Time-Series Forecasting of Financial Data

The problem

Highly volatile price series break the assumptions most forecasting models are built on. The aim was not a trading model but a careful look at how far classical time-series methods can go on real, noisy data.

Research question

Does additional model complexity actually improve forecasting performance?

Each series was tested for stationarity (rolling statistics and the Augmented Dickey-Fuller test), then made stationary by log transform, moving-average and exponential smoothing, and differencing. ACF and PACF plots guided the choice of AR and MA orders, and AR, MA and combined ARIMA models were compared by residual sum of squares and RMSE. auto_arima then searched orders by AIC, and a 30-day hold-out tested an ARMA model on unseen data.

Differencing took the Dogecoin series from non-stationary (ADF p = 0.142) to strongly stationary (p ≈ 3×10⁻¹⁴). ARIMA(2,1,2) on the log series gave an in-sample RMSE of 0.0475, and auto_arima selected order (5,1,4). On Air Passengers, ARIMA(2,1,2) cut the residual sum of squares from 1.50 (AR) and 1.47 (MA) to 1.03.

What it does not show

On the 30-day hold-out, the ARMA(1,5) forecast was nearly flat and its RMSE of 0.0915 was large against a test-period mean of 0.275. Price series like this carry hard limits on predictability, and in-sample fit says little about future accuracy.

Lessons

A better in-sample fit is not the same as a better forecast. Judge models on held-out data and against a naive baseline. The live demo does exactly that: it refits at every step and scores each forecast against a naive one.