Can I trust a regression if variables are autocorrelated?

#1
Hello everyone!
Both variables (dependent and independent) show autocorrelation effects.
When I run regression and estimate the residuals, they are not autocorrelated and durbin-watson statistic is small.
Can I trust my regression output, are the t-statistics reliable?
thank you :)
 

ledzep

Point Mass at Zero
#2
Does your data have time as a variable? Autocorrelation is common in spatial and temporal data, as the measurements which are close together in time would be more similar than the measurement further apart in time.

Now, your Durbin-Watson test is small, which means that there is a positive correlation i.e. that means the assumption of independence is not valid.
This means, your regression output won't be reliable.

One generic solution to address auto-correlation is to use lagged values as your explanatory variable.
 

trinker

ggplot2orBust
#3
ledzep said:
Does your data have time as a variable? Autocorrelation is common in spatial and temporal data, as the measurements which are close together in time would be more similar than the measurement further apart in time.
It's also an indication of heavily nested data that is generally approached with HLM such as a class, in a school, in district, in a county, in a state etc.
 
#4
Does your data have time as a variable? Autocorrelation is common in spatial and temporal data, as the measurements which are close together in time would be more similar than the measurement further apart in time.

Now, your Durbin-Watson test is small, which means that there is a positive correlation i.e. that means the assumption of independence is not valid.
This means, your regression output won't be reliable.

One generic solution to address auto-correlation is to use lagged values as your explanatory variable.
Yes, my variables are time series. They appear to be stationary and autocorrelated
Apologies, I made a mistake: my durbin-watson statistic is greater than upper critical value, so there is an evidence that error terms are not positively correlated. Also when I plot ACF for errors it looks like there is no correlation there and Ljung-Box statistic is smaller than critical value.
I was hoping I could avoid lagging as I don't really understand how to do it.
 

spunky

Doesn't actually exist
#5
it does seem like a mixed-effects regression/ multilevel/ hierarchical linear model might be your best option here... there is a way in which you can do it with regular OLS regression but it requres A LOT of dummy coding and interactions so it may/may not work..
 
#6
it does seem like a mixed-effects regression/ multilevel/ hierarchical linear model might be your best option here... there is a way in which you can do it with regular OLS regression but it requres A LOT of dummy coding and interactions so it may/may not work..
Oh dear.. thanks anyway.