Time Series Unobserved Components Model

I have real price data for 55 years and want to study its trends. for this i am trying to estimate the Unobserved Components (UC) Model. Which software will be better eviews or stata? Also what are the steps to estimate UC model?

• Here is some example with R if you would ever be interested. – Richard Hardy Feb 18 '15 at 9:08

Your second question (steps to estimate UC model) is too broad to be covered here. Below I give you some references.

• Some issues to be considered when fitting the basic structural model by maximum likelihood in the time domain are discussed in this document.
• Section 6 in this document describes the process of fitting these models by maximum likelihood in the frequency domain.
• The Expectation-Maximization algorithm is an alternative approach to estimate the parameters of the basic structural model, a discussion is given here.
• The Special Volume Statistical Software for State Space Method of the Journal of Statistical Software includes two papers and sample code related to EViews and Stata. Bayesian methods to fit state space models are illustrated in the issue number 4 of this volume.

The following textbooks are good references to study these methods:

• Durbin, J. and Koopman, S. J. (2001). "Time Series Analysis by State Space Methods". Oxford University Press.
• Harvey, A. C. (1989). "Forecasting, Structural Time Series Models and the Kalman Filter". Cambridge University Press.
• Thanx i have gone through the references and have been able to apply the model in stata version 12. I want to use a trend and cyclical components however i am facing the following problems: 1) for Unobserved Components (UC) Model can i use a log-difference (first difference) transformation instead of a log OR difference transformation? What is the difference between these? 2) How to I recognize the cyclical components? 3) What are the coefficients that I need to look for in order to estimate the results. – user68411 Mar 9 '15 at 5:03
• Taking differences removes the trend of the series. Taking logarithms may render the variance of the data more homogenous over time (especially when an increasing variance is observed) and can also alleviate the effect of potential outliers. If your model does not include a component for the trend you may need to take first differences if the data exhibit a trend. The other questions are not clear to me, but it seems you will be able to get some clues in the documentation of the software you are using. – javlacalle Mar 9 '15 at 14:46
• You may be interested in this post, which briefly introduces frequency-domain filters as a way to extract a cycle in time series. It is based on the work by D.S.G. Pollock and the software IDEOLOG. One of the appeals of this approach is that it provides a straightforward way to extract cycles in a range of frequencies. The spectrum or smoothed periodogram can be used to select the range of frequencies or cycles that are more relevant in the data. – javlacalle Mar 9 '15 at 15:01