## Moving-average :

Moving average is a technique used in technical analysis to smooth out short-term fluctuations in a data series and to highlight the underlying trend. It is calculated by taking the average of a certain number of past data points, typically over a specified period of time.

For example, let’s say we are analyzing the stock price of Company X over the last 10 days. To calculate the 10-day moving average, we would take the average of the closing prices for each of the last 10 days.

Suppose the closing prices for the last 10 days are:

Day 1: $10

Day 2: $11

Day 3: $12

Day 4: $13

Day 5: $14

Day 6: $13

Day 7: $12

Day 8: $11

Day 9: $10

Day 10: $9

The 10-day moving average would be calculated as follows:

(10 + 11 + 12 + 13 + 14 + 13 + 12 + 11 + 10 + 9) / 10 = $11.50

Now let’s say a new day comes and the closing price for that day is $8. We would then recalculate the moving average by dropping the oldest data point (Day 1) and adding the newest data point (Day 11):

(11 + 12 + 13 + 14 + 13 + 12 + 11 + 10 + 9 + 8) / 10 = $11.00

As you can see, the moving average provides a smoother representation of the data series, as it filters out the short-term fluctuations and highlights the underlying trend.

Another example of using moving average is in forecasting future values. Let’s say we are analyzing the monthly sales data for a particular product over the last 6 months. The data looks like this:

Month 1: $10,000

Month 2: $12,000

Month 3: $11,000

Month 4: $13,000

Month 5: $12,000

Month 6: $11,000

To forecast the sales for the next month, we can use a 3-month moving average. We would calculate the moving average by taking the average of the last 3 months:

(12,000 + 11,000 + 13,000) / 3 = $11,667

This tells us that we can expect the sales for the next month to be around $11,667. However, this forecast may not be very accurate because it is based on only 3 data points. To improve the accuracy of the forecast, we can use a longer moving average, such as a 6-month moving average, which would take into account all 6 months of data.

In conclusion, moving average is a useful technique for smoothing out short-term fluctuations in a data series and highlighting the underlying trend. It can also be used in forecasting future values, although the accuracy of the forecast can be improved by using a longer moving average.