I have the three variables with two variables having quarterly data and for 3rd I have yearly data. Can we convert the Yearly data of 3rd variable into quarterly data?
To convert the yearly data into quartely data you can use "Ecotrim" software for univariate and multivariate temporal disaggregation developed by Eurostat. Based on mathematical/statistical techniques, Ecotrim produces high frequency estimates (short term statistics) starting from low frequency data.
Normaly, yes, Ecotrim is free. Other possibility, you can also other try to test a similar progam. See the web sites of eurostat, OECD, ECB for more information of Ecotrim.
There are a few methods which can disaggregate time-series but besides the original annual series you need to have a quarterly/monthly indicator series from which the seasonal cycle will be inferred.
These benchmarking and extrapolation methods try to conserve as much as possible from the quarter-to-quarter changes in new series with simultaneously having a binding constraint that the sum of four quarters is same as one value in annual series.
arg min {x} t(x)Ax such that Ra=c, where x is error between bench-marked series a and original higher frequency series b. Vector c contains annual values and R is a matrix of constraints.
Naveed, it depends on the series you are looking on. If you let me know the series, would be helpful. Yes, using ecotrim is a general option. Agree with Youssef.
Please keep in mind that all tests will be joint tests about the model and the way you change the frequency. So my aim is to go on with the original data, and avoid converting series. Instead of GDP you can also use the industrial production index, or an other proxy. This makes more sense to me.
I would suggest aggregating the quarterly data into yearly data to match with the GDP variable in your model. This is because variable measurement errors can cause more serious damage to estimation results as compared with the aggregation bias problem.
In addition to Ecotrim, the packages for temporal disaggregation are available in different platforms e g. in R package tempdisagg is used for this purpose. But this kind of disaggregation is based on some assumptions (about seasonality etc) and I agree with Philippe that any econometric model based on disaggregated data will have a joint test problem. The best solution is to use alternative proxy variable.
If you have data with mixed frequency you can also think to used "Mixed Data Sampling Models (MIDAS), Ref for example: Ghysels, Eric, Arthur Sinko, and Rossen Valkanov. "MIDAS regressions: Further results and new directions." Econometric Reviews 26.1 (2007): 53-90.
I want to go by Badhani and Philippe s comments. You need to disaggregate the yearly data for meaningful analysis and comparison. You can then weight the cost and benefits
The idea is that measurement error in variables can destroy your results. And by changing frequencies, you will include measurement error into your analysis. If in the model y=ax+b measurement error is in x, you have a huge problem and a will be biaised. If it is in y, it is ok.
I don t know what your model is, but that is something you have to considéré, I feel.
I have similar problem with 12 independent annual time series variables for 18 year period, but my chair advised that the period is not enough for a parametric regression, therefore, it has to be disaggregated to quarterly time series. Any advise will be highly appreciated. How can I disaggregate these variables, any recommended software is ok.