What do significant autoregressive coefficients mean?

In summary: However, if you are doing something new, it would be helpful to include some formal tests to see if there are any unusual influences.
  • #1
vanitymdl
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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
 
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  • #2
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.
 
  • #3
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?
 
  • #4
vanitymdl said:
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.
 
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1. What is the definition of an autoregressive coefficient?

An autoregressive coefficient is a parameter that measures the relationship between a variable and its past values. It is used in autoregressive models, which are statistical models that use past values of a variable to predict its future values.

2. How do significant autoregressive coefficients affect a time series model?

Significant autoregressive coefficients indicate that past values of a variable have a strong influence on its current value. This means that the time series model is a good fit for the data and can accurately predict future values.

3. What do non-significant autoregressive coefficients indicate?

Non-significant autoregressive coefficients suggest that past values of a variable do not have a significant impact on its current value. This could mean that the time series model is not a good fit for the data and may not accurately predict future values.

4. How are autoregressive coefficients calculated?

Autoregressive coefficients are typically calculated using statistical software or programming languages such as R or Python. The most common method is to use the least squares method, which minimizes the sum of squared errors between the actual and predicted values.

5. Can autoregressive coefficients change over time?

Yes, autoregressive coefficients can change over time as the relationship between a variable and its past values may vary. This is why it is important to regularly update and reevaluate time series models to ensure they are still accurately predicting future values.

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