A What do significant autoregressive coefficients mean?

[vanitymdl]

I am building a business cycle index, which include 4 variables that drive the index. Each variable I also include autoregessive coefficients that are all significant and negative. I was wondering what is the significance of this? In other words, what is the significance of have autoregessive terms that are negative and significant

 

[FactChecker]

Just to clarify -- are you including the prior values of independent variables in a regression, or including autoregressive coefficients of independent variables in a time series analysis of some sort?

It is not a surprise to see negative autoregessive coefficients in business data. Suppose companies save up money during slow times for big purchases later. Or make big purchases and then conserve later. Those natural behaviors will show up as significant negative coefficients.

 

[vanitymdl]

To go into a little bit of detail I am creating a coincident business cycle based on the Stock and Watson Methodology. The model includes 4 main indicators (employment, unemployment, wages and retail sales). On that end, I included autoregressive terms for each indicator so I am including autoregressive coefficients of independent variable. Turns out that all of my autogressive terms for each indicator are significant and negative. I know this implied negative serial correlation, but is there any other significance to this?

 

[FactChecker]

To go into a little bit of detail I am creating a coincident business cycle based on the Stock and Watson Methodology. The model includes 4 main indicators (employment, unemployment, wages and retail sales). On that end, I included autoregressive terms for each indicator so I am including autoregressive coefficients of independent variable. Turns out that all of my autogressive terms for each indicator are significant and negative. I know this implied negative serial correlation, but is there any other significance to this?

As I implied above, there are natural ways that negative autocorrelations can occur. It is up to the subject-matter expert to theorize the reason for them. It is not a statistical question; it is an economics question.
1) Looking at your variables, it is clear that they are all highly correlated, so it is natural that anyone of them having a negative autocorrelation at a certain time lag would imply the same for the others.
2) You do not say what the time lags of your autocorrelations are or if you include several different time lags for each variable. If there is a negative correlation at one time lag, there should be a positive correlation at twice that time lag.
3) Much of your data is heavily correlated. You need to be careful not to include influences that are already included in other variables or time lags. If you are using an established procedure, that should already be taken care of.