Need help with time series

[DGu]

I have time series survey data, with different respondents at each interval with an attitudinal DV (say, happiness). I'd like to compare two groups of respondents (say, males and females).

1) What is the best test to compare these two groups to determine whether they are significantly different overall from one another (i.e., average happiness)?

2) Also, what's the best test to compare the trends seen in the two groups (e.g., males and females trending in different directions in terms of their happiness over time)?

Thanks!

 

[hlsmith]

Well you first need to clarify the following, are there any individuals that are in both periods? If so, can you determine who they are?

 

[DGu]

No, each respondent is unique. No respondent is present in multiple periods.

 

[noetsi]

I am not sure how this is time series. It seems you are making a cross sectional comparison of gender. Unless you think these differences are changing over time. There is no simple way I know of to do time series so if you can avoid it you should.

The simplest way I know of to do a time series regression is either ARDL or regression with ARIMA error. I recommend the former as it deals better with non-stationarity. There are other alternatives such VAR or VECM, but if you have not done time series those are not good places to start

If all you are concerned with is the SE than there are HAC standard errors that in theory correct for this. I would warn, after years of trying to learn time series, that this is one of the more complex areas of statistics and (IMHO) people do time series when they probably do not need to. Cross sectional comparisons are not time series.

 

[DGu]

I am not sure how this is time series.

Fair enough. If having different respondents at each interval technically means it's not time series then I'm fine with that : ).

Unless you think these differences are changing over time.

Indeed, the data do in fact show changes over time.

The simplest way I know of to do a time series regression is either ARDL or regression with ARIMA error. I recommend the former as it deals better with non-stationarity.

Can the coefficients be compared to make an insightful comparison about what's going on with each group?

I would warn, after years of trying to learn time series, that this is one of the more complex areas of statistics and (IMHO) people do time series when they probably do not need to.

I'm more than happy to find a simpler solution to analyzing my data, so long as that solution is suitable for the data and the research question.

Many thanks!

 

[noetsi]

I am not sure what you mean the data shows changes over time.

This is what I mean (its called a structural break technically)

A one unit change in X leads to a five unit change in Y from 1970 to 1975. In 1976 the process changes, for many reasons and a one unit change in X leads to a 9 unit change in Y (or alternately has no impact at all from then on).

ARDL, to address another point, shows the relationship between factors over time (including that a given X might have an impact at time 1, time 2 later, etc. So X occurs this month and has an immediate impact on Y. It also has a different immediate impact next month. And possible 6 months from now. If you have this type of issue you need to do time series, probably with a structural break as well.

 

[DGu]

I am not sure what you mean the data shows changes over time.

(Hypothetically...) Early on the males and females exhibit very similar degrees of happiness, but over time one group goes up and the other goes down, such that a significant gap emerges between male and female happiness.

This is what I mean (its called a structural break technically)

A one unit change in X leads to a five unit change in Y from 1970 to 1975. In 1976 the process changes, for many reasons and a one unit change in X leads to a 9 unit change in Y (or alternately has no impact at all from then on).

Makes sense. Although in my case the independent variable (gender) is categorical, so it doesn't have units that change.

ARDL, to address another point, shows the relationship between factors over time (including that a given X might have an impact at time 1, time 2 later, etc. So X occurs this month and has an immediate impact on Y. It also has a different immediate impact next month. And possible 6 months from now. If you have this type of issue you need to do time series, probably with a structural break as well.

OK, I'll further explore all of this. Thanks!

 

[noetsi]

Technically a categorical variable has a one unit change I believe although I could be wrong.