Time Series Fundamentals
Once variables are indexed by time, ordinary modelling intuition breaks. Trend, autocorrelation, seasonality, structural breaks, and lag effects all create patterns that can easily be mistaken for signal. Time series methods exist to separate real temporal structure from statistical illusion.
Time changes the modelling problem
Cross-section vs time series
In cross-sectional modelling, observations are usually treated as independent. In time series, that assumption breaks immediately: today depends on yesterday, and often on much more than yesterday.
This dependence is not a nuisance around the model. It is the model.
Credit-risk applications
Time series logic appears everywhere in risk work: IFRS 9 macro-economic overlays, PIT calibration, stress testing, default-rate forecasting, and model monitoring.
If the temporal structure is mishandled, the result can look statistically impressive while being fundamentally invalid.
A useful order for learning time series
Start with stationarity
Before asking which model to use, first ask whether the series has stable statistical properties over time.
Then inspect autocorrelation
ACF and PACF reveal the shape of dependence and often tell you more than a long list of coefficients.
Then build with ARIMA components
AR captures memory, I handles non-stationarity, and MA absorbs forecast errors. Those three pieces define a large share of classical forecasting logic.
Then connect it to risk use cases
In IFRS 9 and stress testing, the real question is not just “can you forecast?” but “can you forecast in a way that is economically interpretable and defensible?”
Stationarity is the entry ticket
A stationary series has stable mean, variance, and dependence structure. Most classical time series tools rely on that assumption either directly or after transformation.
ACF & PACF — the fingerprint of the process
ACF shows correlation by lag. PACF shows the direct correlation left after removing the effect of intermediate lags. Together they are the fastest classical guide to AR and MA structure.
ARIMA(p,d,q) — memory, differencing, and error structure
ARIMA is still the core classical workhorse. AR carries forward past values, I handles non-stationarity, and MA carries forward past shocks. Move each component and watch the process change.
Macro-economic PD projection under scenarios
This is where the theory starts feeling useful. A macro-economic satellite model translates GDP or similar drivers into default-rate projections under base, optimistic, and adverse scenarios.
Time series models in credit risk
| Model | Main use | Stationarity required? | Main assumption | Typical risk use |
|---|---|---|---|---|
| ARIMA | Univariate forecasting | After differencing | Linear dynamics | Default-rate forecasting, macro projection |
| VAR | Multi-series interaction | Usually yes | Joint linear dependence | GDP, unemployment, DR systems |
| VECM | Cointegrated systems | I(1) + cointegration | Long-run equilibrium | Level relationships across macro series |
| Regression + ARMA errors | Macro → DR | Residual stationarity | Exogenous drivers | Standard IFRS 9 satellite logic |
| Markov-switching | Regime changes | Within regime | Discrete states | Boom / bust regime analysis |
| GARCH | Volatility | Usually returns stationary | Vol clustering | Market risk, stress volatility |
Concepts every validator should keep
ADF is not a ritual
Stationarity tests are not decorative. They decide whether classical inference is even valid in the first place.
The macro-model trap
Two trending variables can look strongly related without any real economic connection. Always be suspicious of “beautiful” level regressions.
Sometimes levels can still be valid
If a non-stationary combination is itself stable, then the right object is usually cointegration or VECM, not plain OLS in levels.
Economic effects are rarely immediate
Macro deterioration today often affects default rates with a delay. Lag choice is not just statistical tuning; it is economic timing.
Forecast accuracy is the real test
In-sample fit is cheap in short macro series. Out-of-sample forecast behaviour is where the model proves whether it knows anything real.
Weighted ECL is not linear
Probability-weighted scenarios matter because the loss function is nonlinear. A symmetric scenario set can still create asymmetric provision impact.
What to leave this page with
Time series modelling starts by respecting time itself. Stationarity, autocorrelation, lag structure, and structural breaks are not technical side notes; they are the substance of the problem.
The useful order is: first test stationarity, then inspect ACF and PACF, then build the right ARIMA-style structure, then bring that logic into macro-credit forecasting and IFRS 9 scenario modelling.
Once that structure is clear, macro models stop looking like ad hoc overlays and start looking like disciplined temporal systems.