇒ Madhu Gupta, Jing Gao, Charu C Aggarwal, and Jiawei Han. (2014). “Outlier Detection for Temporal Data: A Survey.” In: Knowledge and Data Engineering, IEEE Transactions on, 26(9).
- QUOTE: … Parametric models for time series outliers [15] represents the first work on outlier detection for time series data. Several models were subsequently proposed in the statistics literature, including autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), vector autoregression (VARMA), CUmulative SUM Statistics (CUSUM), exponentially weighted moving average, etc.