I need to use Exponential Regression to forecast the future earnings of a company. I have the past 10 years of quarterly data.
I can do linear regression but the data is not in a linear fashion. It is more exponential in nature. I want to do an exponential transformation on the data and then use linear regression on that.
My question is, when I calculate the exponential growth from quarter to quarter, should I annualize this number or should I keep it as is.
For example, let's say I have the following data:
Date Profit Growth Annualized Growth Rate
01/01/2005 100.00
04/01/2005 101.50 1.50% 6.08%
07/01/2005 103.02 1.50% 6.02%
10/01/2005 104.00 0.95% 3.76%
01/01/2006 106.00 1.92% 7.63%
04/01/2006 107.40 1.32% 5.36%
07/01/2006 109.90 2.33% 9.34%
10/01/2006 110.30 0.36% 1.44%
01/01/2007 112.90 2.36% 9.35%
04/01/2007 114.30 1.24% 5.03%
07/01/2007 116.10 1.57% 6.32%
10/01/2007 117.80 1.46% 5.81%
01/01/2008 119.50 1.44% 5.73%
04/01/2008 121.30 1.51% 6.04%
07/01/2008 123.90 2.14% 8.60%
10/01/2008 125.00 0.89% 3.52%
01/01/2009 126.40 1.12% 4.44%
04/01/2009 128.80 1.90% 7.70%
07/01/2009 130.10 1.01% 4.05%
10/01/2009 132.00 1.46% 5.79%
01/01/2010 134.90 2.20% 8.72%
04/01/2010 136.20 0.96% 3.91%
07/01/2010 138.50 1.69% 6.77%
10/01/2010 140.20 1.23% 4.87%
01/01/2011 142.90 1.93% 7.64%
04/01/2011 145.10 1.54% 6.24%
07/01/2011 147.80 1.86% 7.46%
10/01/2011 149.40 1.08% 4.29%
01/01/2012 151.50 1.41% 5.58%
04/01/2012 154.00 1.65% 6.62%
07/01/2012 159.00 3.25% 13.02%
10/01/2012 158.20 -0.50% -2.00%
01/01/2013 162.00 2.40% 9.53%
04/01/2013 163.45 0.90% 3.63%
07/01/2013 165.00 0.95% 3.80%
10/01/2013 168.50 2.12% 8.42%
01/01/2014 170.30 1.07% 4.24%
04/01/2014 174.30 2.35% 9.53%
07/01/2014 175.00 0.40% 1.61%
10/01/2014 178.00 1.71% 6.80%
01/01/2015 181.50 1.97% 7.80%
04/01/2015 185.00 1.93% 7.82%
I want to take this data and say based on this, I project that the Profit in 4/1/2025 will be X.
What would be the best approach to do this?
My thinking is to use either the Growth or the Annualized Growth Rate (not sure which), do a linear regression on that. Then using that linear regression I could forecast that for quarter X the growth rate will be Y so therefore the profit should be Z. Then for quarter X+1 the growth rate will be Y+1 so therefore the profit should be Z+1. (not literally plus 1 but you get the point).
Am I on the right track?
Best Answer
This seems to be a lot simpler than you are imagining. You have quarterly data (please note, in an international forum, that presenting dates as month/day/year is not a universal default). You can fit an exponential directly in various ways, including as a generalized linear model with log link.
Here are some sample Stata results. Any good software should allow something similar if not identical. A quirk here is that for Stata quarterly dates are defined by an origin 1960q1 = 0, but this affects only the intercept below. An equation would be in those terms, with some rounding, exp(1.918 + 0.0149 quarter).
The key qualification here is whether you want to apply exponential smoothing instead. Otherwise the small print is that standard errors are very small, yet different assumptions about error family would change them. Nor does the model fit take any account of error dependence structure in time.
To get a forecast for a future time, plug in the future time to the equation.
In turn, this analysis may go further than is deserved, as these data are too well behaved for me to believe that they are real data. Similarly, the idea that you can get credible forecasts a decade ahead is one of the conventional absurdities in this area, so I leave that there.