Polynomial equation for sales forecast

[stat_sas]

Hi Experts,

I've 12 months data (Number of orders) and trying to explore a model which can be used for forecasting. I found 2nd degree polynomial model which seems to represent pattern in a better way.  Value of R²=0.70. Please see below the equation.

y = 308.77x² - 2662.8x + 31837

Can we use polynomial equation for sales forecast? My concern is when we go further into fututre orders per month will soon be doubled which business people will not accept. Any suggestions on this one please. I've attached chart for your review please.

Regards,

   
 
 
 
 
 
 
 
 
 
 
 

[PaigeMiller]

Hard to say, without more VERY BASIC information

What is x?

What is y?

[stat_sas]

Hi Paige,

x is month (From 1 to 12)

y is number of orders

Please see below table that contains month, orders and predicted orders. At month 20 predicted orders become almost 100,000.

Regards,

y = 308.77x2 - 2662.8x + 31837
month	Orders	Predicted Orders
1	26156	29482.97
2	32396	27746.48
3	27415	26627.53
4	24129	26126.12
5	30350	26242.25
6	21992	26975.92
7	24705	28327.13
8	36434	30295.88
9	28858	32882.17
10	37353	36086
11	43137	39907.37
12	42119	44346.28
13	49402.73
14	55076.72
15	61368.25
16	68277.32
17	75803.93
18	83948.08
19	92709.77
20	102089

[PaigeMiller]

The idea that month number has a quadratic relationship with orders ... well, let me just say that this is bizarre ... I wouldn't use such a model, even if the R-squared was 0.7. You have discovered a coincidence, not a predictive model.

Normally, forecasts of economic activity ... in this case orders ... are based upon time series models, perhaps with some seasonality built in, with X being some measures of customer's economic well being, or the economic well being of the economy as whole (or both)

[udo_sas]

Hello -

This might be a little bit off topic, but R square should not be used for time series forecasts. For one thing, it overlooks bias in forecasts. A model can have a perfect R square, yet the values of the forecasts could be substantially different from the values for all forecasts. Also, a model could have an R square of zero but provide perfect forecasts if the mean were forecasted correctly and no variation occurred in the data.

See: http://repository.upenn.edu/cgi/viewcontent.cgi?article=1182&context=marketing_papers for more details.

Thanks,

Udo

[PGStats · Accepted solution]

I agree with Paige Miller. Fitting a quadratic curve to a time series is perilous. With twelve points, you will necessarily have to make many assumptions to build any kind of predictive model. For example

1) There is a trend that will go on next year

2) There is a seasonal pattern that will repeat next year

Those could lead to the following additive model:

data test;

infile datalines missover;

input month Orders;

yearMonth = mod(month,12);

actual= not missing(orders);

datalines;

1 26156

2 32396

3 27415

4 24129

5 30350

6 21992

7 24705

8 36434

9 28858

10 37353

11 43137

12 42119

13

14

15

16

17

18

19

20

21

22

23

24

;

title;

proc gam data=test;

model orders = param(month) spline(yearmonth);

output out=gamout predicted;

run;

proc sgplot data=gamout;

series x=month y=p_orders/ group=actual;

scatter x=month y=orders;

yaxis min=0;

run;

[stat_sas]

Thanks PG for suggesting a solution.