Exponential growth/decay point detection in a time series plot

I am working on a set of time series data. I am trying to locate the point at which an exponential growth begins in the time series. First I calculate a moving average with a fixed window size. Then I compute the rate of change of moving average of the time series plot and calculate the standard deviation of this signal. I am still not able to accurately detect the exponential growth/decay function with the standard deviation function. Any help on how to detect the starting point of the exponential growth/decay from the Standard deviation plot? I am also allowed to use any other approaches after calculating the rate of change of moving average to detect the beginning of the exponential function.

Answer 1

[Image Analyst]

Not sure why you thought that would give you the model parameters. You should use fitnlm() if you have the Statistics and Machine Learning Toolbox:

mdl = fitnlm(tbl, modelfun, beta0);

Attached is a full model for a sample set of decaying data.

[A VP]

Not sure if you understood my question right. My time series has at least 100,000 samples. It has a combination of ramps, straight points, exponential growth. I want to be able to detect the point at which the exponential growth begins.

[Image Analyst]

That could be because you never showed your data. There was no way we could have known that until you told us just now.

Anyway, ramps, flat portions, etc. could all be considered noisy parts of a dataset that could be fitted by an exponential curve, right? If you don't like that then you'll have to create some rules for what constitutes a flat part, a ramp, an exponential part, etc. given that you probably have real data with at least a little noise, not some perfectly noise-free theoretical data that fits curves like that.

Why do you need your data classified into these types of curves (flat, ramp, exponential)? And as you can imagine, where the different curves meet, the meeting location is not definite. I mean a flat part could be considered to extend into the exponential portion at the same time as the exponential portion extending into the flat part, so there are some data points that could legitimately be considered as either type of curve.

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer