The previous post established what stationarity means and how to recognise when a series lacks it. The airline passenger series fails on both counts: a clear upward trend and a repeating seasonal cycle, confirmed by an ACF that barely drops across 40 lags. This post is about what to do about it. The main tool... Continue Reading →
Toe Stop Drag Today I tried the toe stop drag, which is usually one of the first stopping methods people learn on quad skates. At first, the idea sounded simple: one foot stays in front carrying most of the weight, and the other foot drags behind using the toe stop. In practice, not that simple.... Continue Reading →
The previous posts built up a set of forecasting tools; SES, Holt-Winters, ARIMA, SARIMA, and each one quietly assumed something about the series it was working with. That assumption is stationarity. This post is about making that assumption explicit: what stationarity means, how to spot it, and what happens when a series violates it. Time... Continue Reading →
ARIMA captured the trend but left the seasonal cycle untouched. To handle both at once, SARIMA (Seasonal ARIMA) extends the model with a second set of parameters that operate at the seasonal lag rather than the observation lag. The result is a unified framework that handles trend and seasonality simultaneously. The parameters SARIMA(p,d,q)(P,D,Q)m has two... Continue Reading →
The previous post showed that AR, MA, and ARMA break down on the airline series because they assume stationarity. The common fix is to difference the series manually and then fit ARMA on the result. ARIMA formalises exactly this. The โIโ stands for integrated, and it refers to the differencing step being built directly into... Continue Reading →
Acceleration (But Not Yet) Today I looked into acceleration. Not because Iโm ready for it; Iโm definitely not. Right now, I still donโt feel stable enough to go faster on purpose. So Iโm continuing to focus on balance and control. But understanding acceleration early actually helps. It changes how you think about movement, even at... Continue Reading →
The smoothing methods from the previous posts; SES, DES, Holt-Winters work by taking weighted averages of past observations. This post introduces a different family: AR, MA, and ARMA models. Instead of smoothing, these treat forecasting as a regression problem. The predictors are either past observed values, past forecast errors, or a combination of both. The... Continue Reading →
SES models the level, while DES builds on this by incorporating a trend component. Naturally, this leads to the question of how to handle seasonality. For that reason, Triple Exponential Smoothing, better known as the Holt-Winters methodโextends the DES framework by introducing a third component. Specifically, it adds a seasonal term that captures recurring patterns,... Continue Reading →
The previous posts showed that SES, no matter how well you tune ฮฑ, always produces a flat forecast. The model only tracks the current level, and when the series is trending, that flat line consistently falls behind. Double Exponential Smoothing (DES), also known as Holtโs linear method, fixes exactly this by adding a second component:... Continue Reading →
Why Everything Falls Apart When You Speed Up Yesterdayโs focus was push and glide. Today I realized something frustrating. I can do the movement slowly, but as soon as I try to go a bit faster, everything breaks. Balance disappears. The form disappears. Confidence disappears. Apparently, this is normal. Stability First, Speed Later From what... Continue Reading →
