How to extrapolate this simple trend line into the future for the purpose of forecasting in Matlab?

We have the following data points in variable data pertaining to a problem that we are solving:

                9996792524
8479115468
11394750532
9594869828
10850291677
10475635302
10116010939
11206949341
11975140317
11526960332
9986194500
11501088256
11833183163
13246940910
13255698568
13775653990
13567323648
14607415705
13835444224
14118970743


This corresponding date numbers are stored in a variable timevalues:

          735678.574305556
735710.586805556
735863.672916667
735888.539583333
735921.589583333
735941.590972222
735986.583333333
736021.481944444
736043.498611111
736063.5
736083.504166667
736223.35625
736250.45
736278.452083333
736314.327777778
736356.239583333
736383.209722222
736411.10625
736431.925694444


We fit a 9th degree polynomial to this data and then plot it as follows:

data9 = fit( timevalues, data, 'poly9', 'Normalize', 'on' );
plot(data9,timevalues,data);


Now we need to extrapolate this trend / polynomial into the future or for further values of timevalues on the X-axis. How do we do that?

UPDATE: Description of our problem We have bits per second observed on our border firewall device -- which is what these values are. There are a LOT of such values over 1 minute intervals in the last 4 years (more than a million). Not all values are useful because we just want to see how the trends in peaks is rising in time since we want to increase our load capacity before we hit 'max' some day. In other words, we are not interested in valleys or average values but 'peaks'. So we used the findpeaks() function in Matlab to find the peaks in our data (which is what the values above are). Now we are trying to fit a trend line on these peaks and extrapolate it to see how we need to increase capacity on border device.

• You don't. This is about the worst possible way of extrapolating a time series that could be conceived. Consider changing your question into one where you describe your data and objectives and ask for reasonable ways of achieving those objectives, rather than proposing a method that is guaranteed to fail: the answers will be much more helpful.
– whuber
Commented Jul 21, 2016 at 20:26
• @whuber Updated my question to include a general description of the problem in the end. Please advise on the best possible approach. Actual Matlab or R code might help better than theories. Thank you. Commented Jul 21, 2016 at 20:38