In one of the comments to my previous post about the Simple Moving Average on LinkedIn, a reader mentioned that they use a Weighted Moving Average with their own weighting scheme. This can work well although defining the weights can be a nuisance: a Weighted Moving Average of order 12 needs 12 weights that someone … Read more
Have you ever tried to identify ARIMA for your data? The old school Box-Jenkins methodology implies analysing ACF/PACF plots and selecting the orders iteratively. This approach has a fundamental flaw I discussed in one of my earlier posts. Brute force does not help either: even p ≤ 3, d ≤ 2, q ≤ 3 gives … Read more
And here is another forecasting method that is hard to beat in practice. In a recent competition, it gave data scientists huge headaches and even outperformed some powerful ML methods. What’s the name of this beast?! Simple Moving Average! The idea behind the Simple Moving Average (SMA) is to take the average of the last … Read more
ETS is powerful. ARIMA is powerful. But when you need both, you are typically left with fitting ARMA to the residuals of ETS, which biases the parameters. There is a much neater solution: combine them in one state space model to estimate everything jointly… The standard practice when ETS is not enough to capture the … Read more
Here is a confession. I don’t like the idea of “forecastability”. I think it does not bring value and can be harmful in some cases. Let me explain. One of the definitions I see on the internet: “A measure of the degree to which something may be forecast with accuracy”. This definition is so disturbing … Read more
A reader left a comment under the MSARIMA post on LinkedIn saying that in order to compare ARIMAs via information criteria, we need to make sure that the candidate models have the same order of differencing. They are right — for the conventional ARIMA. BUT! In the state space formulation, the problem disappears. Here is … Read more
ARIMA has been a workhorse for decades. But the standard implementations quietly hard-code assumptions: one seasonal cycle, Gaussian errors, regressors handled separately etc. This is fine for textbook well-behaved data. But what do you do when you face real data? The conventional implementations (statsmodels or pmdarima in Python, stats in R) do their job well: … Read more
This is a public service announcement! We had to shift things around, and our open course, Demand Forecasting Principles, now runs in November. Eight live sessions over four weeks, every Tuesday and Thursday from 3pm to 5pm UK time, starting 3 November. Nikos Kourentzes and I will deliver it together. The course is built around … Read more
There is another forecasting method that is extremely popular, hard to beat, and has no parameters to estimate. It also has “Naïve” in its name. Do you know what I’m talking about? It is called “Seasonal Naïve”. While the simple Naïve copies the last observed actual into the future as a forecast, the seasonal one … Read more
Why train a forecasting model on one-step-ahead errors when you care about 10-step-ahead accuracy? This is the core motivation behind multistep losses in dynamic models. This has connection with the so-called “direct forecasting strategy”. And here what it is and how to work with it in Python. Conventional maximum likelihood estimation minimises one-step-ahead errors. It … Read more