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What Are Moving Averages?

Moving Average

A Moving Average (MA) is a statistical technique used to smooth out a Time Series, thereby canceling the effect due to random variation. A Moving Average (MA) is a trend-following or lagging indicator because it is based on past prices and if applied properly, it reveals the underlying trend, seasonal and cyclic components in the Time Series.

Moving Average as the term implies, drops Old observations of the Time Series as the new values come in, allocating equal weight to each averaged sets. The technique drops the first observation in the series to include a newer observation, thereby introducing a Lag.

The Moving Average is a better way of working with data involving trend, while the Mean is a better estimator when dealing with un-trended data.

The time lag depending on the time period you have decided to use, it also depends on your research ( a length of 100 MA will have more lag than that of 10 and will be most suited for a long term research while 10 for a short term)

SIMPLE MOVING AVERAGES

This is the easiest and simplest to compute Moving Averages technique, as it is carried out using the usual arithmetic mean procedure on a specific weight class, which will then travel through the Time Series observations, discarding the first data to include the most recent data.

E.g Assume I have a set of random Time Series data, say 13, 10, 15, 8, 12, 11 at times 1 to 6, which has a mean of 11.5 . The moving average procedure choosing a weight of 3.

(13+10+15)÷3 =12.6
then dropping the first observation 13 to include the 8

(10+15+8)÷3=11.6
Then dropping 10 to include 12 and so on.......

represented in the table below

time(t) y(t)     Averages   Errors(e)     e²

1          13
2          10
3          15         12.6          2.4              5.76
4           8           11             -3                9
5          12         11.6          -0.4             0.16
6          11         10.3          0.7              0.49

The SSE = 15,41
MSE =3.8525

In this example, the Moving Average is a better estimator than the Mean, let's use the Mean for the random data for example

Time(t)  y(t)    Averages  Errors   e²

1             13        11.5         1.5      2.25
2             10        11.5       - 1.5      2.25
3             15        11.5         3.5     12.25
4              8         11.5       - 3.5     12.25
5              12       11.5         0.5       0.25
6              11       11.5       - 0.5       0.25

SSE = 29.5
MSE = 4.92

it is estimator with the lowest MSE is always chosen as best and in this case, the Moving Average procedure produced the best with MSE =3.8525 higher than the Mean whose MSE is higher with a value of 1.07.

Looking at the calculations on the Moving Average example, you might not really detect the gradual downward trend in the data by the moving average procedure has just shown us the direction headed in the long run.

TAKE NOTE

🔊    The Moving Average is the best for data that exhibits trend and will also help in detecting the magnitude and directions of a trended Time Series.

🔊    Comparisons - if a shorter-term simple moving average is above a longer-term average, an uptrend is expected. On the other hand, a long-term average above a shorter-term average signals a downward movement in the trend

For Advanced forms of the topic Click On the following.
⏩   Weighted Moving Average

⏩   CENTERED MOVING AVERAGE

⏩   Exponential Smoothing Or Exponential Moving Average

🚏   Click Here To Get Back To The The Time Series Introduction Page

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About Jehoshaphat Ikpeme

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