Time Series Foundations
Stationarity, autocorrelation, ARIMA and state space models, seasonality and honest backtesting.
7concepts
133flashcards
50minutes of reading
- 01 Seasonality and Decomposition Splitting a series into trend, seasonal and remainder components, and the choice between additive and multiplicative structure that determines whether the seasonal pattern grows with the level.
- 02 Autocorrelation and ARIMA Reading the autocorrelation and partial autocorrelation functions to identify how much of a series is explained by its own past, and what the AR, I and MA components each represent.
- 03 Backtesting and Temporal Validation Random cross-validation on time series lets a model learn from the future, and the alternatives all trade honesty against how much of the data can be used.
- 04 Exponential Smoothing and the ETS State-Space Form How a one-line recursive average became a family of likelihood-based models with prediction intervals and automatic selection, and why that family remains the benchmark sophisticated forecasters most often fail to beat.
- 05 Stationarity and Differencing Almost every time series method assumes the statistical properties do not change over time, and the transformations that enforce that assumption also change what the model is predicting.
- 06 Vector Autoregression and Granger Causality How a VAR models several series as jointly driven by their own pasts, what a Granger causality test actually establishes, and the specific ways predictive precedence differs from causation.
- 07 The Kalman Filter and Linear Gaussian State-Space Models How two alternating steps, predict and update, compute the exact posterior of a hidden state in a linear Gaussian model, why the same machinery yields the likelihood and a smoother, and what breaks when the model is wrong.