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In statistics, a moving average (rolling average or running average or moving mean [1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
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.
SAP: the APO-FCS package [17] in SAP ERP from SAP allows creation and fitting of ARIMA models using the Box–Jenkins methodology. SQL Server Analysis Services: from Microsoft includes ARIMA as a Data Mining algorithm. Stata includes ARIMA modelling (using its arima command) as of Stata 9. StatSim: includes ARIMA models in the Forecast web app.
ARMA is appropriate when a system is a function of a series of unobserved shocks (the MA or moving average part) as well as its own behavior. For example, stock prices may be shocked by fundamental information as well as exhibiting technical trending and mean-reversion effects due to market participants. [citation needed]
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned ...
The ADX combines them and smooths the result with a smoothed moving average. To calculate +DI and -DI, one needs price data consisting of high, low, and closing prices each period (typically each day). One first calculates the directional movement (+DM and -DM): UpMove = today's high − yesterday's high DownMove = yesterday's low − today's low
The average rate for shorter 15-year terms is 6.11% for purchase and 6.13% for refinance, down 3 basis points from 6.14% for purchase and 2 basis points from 6.15% for refinance this time last ...
The idea is do a regular exponential moving average (EMA) calculation but on a de-lagged data instead of doing it on the regular data. Data is de-lagged by removing the data from "lag" days ago thus removing (or attempting to) the cumulative effect of the moving average.