# Analyzing ratios or numerator/denominator, with weights, measured over time at irregular intervals

I have gathered information on the rate increases allowed by a government regulator over about 17 years. As background, utilities in this area must apply to the regulator if they wish to raise their rates, in exchange for being granted a quasi-monopoly in the market.

In this period, there are 65 'usable' decisions -- those with sufficient documentation. Each decision in a rate can be characterized by several bits of information:

1. The utility company
2. The utility company's industry (electricity, wastewater, natural gas, etc.)
3. The total revenue increase sought by the utility
4. The total revenue increase granted by the regulator
5. The % increase in revenues sought by the utility (implicitly, their total revenues)
6. The % increase in revenues granted by the regulator
7. The utility's rate of return on its operations in the status quo
8. The projected rate of return after the rate increase

The 65 decisions are not evenly spaced over the 17-year period in question. To make matters potentially more complicated, some observations occur on the same date (four observations over two dates).

From an exploratory point of view, I'm interested in detecting inflection points over time in these data, particularly in terms of the percent of the sought revenue increase ultimately granted by the regulator (#2/#1, above), the rate of return projected after the revenue increase, and the % increase in revenues granted by the regulator. I'm also interested in what (for lack of knowledge in this field) I'd call breakpoints or cleavages -- are there ways I could run a 2 sample t-test on all pairs of samples that have no chronological overlap? (e.g., sample 1 from time t0 to tn, sample 2 from t(n+1) to tf)

From a research question perspective, I'm interested in whether the decisionmaking manifest in these data appear to have been impacted by a policy change that occurred at a known time, which (I would think), I could model as a categorical variable (0 = before change, 1 = after change) -- and if so, what was the sign of the impact, and was there a lag. Are there precautions I should be aware of with respect to the timed nature of these data? I consulted some materials on time series analysis but I'm a little confused as to what to do with irregularly spaced observations.

As a final note, I guess I'd add that I'm working in R, but am flexible on that point.

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Well most time series methods do require equally spaced observations, if the data is irregularly spaced it becomes tricky but if you search I bet you will find some literature on it and you may even find something that will be helpful. The idea of detecting an inflection point in a time series curve seems overly ambitious unless the nosie component is really negligable. –  Michael Chernick May 4 '12 at 19:35
Thanks for the feedback Michael. I am finding literature but I'm afraid some of it (ok, much of it) is going over my head. I also just noticed (and added to the post), that four of the 65 observations have non unique dates -- that is, two on the same date, two on another date. –  dubhousing May 4 '12 at 20:27