I am working on a paper and I need to check if the yearly increase in tax revenues makes sense i.e. if it fits the past trends of increases/decreases. I am not sure if I can conduct a predictive linear regression with x as my time series and y as the % increase in tax revenue.
For example, here is my sample dataset:
Year Revenue % change
2000-2001 68,305 1%
2001-2002 69,198 1.3%
2002-2003 83,099 20.07%
2003-2004 105,088 26.48%
2004-2005 132,771 26.34%
2005-2006 165,216 24.44%
Now based on these trends, I would like my model to predict a reasonable value for % change in 2006-2007. I know the value is 39.32%. If the predicted value from my model is way off from the actual value, I would say that the revenue has significantly increased. However, if these two values are not very different I would say that the change in revenue from 2005-2006 to 2006-2007 was not very significant. Can I achieve this given that my x values are time series?
Thanks in advance for the help!
As I'm sure you know, "significant" can be a rather misused word in statistics. We should carefully define the question you seek to pose and then use statistics to figure out where the threshold should be between "yes" and "no".
Perhaps you want to fit a model f(x) to the data from years 2000 to 2005, and then calculate the probability of getting a new data point of y=24.44% at x=2006 if that model f(x) were valid? If the probability is very small then there is "significant" evidence to reject the model f(x), suggesting that perhaps some economic condition has changed. You can use regression analysis to calculate a prediction interval at x=2006. Bates and Watts is a good introductory textbook on regression analysis.