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Forecasting season of sales

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Few facts, courtsey a news item in ET.

  1. During mango season, which typically strethes from April to June, battery makers such as Eveready and Nippo observe a steep spikes in sales.
  2. GSKCH has observed a huge spurt in the health drink, Horlicks, in period of exams, that is typically March.
  3. Dabur India also sells half of their annual volume of Shankha Pushpi (a drink that makes people intelligent :))  in period between January and March- the phase before board examination. The sale of product Chywanprash picks up on onset of winter.
  4. Reebok, Nike and Puma – sports brands – observe sharp spurt on sales (particularly women’s apparel and shoes) during the begining of a year.

While I leave the task of finding and establishing casuality of  above observations on imaginative mind of  readers; here from perspective of data analyst,  I will explore the famous air-passenger data of Box-Jenkins to see the trick in finding patterns, seasonality in data.

Airpassenger Data

Looking at the plot of monthly air passenger volume, we can infer

  • There seems to be a pattern in  number of passengers travelling.
  • Number of travellers seems to pick on June or July, then it goes down till the end of a year.
  • There has been a continuous increase in number of travellers YOY.
  • Amplitude of season changes increases with overall trend.
  • There is seasonality, but we can not be sure of the lag – time after which the data follows pattern- by merely looking at the plot.

Having observed these traits in the behaviour of air passengers the next question that pops up in mind is, Intuitively it does seem possible to forecast number of air passengers in year 1961 on monthly basis, but How ?

To answer the How, first let us plot a linear or exponential, the best fit trend line on above data.


We see that exponential function fits well in the data. Now,  to remove trend from data we subtract trend plot with actual plot.  In addition to  this transformation, we need to remove the varying/ increasing amplitude also. We need to stabilise variance. This can be done through logrithmic transformation; however, in this particular example since first transformation has made the series negative for few data points, a simple log won’t work. Taking log of magnitude will be a viable idea here. For a moment suppose we have stabalized the varying variance.

Our next step would be to find out the lag, time period after which history repeats itself, that is the curve start repeating itself.  This can be done looking at the autocorrelation matrix. Basicly, by autocorrelation we mean how data is correlated to itself. We lag the variable by one data point and see it’s correlation with unlagged variable. Then we lag it by two data points and observe it’s correlation with unlagged variable. The point where we get maximum correlation, we say that the variable repeats itself after that period.

Uptill now, we have been trying to perform all necessay calculation


Written by SK

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Written by SK

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