# Find the moving average of the time series of quarterly production (in tons) of coffee in an Indian State as given below. After that, come...

Find the moving average of the time series of quarterly production (in tons) of coffee in an Indian State as given below. After that, come up with a trend line to approximate the production in future.

Production (in Tons)

## Answers

So, T = 9.9673-0.1135 ? Quarter

number Notes:

Any number of years moving average can be used. Quarterly moving average has been chosen in this case.

Since it is not centred, centering is done as shown.

The trend can also be obtained from the time series as required here.

The summation for quarter numbers and the actual production are obtained. The additional values of

summation of x2 (quarter number squared) and summation of xy (production ? quarter number) are

obtained from the additional columns indicated.

The values of a and b of the trend line equation can then be obtained as

shown. Though not required;

It was possible to obtain deseasonalised data before obtaining the tend line. This means a better

forecasting equation is obtained (moving average and trend equation would have been used)

Seasonal factor S is obtained by averaging the error variation A/T for each quarter as per the second table.

Since the summation of the average is not equal to 4 (seasonal aspect) it has to be corrected by the factor

4/3.941.

The deseasonalised data is then obtained. Notice the way here a multiplicative model was chosen because

of the way the seasonal aspect keeps on changing.

Determination of S

raphael answered the question on

*January 11, 2019 at 04:50*

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