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I have a dataset of retail products which contains weekly sales for 12 different items in a single category. For each item, I have three dummy variables representing different types of advertising (FrontCover,BackCover,Inside) that could be run for that item that week. The data is weekly, and seasonal for a year so I have the frequency set to 52.

I have a two part question:

1. How can I convert the advertising coefficients to % lifts when the data is seasonal?

What I can do now is subset the data for a single item, and run multiple regression using tslm() from the R forecast package and read the coefficients to determine the lift for that item. However with tslm() I also have 51 other seasonal coefficients. How can I state this as a %?

    x
(Intercept) 601.7857143
data.subset$Ad.Front	249.4285714
    data.subset$Ad.Inside    243.4285714
data.subset$Ad.Back 78
season2 92.5
season3 113.2142857
season4 -31.71428571
season5 189.7142857
season6 -25.21428571
season7 124.5
season8 77.21428571
season9 71.71428571
season10    -25.5
season11    -161.2142857
season12    47.21428571
season13    -13
season14    -47.5
season15    9.214285714
season16    -33.5
season17    -76.5
season18    54.71428571
season19    52.71428571
season20    -90.78571429
season21    -27.28571429
season22    -124.2857143
season23    -101.2857143
season24    -23.71428571
season25    38.71428571
season26    -225.2142857
season27    -47.78571429
season28    -46
season29    27
season30    43.28571429
season31    1498.5
season32    791.7142857
season33    666.7857143
season34    1913.5
season35    1657
season36    119
season37    -205.7857143
season38    -420.2142857
season39    -152.7857143
season40    -360.2142857
season41    -123.7857143
season42    77.21428571
season43    -40.78571429
season44    -10.78571429
season45    -48.78571429
season46    73.21428571
season47    81.21428571
season48    26.21428571
season49    -1.785714286
season50    25.21428571
season51    -105.2142857
season52    -161.2142857

2. My second question is how do I extrapolate this for the entire category? If I have the above information for 12 items, how can I look at the coefficients collectively? That is, I want to say "Front page advertising has x% lift for Category A".

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51 seasonal coefficients is too much for your data set, you need at least 500 observations for this to make any sense at all. It's better to start with quarterly or monthly dummies, if you want to use dummies approach. Alternatively, you can use multiplicative seasonal ARIMA class of models. You could also de-seasonalize the series nonparametrically, e.g. Census X-13 tool, then work on seasonally adjusted series and ads variables.

Also, you have to think about the feedbacks: was advertising impacted by the sales? If that's the case, then you have to deal with this issues (endogeneity). One way is to introduce lags on ad variables.

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  • $\begingroup$ I'm finding this to be challenging. The life cycle of an individual product is about 18 months yet the category follows calendar seasonality. Additionally, a product can be advertised every other week. Some months may have 2 weeks of advertising, others may be just 1. Additionally, a month may have a weekly drive time like Black Friday. So I had used weekly data because it meshed with the weekly dummies. Another reason is that there is a relationship between seasonality & advertising. Products are heavily advertised during holidays, but holidays also naturally drive sales. $\endgroup$ – ElPresidente Mar 26 '15 at 19:26
  • $\begingroup$ When ads are correlated with seasonality, it's almost impossible to separate the impact of these factors in observational studies. Do you have experimental data: i.e. when you deliberately change advertising to see their impact on sales? $\endgroup$ – Aksakal Mar 26 '15 at 20:44
  • $\begingroup$ Not much historical data, but I'm thinking maybe I should do this without regression and just look at % gain against +/-1 week for advertisements (excluding heavily seasonal periods). Are you familiar with any research papers or reading I can do for time-series analysis specifically focused to retail? $\endgroup$ – ElPresidente Mar 27 '15 at 17:06

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