Page 175 - Data Science Algorithms in a Week

Time Series Analysis

Sales for
November
Year 2010 2011 2012 2013 2014 2015 2016 2017 Average
Actual 16.9 16.5 18.7 20.5 20.4 22.4 23.7 24
sales
Sales on 14.0778333333 15.3568333333 16.6358333333 17.9148333333 19.1938333333 20.4728333333 21.7518333333 23.0308333333
the trend
line
Difference 2.8221666667 1.1431666667 2.0641666667 2.5851666667 1.2061666667 1.9271666667 1.9481666667 0.9691666667 1.8331666667
Sales for
December
Year 2010 2011 2012 2013 2014 2015 2016 2017 Average
Actual 17.4 20.1 19.7 22.5 23 23.8 24.6 26.6
sales
Sales on 14.1844166667 15.4634166667 16.7424166667 18.0214166667 19.3004166667 20.5794166667 21.8584166667 23.1374166667
the trend
line
Difference 3.2155833333 4.6365833333 2.9575833333 4.4785833333 3.6995833333 3.2205833333 2.7415833333 3.4625833333 3.5515833333
We cannot observe any obvious trends in the differences between actual sales and sales on
the trend line. Therefore, we just calculate the arithmetic means of these differences for
every month.

For example, we notice that sales in December tend to be higher by about 3551.58 USD
compared to sales predicted on the trend line. Similarly, sales for January tend to be lower
on average by 2401 USD compared to sales predicted on the trend line.

Making the assumption that the month has an impact on the actual sales from our
observations of the variation of sales across the months, we take our prediction rule:

sales = 1.279*year -2557.778
We then update it to the new rule:

sales = 1.279*year - 2557.778 + month_difference

Here, sales is the amount of sales for a chosen month and year in the prediction, and
month_difference is the average difference in our given data between actual sales and sales on
the trend line. More specifically, we get the following 12 equations and predictions for sales
for the year 2018 in thousands of USD:
sales_january = 1.279*(year+0/12) - 2557.778 - 2.401

= 1.279*(2018 + 0/12) - 2557.778 - 2.401 = 20.843

sales_february = 1.279*(year+1/12) - 2557.778 - 1.358
= 1.279*(2018+1/12) - 2557.778 - 1.358 = 21.993

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