I have a univariate time series with 36 data points (monthly data for 3 years). The general trend of this time series is relatively steep decline, but for the most recent one year, it is almost flat and looks even increasing with a close look. So the goal is to confirm statistically that we have an inflection point. What is a good way to test this?
Solved – How to analyze an inflection point in univariate time series
hypothesis testingtime series
Best Answer
Try Chow test. The idea is to estimate the model on first 32 points, then forecast using the estimated model and compare to 4 points at the end. When you estimated the model, you got the error variance. You can compare the forecast error to the error variance. If it's too big, then you can claim that the model parameters have changed. Unless you have extremely tight fit in training sample (32 points), the power of this test is going to be very weak.
The same will go for any other statistical test. You are talking about showing the difference of the trend of only 4 observations from previous 32 observations. I'm afraid that you won't be able to accomplish your goal based solely on statistical tests. You'll need some support from business domain, understanding the underlying phenomenon.