I try to interpolate a variable (debt/GDP) ration, which is available on a annual basis into monthly. The data starts from January 1999 and ends September 2011.
Could you kindly advice what should be the first value of xx?

Many thanks,
Leon

I used the cubic spline method to interpolate a dependent variable for a regression. Is there any other way except for the Newey-West standard errors to deal with the serial correlation induced by the cubic spline interpolation?

Thank you

This is what I’ve been looking for. I tried it, and it works well.
By the way, I have a question for you. Does this method still work on data with seasonality?
I have a data set with seasonality, and I tried to verify if your method fits. When I plot two sets of data (the real and the splined one) in one figure, the splined data looks very smooth as compared to the real one, it seems like a trend of the real one. Is this good?

Thanks a lot!

It all depends on what you’re trying to accomplish. If you’re trying to do forecasting, or trying to find a best-fitting polynomial for the entire data set, you can use non-parametric regression methods, and basically fit a high-degree polynomial (basically, a huge Taylor expansion) to your data set. Stata will do this.

The problem with this is that it can be very computationally intensive. Also, how do you know the correct degree of the polynomial you should be fitting to your data? 10th degree? 10,000th degree? For more on this, just Google around for non-linear regression methods.

However, if instead you’re simply trying to estimate data values between known points, there are many interpolation methods available. Cubic spline is just one of many, and is a pretty crude and simple method compared to some of the others.

Could I use polynomial interpolation to generate a single polynomial over the whole set of data and use that instead? What is the advantage of using cubic splines?

Thanks

As a general rule, you should use the reported annual figures unless you have some highly compelling reason to interpolated the data between those points. The reason is simple: you don’t actually have knowledge of the data-generating process on a quarterly basis. You only know annual values. The data could be highly erratic on a quarterly basis, or perhaps linear, or follow some other unknown process. There is no reason a priori to assume the data-generating process follows a cubic polynomial between known points.

Another complication is that if you use cubic-spline interpolated values in regression analysis, you’ll be generating perfect autocorrelations between the quarterly values within each year. That is, they will be related perfectly by a cubic polynomial by design. Thus, you’ll need to use different standard errors that account for this, and be aware that autocorrelation is present in your residuals.

Bottom line: using cubic spline interpolation does not really give you “more” data than you originally began with. That’s simply not possible. So be careful about not giving a misleading impression that you “have” quarterly figures if you use a cubic spline, when in fact those are just approximated points based on the assumption of polynomial behavior of the underlying data-generating process between known points.

I have data from 1960-2011 to study Ecaudor’s import demand function. However, the data from 1960-1990 are in annual form; from 1990-2011 I can access the data in either quarterly or annual format. These data are taken from the IMF’s database.

Is it better to stick with annual data, or should I transform the annual data into quarterly data? Will this cause problems?

thank you very much

In that case, you just need to change the “x” values to reflect that you have data for the third month rather than the second. So your “x” values should be (3, 6, 9, …). I think that will work for you. Do the spline interpolation that way and just check that all the point for the 3rd, 6th, etc. months match your original data. Thanks.