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Sabtu, 09 Juni 2018

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Custom Writing at $10 & moving averages
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In statistics, the average average average scrolling or average run ) is calculated for analyzing data points by creating a series of averages from different subsets of complete data sets. This is also called moving mean ( MM ) or rolling mean and is a type of impulse response filter is limited. Variations include: simple, cumulative, or weighted forms (explained below).

Given a fixed set of numbers and subset sizes, the first element of the moving average is obtained by taking the average of the initial fixed portion of the series of numbers. Then the subset is modified with "forward redirects"; ie, excluding the first number of series and including the subsequent value in the subset.

Moving averages are generally used with time series data to smooth short-term fluctuations and highlight long-term trends or cycles. The threshold between short and long run depends on the app, and the moving average parameters will be set accordingly. For example, it is often used in technical analysis of financial data, such as stock prices, returns or trading volumes. It is also used in economics to examine gross domestic product, employment or other macroeconomic time series. Mathematically, moving averages are a type of convolution and so can be seen as an example of a low-pass filter used in signal processing. When used with non-time series data, moving averages filter out higher frequency components without a dedicated connection to time, although usually some sort of order is implied. Simply seen it can be considered as data tidying.


Video Moving average



Simple moving average

Ketika menghitung nilai-nilai yang berurutan, nilai baru masuk that dalam jumlah dan nilai lama turun, yang berarti penjumlahan penuh setiap kali tidak diperlukan untuk kasus sederhana ini,

                                                    p               Ã,¯                                           SM                         =                                         p               Ã,¯                                                         SM                         ,                           prev                                                                              p                              M                                      n                         -                                            p                              M                -                n                                      n                             {\ displaystyle {\ overline {p}} _ {\ text {SM}} = {\ overline {p}} _ {{\ text {SM} }, {\ teks {prev}}} {p_ {M} \ over n} - {p_ {Mn} \ over n}}  Â

The period chosen depends on the type of movement of interest, such as short, medium, or long term. In financial terms, the moving average rate can be interpreted as support in a declining market, or resistance in a rising market.

If the data used is not centered around the mean, simple moving averages lag behind the latest datum point by half the sample width. A SMA can also be disproportionately affected by dotted old datum points or new incoming data. One characteristic of SMA is that if the data has periodic fluctuations, then applying the SMA period will eliminate such variation (the average always contains one complete cycle). But very regular cycles are rare.

For some applications, it is advantageous to avoid induced shifts by using only 'past' data. Therefore, the central moving average can be calculated, using data that are both placed on either side of the point in the circuit where the average is calculated. This requires using the odd number of datum points in the sample window.

The main drawback of SMA is that it allows through a large number of signals shorter than the length of the window. Worse, it's actually reversing it . This can cause unexpected artifacts, such as peaks in smoothed results to appear where there is a trough in the data. This also leads to less smooth results than expected because some of the higher frequencies are not deleted correctly.

Maps Moving average



Cumulative moving average

In cumulative moving averages , the data arrives in the ordered datum stream, and the user wants to get the average of all data up to the data stream point. For example, an investor may want an average price of all stock transactions for a particular stock up to the current time. As each new transaction takes place, the average price at the time of the transaction can be calculated for all transactions up to that point using the average cumulative, usually the average weighted average of the order n values ​​                        x              Â 1                          .         ...         ,                  x                 Â ·                                 {\ displaystyle x_ {1}. \ ldots, x_ {n}}   to the current time:

                                                 CMA                                       Â ·                           =                                  Â                x                       Â 1        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       Â                           ?                Â                x                                  n        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,       Â                  Â ·                                   .               {\ displaystyle {\ textit {CMA}} _ {n} = {{x_ {1} \ cdots x_ {n}} \ over n} \,.}  Â

Metode brute force untuk menghitung ini adalah untuk menyimpan semua data dan menghitung jumlah dan membagi dengan jumlah poin datum setiap kali titik datum baru tiba. Namun, dimungkinkan untuk memperbarui rata-rata kumulatif sebagai nilai baru,                               x                      n                     1                              {\ displaystyle x_ {n 1}}   menjadi tersedia, menggunakan rumus

