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thumb In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating series of averages of different subsets of the full data set. It is also called a moving mean (MM)〔(Hydrologic Variability of the Cosumnes River Floodplain ) (Booth et al., San Francisco Estuary and Watershed Science, Volume 4, Issue 2, 2006)〕 or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms (described below). Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next number following the original subset in the series. This creates a new subset of numbers, which is averaged. This process is repeated over the entire data series. The plot line connecting all the (fixed) averages is the moving average. A moving average is a set of numbers, each of which is the average of the corresponding subset of a larger set of datum points. A moving average may also use unequal weights for each datum value in the subset to emphasize particular values in the subset. A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly. For example, it is often used in technical analysis of financial data, like stock prices, returns or trading volumes. It is also used in economics to examine gross domestic product, employment or other macroeconomic time series. Mathematically, a moving average is a type of convolution and so it can be viewed as an example of a low-pass filter used in signal processing. When used with non-time series data, a moving average filters higher frequency components without any specific connection to time, although typically some kind of ordering is implied. Viewed simplistically it can be regarded as smoothing the data. ==Simple moving average== thumb In financial applications a simple moving average (SMA) is the unweighted mean of the previous ''n'' data. However, in science and engineering the mean is normally taken from an equal number of data on either side of a central value. This ensures that variations in the mean are aligned with the variations in the data rather than being shifted in time. An example of a simple equally weighted running mean for a n-day sample of closing price is the mean of the previous ''n'' days' closing prices. If those prices are then the formula is : When calculating successive values, a new value comes into the sum and an old value drops out, meaning a full summation each time is unnecessary for this simple case, : The period selected depends on the type of movement of interest, such as short, intermediate, or long-term. In financial terms moving-average levels can be interpreted as support in a falling market, or resistance in a rising market. If the data used are not centered around the mean, a simple moving average lags behind the latest datum point by half the sample width. An SMA can also be disproportionately influenced by old datum points dropping out or new data coming in. One characteristic of the SMA is that if the data have a periodic fluctuation, then applying an SMA of that period will eliminate that variation (the average always containing one complete cycle). But a perfectly regular cycle is rarely encountered.〔''Statistical Analysis'', Ya-lun Chou, Holt International, 1975, ISBN 0-03-089422-0, section 17.9.〕 For a number of applications, it is advantageous to avoid the shifting induced by using only 'past' data. Hence a central moving average can be computed, using data equally spaced on either side of the point in the series where the mean is calculated.〔The derivation and properties of the simple central moving average are given in full at Savitzky–Golay filter〕 This requires using an odd number of datum points in the sample window. A major drawback of the SMA is that it lets through a significant amount of the signal shorter than the window length. Worse, it ''actually inverts it''. This can lead to unexpected artifacts, such as peaks in the smoothed result appearing where there were troughs in the data. It also leads to the result being less smooth than expected since some of the higher frequencies are not properly removed. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Moving average」の詳細全文を読む スポンサード リンク
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