## Friday, June 3, 2016

### Imagining the Future

Gray: "percent change from year ago" of Real GDP.
Red: The Hodrick-Prescott of the Gray line.
Black: A fifth order polynomial trend line placed by Excel. Yeah, I don't know what a fifth order polynomial is, either. But it seems to fit the red line pretty well.

 Graph #1
Imagine the Future: Copy the black line and paste it onto the end of itself. RGDP growth peaks at 2.3% in 2022, and eventually falls below zero. Shown below in green:

 Graph #2. Click Graph for Larger Image
In case you were wondering: I used Excel's trend line formula to calculate values for the green line. Subtracted 2 from the first calculated value to get the first predicted value and repeated that calc for each subsequent value.

I originally increased the Excel calc to 12 decimal places, but the accuracy was off quite a bit. So I went with 20 decimal places. Now the green line matches the black from 1948 to 2016.

If the RGDP growth trend falls as much in the next 68 years as it has in the last 68, the growth trend will be below zero. To me this says the decline we have had is more troubling than I thought.

// The Excel file

#### 2 comments:

Oilfield Trash said...

Polynomial

A polynomial trendline is a curved line that is used when data fluctuates. It is useful, for example, for analyzing gains and losses over a large data set. The order of the polynomial can be determined by the number of fluctuations in the data or by how many bends (hills and valleys) appear in the curve. An Order 2 polynomial trendline generally has only one hill or valley. Order 3 generally has one or two hills or valleys. Order 4 generally has up to three.

The Arthurian said...

... and I count 4 hills and valleys, 4 bends in my order 5 polynomial. Gotcha. Thanks Oilfield.

Actually, I did try extending the trend line 20 years out into the future. I thought it might generate more hills and valleys that I could use as a sim of the future. No way! The line just went up and up. I got only the four bends in the line, as shown, and no hint of another bend after that.