                                                      CMA                                            n                     1                         =                                                            x                                  n                                  1                                                        n               ?                                                                    CMA                                                                    n                                                                    n                          1                                     .            {\ displaystyle {\ textit {CMA}} _ {n 1} = {{x_ {n 1} n \ cdot {\ textit {CMA}} _ {n}} \ over {n 1}}.}  Â

Thus the current cumulative average for the new datum point equals the previous cumulative average, times n , plus the most recent datum point, all divided by the number of points received so far, n 1. When all datum points arrive ( n = N ), then the cumulative average will be the same as the final average. It is also possible to store the entire datum point as well as the number of points and divide the total by the number of datum points to get the CMA each time a new datum point arrives.

Derivasi rumus rata-rata kumulatif sangat mudah. Menggunakan

                              x                      1                               ?                        x                      n                         =        n         ?                                           CMA                                            n                              {\ displaystyle x_ {1} \ cdots x_ {n} = n \ cdot {\ textit {CMA}} n {n}}  Â

dan juga untuk n 1 , terlihat itu

                                                                                                   x                                         n                                           1                                                                                                     =                  (                                     x                                         1                                                                      ?                                                      x                                         n                                           1                                                     )                  -                  (                                     x                                         1                                                                      ?                                                      x                                         n                                                     )                                                                  {\ displaystyle {\ begin {aligned} x_ {n 1} & amp; = (x_ {1} \ cdots x_ {n 1}) - (x_ { 1} \ cdots x_ {n}) \\ [6pt] \ end {aligned}}}   

The weighted average is the average that has the multiplier to assign different weights to the data at different positions in the sample window. Mathematically, moving averages are the convolution of datum dots with fixed weighting functions. One application removes pixelisation from digital graphic images.

Dalam analisis teknis data keuangan, rata-rata bergerak yang tertimbang (WMA) memiliki arti khusus dari bobot yang menurun dalam perkembangan aritmatika. Dalam n -hari WMA hari terakhir memiliki berat n , yang terbaru kedua n Â-1, dll., Turun ke satu.

                                                WMA                                    M                              =                                                 n                                 p                                     M                                                               (                n                -                1               )                                 p                                     M                    -                    1                                                              ?                               2                                 p                                     (                    M                    -                    n                                       2                   )                                                                                p                                     (                    M                    -                    n                                       1                   )                                                                          n                               (                n                -                1               )                              ?                               2                               1                                                   {\ displaystyle {\ text {WMA}} _ {M} = {np_ {M} (n-1) p_ {M-1} \ cdots 2p_ { (M-n 2)} p _ {(M-n 1)} \ over n (n-1) \ cdots 2 1}}   

Denominator adalah angka segitiga yang same dengan                                                        n              (              n                          1               )                         2                         .             {\ displaystyle {\ frac {n (n 1)} {2}}.}   Dalam kasus yang lebih umum penyebut akan selalu menjadi jumlah dari bobot individu.

The graph on the right shows how the weight decreases, from the highest weight to the latest datum points, down to zero. This can be compared with the weight in the exponential moving average that follows.

Moving Average| What is moving average method in Hindi - YouTube
src: i.ytimg.com


Exponential moving average

An exponential moving average (EMA) , also known as exponentially weighted moving average (EWMA) , is a type of infinite impulse filter filter that applies exponentially decreasing weighting factors. Weighting for each of the older datum decreases exponentially, never reaching zero. The graph on the right shows an example of weight loss.

EMA untuk seri Y dapat dihitung secara rekursif:

                           S                      t                         =                              {                                                                                Y                                          1                                                        ,                                                  t                   =                  1                                                                              ?                   ?                                      Y                                          t                                                                         (                  1                  -                  ?                   )                   ?                                     S                                          t                      -                      1                                                        ,                                                  t                   & gt;                  1                                                                                    {\ displaystyle S_ {t} = {\ begin {cases} Y1, & amp; t = 1 \\\ alpha \ cdot Y_ {t} (1- \ alpha) \ cdot S_ {t-1}, & amp; t & gt; 1 \ end {cases}}}  Â

Where:

  • The coefficient ? indicates the rate of weight reduction, the constant smoothing factor between 0 and 1. The higher the ? reduces long observations faster.
  • Y t is the value in the time period t .
  • S t is the EMA value for each time period t .

