PITSTOP

If there’s anything we’ve learnt after spending time with hidden Markov models (HMMs), it’s that HMMs are based on a powerful idea: the world has a hidden state that evolves over time, and all we ever get to observe is noisy, indirect measurements of that state. HMMs gave us a clean framework for reasoning about […]

This is a story of cointegration: of common misconceptions about the relationship between multiple time series and how cointegration brings a new perspective to this. Much of the concept of cointegration I’ve encountered comes with in-depth technical details and derivations that often makes it more challenging than it looks, so I thought I’d like to […]

My fiancée has this supernatural ability she calls gut feeling where she’s able to somewhat accurately able to sense a hidden truth. The other day, she told me out of the blue that she felt a little nauseous, and then out of the blue, that perhaps so-and-so we’re broken up. Then we’d stalk their socials […]

Previously, we’ve taken a look at the continuous Fourier transform (FT), which is a powerful tool for decomposing a signal into its constituent frequencies. However, as we’ve briefly mentioned in the conclusion of that article, in practice, we never actually observe a continuous signal. Therefore, the tool is useless and we end our discussion here. […]

In my previous post, we delved quite deep into time series models like AR, MA, ARMA, and ARIMA. Essentially, by capturing different aspects of a series’ memory, these models usually effectively extract autocorrelation out of data into their structural parameters. I actually have to apologize—to simplify definitions, I intentionally omitted an important label: univariate. These […]

As a brief break from my usual, more rigorous content, I thought it’d be fun to explore some games. Of course, to stay consistent with the themes of my blogs, these games will still be rooted in statistics. As we’ll soon see, the puzzles revolve around how uncertainty behaves and how small changes can dramatically […]