User:Lisaholden/Temp/Time series steps.doc

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STEP 1Print a graph of the raw data to see if the time-series is seasonal/cyclical.

The length of the cycle will indicate how many points will be needed for the moving mean otherwise we use the number of time periods that are repeated each time.



The season/cycle repeats every 5 days.

So a five point moving mean will be needed.

STEP 2Work out the moving mean to ‘smooth out’ (eliminate) any seasonal effects and give an indication of the long term trend.



This tells us that the absences are reducing at a rate of 0.0643 students per day.STEP 3Find the trend line (line of best fit) and its equation. This shows us the long term trend.

STEP 4Work out the difference (this is the individual Seasonal Effect) between the raw data and moving mean.



STEP 5 Work out the mean of the Individual Seasonal Effects for each repeating time period.

Eg. Mean of Wednesday’s seasonal effects = [-5.6 + (-5.2) + (-13.4)] = -8.067

3

Each of these, are the Seasonal Adjustments that need to made to the trend-line to be able to give a better prediction than just using the trend-line alone.

This evens out the differences and makes all the peaks and troughs the same size rather than varying.

STEP 6 Using the equation of the trend line, substitute in the time period that you have been asked to forecast.

Eg. How many students are expected to be absent on the fifth Wednesday?

The fifth Wednesday is time period 23.

Equation of trend line No. of students = -0.0643 x Time Period + 16.443

No of students = - 0.0643 x 23 + 16.443

No of students = 14.9641

STEP 7.Because we have assumed the trend line to be LINEAR we must adjust the ‘outcome’ by ADDING the Seasonal Adjustment.

Eg. For the fifth Wednesday substituting into the equation of the trend line gave 14.9641

BUT we must add on the -8.067 that is the adjustment for Wednesdays.

So the predicted number of absences for that Wednesday is:

14.9641 + (-8.067) = 6.897 students

from trend line equationSeasonal adjustment



14 - 8.067

 = 6.897

The final forecast!14.9641 from trend line equation'-8.067 Seasonal adjustment (for Wednesdays)Forecast Area''