I would not make much of the current gyrations, up and down. As the graph below shows, right now we are at the highest seasonal peak of layoffs/firings. Each year you can see a massive increase in initial claims just around the new year. This makes estimating the trend very difficult. (Translation, put very large error bars on data around the new year)
I wonder how many financial models out there reduce the weight of this data (and other series) when they are less accurate?
Here's the two data series on a year over year basis. While initial claims are still declining the rate of decline appears to have leveled off.
Source: Federal Reserve