Most people would blame the wireless. Since it's usually the cause.
But anyhow. I am not experience with that type of model you are using.
But minor questions :
Do you use alot of other wireless things near your computer or the router?
i.e wireless mouses, keyboards, headsets, etcetera.
Do you maybe even have a TV receiver or similar close? Or other equipment that uses wireless?
Because wireless equipment tend to intercept each others signals, thus making them a bit slower, and in worst cases not work at all.
But. If you try using wired? Put a wire in your route and to your computer.
If you can that is.
So can you check if the lag spikes disappears. If it does then it's obviously the wireless/router and not the internet itself.