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 →
The previous post covered what Simple Exponential Smoothing is and how the formula works. This post is about actually applying it, checking the series structure, splitting the data, fitting SES, and measuring how well it did. Checking the structure of the series Before fitting anything, it helps to confirm what youโre working with. The airline... Continue Reading →
Up to this point, the methods weโve looked at; decomposition, regression with Fourier terms, have all been about understanding the structure of a time series: pulling apart trend, seasonality, and remainder into interpretable pieces. Those methods are useful for analysis, and they can be extended to produce forecasts. But thereโs a separate family of forecasting... Continue Reading →
In the previous posts we used dummy variables to handle seasonality in regression: one binary column per month, one per day of the week, and so on. That works well for clean cases, but it runs into real problems as soon as the data gets more complex. An alternative is to model seasonality using Fourier... Continue Reading →
Day 6 was the first session focused entirely on actual movement. Pushing off and gliding forward. Step Out and In The starting drill is static, no movement yet. Standing still, step one foot out to the side and bring it back. Left leg stays planted, right leg steps wide and returns. Ten reps each side.... Continue Reading →
X-11 and SEATS solved a lot of problems classical decomposition couldn't handle. But they came with their own hard constraints: monthly or quarterly data only, no direct support for other frequencies, limited user control over how flexible the decomposition should be. In 1990, a team led by Robert Cleveland at Bell Labs published a method... Continue Reading →
Classical decomposition works. The logic is sound, the steps are clear, and a century later the basic structure still shows up in every serious decomposition method. But by the 1950s, the people who actually had to produce official economic statistics, unemployment figures, retail sales, GDP, including staff at statistics agencies, ran into its limits constantly.... Continue Reading →