S 1 can be initialized in a number of different ways, most often by setting S 1 to Y 1 as shown above, although other techniques exist, such as setting the S 1 to the first 4 or 5 observations. The importance of the S 1 initialization effect on the resulting moving average depends on ? ; smaller ? the value of making the choice S 1 is relatively more important than the value ? bigger, because it's higher ? discounts longer observations faster.

Anything done for S 1 assumes something about the value before the data is available and always wrong. Given this, the initial results should be considered unreliable until the iteration has time to meet. This is sometimes called the 'spin-up' interval. One way to assess when it can be considered reliable is to consider the accuracy required of the outcome. For example, if 3% accuracy is required, starting with Y 1 and retrieving data after five time constants (defined above) will ensure that the calculation has accumulated into 3% only & lt; 3% of Y 1 will remain in the results). Sometimes with a very small alpha, this means a few useful results. This is analogous to the problem of using convolution filters (such as weighted average) with very long windows.

untuk apa saja yang cocok k ? {0, 1, 2,...} Berat titik data umum                              Y                      t             -            saya                              {\ displaystyle Y_ {t-i}}  adalah                    ?                             (                          1              -              ?                         )                                saya             -            1                            {\ displaystyle \ alpha \ left (1- \ alpha \ right) ^ {i-1}}   .

Pendekatan alternatif oleh Roberts (1959) menggunakan Y t sebagai pengganti Y t -1 :

                           S                      t             ,                           Ã, alternate                                     =        ?         ?                  Y                      t                              (        1        -        ?        )         ?                S                      t             -            1                              {\ displaystyle S_ {t, {\ text {alternate}}} = \ alpha \ cdot Y_ {t} (1- \ alpha) \ cdot S_ { t-1}}  Â

Rumus ini juga dapat dinyatakan dalam istilah analisis teknis sebagai berikut, menunjukkan bagaimana langkah EMA menuju titik datum terbaru, tetapi hanya dengan proporsi selisih (setiap kali):

                                                EMA                                    hari ini                              =                                  EMA                                    kemarin                                      ?                     [                                                         harga                                                hari ini                                          -                                              EMA                                                kemarin                                                  ]                           {\ displaystyle {\ text {EMA}} _ {\ text {today}} = {\ text {EMA}} _ {\ text {kemarin}} \ alpha \ kiri [{\ text {price}} _ {\ text {today}} - {\ text {EMA}} _ {\ text {kemarin}} \ right]}   

Memper                                         EMA                                 kemarin                              {\ displaystyle {\ text {EMA}} _ {\ text {kemarin}}}  setiap kali menghasilkan rangkaian kekuatan berikut, menunjukkan bagaimana faktor pembobotan pada setiap titik data p 1 , p 2 , dll., menurun secara exponential:

                                        EMA                                 hari ini                         =                  ?                      [                                         p                                  1                                                        (              1              -              ?               )                             p                                  2                                                        (              1              -              ?                            )                                  2                                                          p                                  3                                                        (              1              -              ?                            )                                  3                                                          p                                   4                                                         ?                        ]                               {\ displaystyle {\ text {EMA}} _ {\ text {today}} = {\ alpha \ left [p_ {1} (1- \ alpha ) p_2 (1-?) 2 2 p3 (1- α) 3 p4 {cdots \ right]}}  Â

sejak                    1                  /                ?        =        1             (        1        -        ?        )             (        1        -        ?                 )                       2                              ?             {\ displaystyle 1/\ alpha = 1 (1- \ alpha) (1- \ alpha) 2 cdots}   .

It can also be recursively calculated without introducing errors when initializing the first estimate (n starts from 1):

Source of the article : Wikipedia

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