I went into this trying to apply the class material to Meridian, and got a useful negative result instead. The classical time series toolkit works well on the kind of series it was designed for, and does essentially nothing on financial returns. Point at the variance instead and it works again.
IE group project, 2026. My part was the NVIDIA volatility model.
Part one: air travel demand
We forecast monthly air travel demand for the US and the EU, 530 observations between two official series, and fitted thirteen methods to each region. Everything was fitted on older data and judged on the final 18 months that no model had seen, then re-run at five different cut off points to check the ranking was not an accident of where we split.
We left the 2020 collapse in. Deleting it would have used hindsight nobody had at the time, and would have thrown away the recovery we were trying to forecast.
Holt-Winters won in both regions. The simplest method that allows the seasonal swing to grow with the market beat everything more sophisticated. SARIMAX, which let us write the pandemic in as two periods of disruption, cut the ARIMA family's error by 24% in the US and gave the best statistical fit on the EU data, and still lost on data it had not seen.
The lesson that carried over
In the EU the model that matched history most closely produced our worst forecasts. That is the same result I hit later when I re-graded Meridian in returns space, and it is the reason both projects choose on held out performance rather than fit.
The other finding was about uncertainty rather than accuracy. US demand was far easier to predict than EU demand, where the seasonal swing is roughly twice as large and the recovery took an extra year. Same method, same industry, materially less certainty. Anyone planning EU capacity should carry a wider error band than the US figures suggest.
Part two: financial returns
Then we pointed the same toolkit at equity returns, and it fell over. The level of a return series is close to unforecastable, which is what a reasonably efficient market should look like.
So we modelled the variance instead. I took NVIDIA, 6,670 daily returns from 2000 to 2026, and the rest of the group took GameStop, Intel, Microsoft and Tesla over a common 2015 to 2025 window so the five were comparable.
Every asset showed volatility clustering and every one needed heavy tails. The ARCH test rejected constant variance everywhere. Student-t innovations beat Gaussian in all five cases, with estimated degrees of freedom between 3.2 and 4.8, all below five and the lowest barely above the point where kurtosis stops being finite. Persistence ran from 0.978 to almost exactly 1.0, so a shock to volatility decays over months, not days. NVIDIA came out as EGARCH with t errors, forecasting about 2.97% a day, roughly 47% annualised.
The interesting disagreement
Asymmetry split the group. Microsoft and NVIDIA both produced the conventional equity leverage effect, where bad news raises future volatility more than good news does.
GameStop produced the exact opposite, a negative and significant term meaning positive shocks raised its volatility more. That is what a short squeeze looks like written into the variance equation, because the violent moves were upward.
There was a second disagreement worth keeping. GameStop had by far the fattest tails, but Microsoft had the most persistently autocorrelated volatility despite having the smallest moves of the five. How violent the clustering is and how regular it is are not the same property, and the two rankings do not agree.
What I took back to the platform
Do not try to forecast the level of a return series with a classical model. Forecast the variance, and use it for sizing and risk rather than direction. That is exactly what the risk component in Meridian does, treating volatility as a factor that feeds regime work and per-stock sizing.
It also gave me a cheap way to sanity check a signal. If something claims to predict returns as reliably as these models predict variance, the first thing to suspect is the test.