Free module · Quantitative toolkit
Time Series Analysis
Markets have memory. Today's price depends on yesterday's, volatility clusters, and trends persist — for a while.
signal · regime
The building blocks
- A time series is a list with a clock.
- A lag means an earlier entry in the same time convention.
- Separate the mean from the size of shocks
- Study memory, volatility and simple state transitions
- Infer hidden regimes using only available observations
Lessons in this module
- Start with time order, lags and differences
- Before GARCH: mean, shocks and changing variance
- Stationarity: the assumption every test makes and every market breaks
- Autocorrelation: momentum, mean reversion, or coin flips
- GARCH: volatility clusters, and you can model the cluster
- Cointegration: a stationary relationship to test
- Forecast horizons, EWMA, and model diagnostics
- Markov chains: a two-state model you can calculate by hand
- Hidden Markov models: predict, observe, update
Practice and apply
- From spread to holding period — Daily spread data. OLS of Δzₜ on zₜ₋₁ gives slope −0.15. Spread σ = 2.4 points. Current z = +4.8
- First difference — Current observation is 18; previous is 15. Find the difference.
- Variance update — Use ω=.00001, α=.1, β=.8, shock .02 and prior variance .0001. Find next variance.
- Predict stress — Current calm/stress probabilities [.8,.2]; calm-to-stress=.1, stress-to-stress=.7. Find tomorrow’s stress probability.
- Normalize evidence — Prior calm/stress [.78,.22], evidence likelihoods [.1,.6]. Find posterior stress.
Work through the practice exercises · Quant development tools