Category: Uncategorized

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 […]

Most statistical models begin with some assumption about the world. In linear regression, we assume the relationship between inputs and output is a weighted sum, while in logistic regression, we assume the log-odds of a class is linear in the features. However, while they do give us interpretable coefficients and elegant closed-form solutions, they’re still […]

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 […]

The irony of the random variable (r.v.) is that although it takes on an “unpredictable” value every time, it’s not exactly random if we understand the shape of its distribution. This is why descriptive statistics matters a lot—they define the boundaries of the set of values an r.v. can take, otherwise known as, again, the […]

One assumption we discussed for linear regression is the independence of error terms. In that setting, we were typically dealing with cross-sectional data, where we assumed that observations don’t influence each other. Time series data is a little special. Over time, observations are rarely ever independent. If we observe that today’s stock price is high, […]