“moving average”的概念、定义、翻译、参考文献-科学参考

moving average

Mathematics

For a sequence of observations x₁, x₂, x₃,…, the moving average of order n is the sequence of arithmetic means

$\frac{x_{1} + \dots + x_{n}}{n}, \frac{x_{2} + \dots + x_{n + 1}}{n}, \frac{x_{3} + \dots + x_{n + 2}}{n}, \dots .$

A weighted moving average such as

$\frac{x_{1} + 2 x_{2} + x_{3}}{4}, \frac{x_{2} + 2 x_{3} + x_{4}}{4}, \frac{x_{3} + 2 x_{4} + x_{5}}{4}, \dots$

may also be used. Its main purpose is to offer a view of the underlying behaviour of volatile sequences, especially those which have periodic variation.
http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averages Illustrations of the moving average from financial markets.

Statistics

A method of smoothing a time series to reduce the effects of random variation and reveal any underlying trend or seasonality. For the time series x₁, x₂,…, x_t the simple three-point moving average would replace the value of x_k, k=2, 3,…, t−1, with $moving average$
Often, different weights are used, as in this five-point moving average which could be used for k=3, 4,…, t−2: $moving average$
Moving average. The graph shows annual sunspot activity (in standardized units) from 1750 to 2000. There is a strong cycle with a period of around eleven years. Also shown is the eleven-year moving average. This removes the obvious cycle but reveals longer-scale fluctuations.
Another possibility is provided by Daniell weights: in the case of an average over m time points, the two end points are given weight , with the others each being given weight .
The four-point moving averages (appropriate for quarterly data) are $moving average$ Twelve-point moving averages are similarly defined and are appropriate for monthly data.
For a cycle with an even period, e.g. quarterly or monthly data, the centred moving averages are the arithmetic means of the successive moving averages as defined above. For example, in the case of quarterly data the first centred moving average is $moving average$ The advantage of these centred moving averages is that the resulting values are associated with a time point rather than the midpoint of the interval between two successive time points.
A graph of moving averages against time may show changes against time which are obscured by cyclical effects. A line of best fit to the moving averages is a trend line, and its slope is the trend. The trend line may be used to forecast future values (in the short term). For example, for monthly data the average deviation of the January data from the trend line can be used as an estimate of the future deviation of the January deviation from the trend line. The deviation can be measured as either a difference or a ratio.
Note that the use of moving averages can introduce spurious cycles (see Slutsky–Yule effect).

Economics

A class of data-smoothing techniques used in the analysis of economic and financial time series. A simple moving average is the arithmetic average of n previous data points. A weighted moving average assigns lower weights to older data points, with the weights declining linearly or exponentially; the latter method is also referred to as exponential smoothing. See also moving average process.

单词	moving average
释义	moving average Mathematics For a sequence of observations x₁, x₂, x₃,…, the moving average of order n is the sequence of arithmetic means $\frac{x_{1} + \dots + x_{n}}{n}, \frac{x_{2} + \dots + x_{n + 1}}{n}, \frac{x_{3} + \dots + x_{n + 2}}{n}, \dots .$ A weighted moving average such as $\frac{x_{1} + 2 x_{2} + x_{3}}{4}, \frac{x_{2} + 2 x_{3} + x_{4}}{4}, \frac{x_{3} + 2 x_{4} + x_{5}}{4}, \dots$ may also be used. Its main purpose is to offer a view of the underlying behaviour of volatile sequences, especially those which have periodic variation. http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averages Illustrations of the moving average from financial markets. Statistics A method of smoothing a time series to reduce the effects of random variation and reveal any underlying trend or seasonality. For the time series x₁, x₂,…, x_t the simple three-point moving average would replace the value of x_k, k=2, 3,…, t−1, with $moving average$ Often, different weights are used, as in this five-point moving average which could be used for k=3, 4,…, t−2: $moving average$ Moving average. The graph shows annual sunspot activity (in standardized units) from 1750 to 2000. There is a strong cycle with a period of around eleven years. Also shown is the eleven-year moving average. This removes the obvious cycle but reveals longer-scale fluctuations. Another possibility is provided by Daniell weights: in the case of an average over m time points, the two end points are given weight , with the others each being given weight . The four-point moving averages (appropriate for quarterly data) are $moving average$ Twelve-point moving averages are similarly defined and are appropriate for monthly data. For a cycle with an even period, e.g. quarterly or monthly data, the centred moving averages are the arithmetic means of the successive moving averages as defined above. For example, in the case of quarterly data the first centred moving average is $moving average$ The advantage of these centred moving averages is that the resulting values are associated with a time point rather than the midpoint of the interval between two successive time points. A graph of moving averages against time may show changes against time which are obscured by cyclical effects. A line of best fit to the moving averages is a trend line, and its slope is the trend. The trend line may be used to forecast future values (in the short term). For example, for monthly data the average deviation of the January data from the trend line can be used as an estimate of the future deviation of the January deviation from the trend line. The deviation can be measured as either a difference or a ratio. Note that the use of moving averages can introduce spurious cycles (see Slutsky–Yule effect). Economics A class of data-smoothing techniques used in the analysis of economic and financial time series. A simple moving average is the arithmetic average of n previous data points. A weighted moving average assigns lower weights to older data points, with the weights declining linearly or exponentially; the latter method is also referred to as exponential smoothing. See also moving average process.
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