Here's an article I found that lists the various dates that updates went into effect. It's difficult to narrow down exactly when the declines in traffic occurred from the graph you attached (too many years of data compresses the relevant time scale), but if the dates of declines seem to correspond roughly with the dates of one or more of the updates (obviously, the decline falling on or after the date of the update, not before), then there's at least a chance the update had something to do with it.
If there's no correlation between the updates and the changes in your traffic, that doesn't mean Penguin and/or Panda had no effect, but it does make it less likely that's the primary cause. Panda, for instance, has been happening periodically since February of 2011, and Penguin since April of 2012. The most likely candidates look like updates that happened in late 2012/early 2013, but it's very hard to tell on the graph you provided how well your traffic losses correlate with the actual dates of the updates.
Of course, even if the dates seem to correspond it's still possible that Penguin and/or Panda had nothing to do with it. Could be one or more of your competitors hired good SEOs or started a new marketing campaign that's attracting more traffic that used to come to you. Or maybe some of the links pointing to your site were devalued for reasons unrelated to any black and white animals. Or the market changed and people simply aren't searching as often for what you offer. Or some technical issue has arisen with the site (unlikely since you haven't been actively working on it, but still possible). Or you got hacked in some subtle way that you haven't yet uncovered.
Sorry I can't be more definitive. You would probably benefit from having a reputable SEO perform a detailed analysis.