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Let's say we want to predict the price of Big Mac for the year 2020. We have 2 indexes that we think might make an influence to Big Mac price determination.

|----------------|----------------|----------------------|----------------|
|     Date       | big_mac_price  |  burger_king_price   |   %inflation   |
|----------------|----------------|----------------------|----------------|
|     2020       |      ?????     |         1.8          |       3        |
|     2019       |       1.5      |         1.6          |       2        |
|     2020       |       2.1      |         2.5          |       1        |
|     2020       |       2.2      |         2.5          |       0        |
|----------------|----------------|----------------------|----------------|

Imagine that we don't have additional data. What kind of methodology would you use to estimate it? In ideal case scenario, after setting our prediction you will be able to set the weight of each of the index. For example:

  • Burger king price will affect it in 79%
  • Inflation will affect it in 21%

I know there might be missing information to this task, but the important thing here is the methodology used to get it, so feel free to invent more data if needed.

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    $\begingroup$ It really depends on the error distributions, their dependence structure, and the form of the relationship $\endgroup$ – Glen_b -Reinstate Monica Mar 20 at 12:09
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Great Question!

The general approach is called a ARMAX model enter image description here

The reason for the generality of approach is that it is important to consider the following possible states of nature which not only provide complications BUT opportunities..

  1. The big mac price might be predicted better using previous big mac prices in conjunction with activity in the two causals
  2. There might be discernable trends in big mac prices due to historical pricing strategy
  3. The big mac price may be related to burger king prices OR changes in burger king prices or the history/trends of burger king prices
  4. The big mac price may be related to inflation , changes in inflation or trends in inflation
  5. There may be unusual values in the history of big mac prices or burger king prices or inflation that should be adjusted for in order to generate good coefficients. Sometimes unusual values are recording errors.
  6. There may be omitted variables (stochastic in nature ) that may be important such as the price of a Wendy's burger .
  7. There may have been one or more variance changes suggesting the need for some sort of down-weighting to normalize volatile data.

The final model can be expressed as a Polynomial Distributed Lag model (PDL) or otherwise known as an ADL model (Autoregressive Distributed Lag).

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One of the possible solutions: Support Vector Regression or SVR. Using machine learning programming the solution will look something like this:

var samples = [[2.5, 0], [2.5, 1], [1.6, 2]];
var targets = [2.2, 2.1, 1.5];

var regression->train(samples, targets);

result = var regression->predict([1.8, 3]);
return result;

In this case the result would be 1.41879.

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