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All have the same trend, but more filtering leads to higher r 2 of fitted trend line. The least-squares fitting process produces a value, r-squared (r 2), which is 1 minus the ratio of the variance of the residuals to the variance of the dependent variable. It says what fraction of the variance of the data is explained by the fitted trend line.
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.
The default state of this template is collapsed. The articles linked here are located in Category:Technical analysis and in its subcategories; See also
In finance, a trend line is a bounding line for the price movement of a security. It is formed when a diagonal line can be drawn between a minimum of three or more price pivot points. A line can be drawn between any two points, but it does not qualify as a trend line until tested. Hence the need for the third point, the test.
Trend analysis is the widespread practice of collecting information and attempting to spot a pattern. In some fields of study, the term has more formally defined meanings. [1] [2] [3]
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 ...
Local regression or local polynomial regression, [1] also known as moving regression, [2] is a generalization of the moving average and polynomial regression. [3] Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced / ˈ l oʊ ɛ s / LOH-ess.
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]