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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.
For example, for monthly data, if there is a seasonality effect, we would expect to see significant peaks at lag 12, 24, 36, and so on (although the intensity may decrease the further out we go). An autocorrelation plot (ACF) can be used to identify seasonality, as it calculates the difference (residual amount) between a Y value and a lagged ...
A simple moving average can be considered to be a sequence of temporal means over periods of equal duration. (If the time variable is continuous, the average value during the time period is the integral over the period divided by the length of the duration of the period.) [1]
In statistical quality control, the EWMA chart (or exponentially weighted moving average chart) is a type of control chart used to monitor either variables or attributes-type data using the monitored business or industrial process's entire history of output. [1]
The default Expert Modeler feature evaluates a range of seasonal and non-seasonal autoregressive (p), integrated (d), and moving average (q) settings and seven exponential smoothing models. The Expert Modeler can also transform the target time-series data into its square root or natural log.
According to the Federal Reserve, the Sahm Rule “identifies signals related to the start of a recession when the three-month moving average of the national unemployment rate rises by 0.50 ...
Example of historical stock price data (top half) with the typical presentation of a MACD(12,26,9) indicator (bottom half). The blue line is the MACD series proper, the difference between the 12-day and 26-day EMAs of the price. The red line is the average or signal series, a 9-day EMA of the MACD series.