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 […]

One of my favorite topics in time series analysis is forecasting, which is the art of modeling memory. What’s memory? In a previous post, we explored this concept in depth through the lens of autocorrelation. On top of understanding how it’s measured, we established that it’s basically a non-negotiable heartbeat for any time series dataset. Now, if autocorrelation […]

In the context of time series analysis, as statisticians, we’re more than comfortable with thinking about data in the time domain. Here, we have values which evolve across time, and the questions we’re interested in often follow this perspective: Is the series trending? Is it noisy? Is today’s data dependent on yesterday’s? This view is […]