Monograph Articles
Review articles, explainers, and learning notes.
Browse refined Monograph writing by subject, difficulty, topic, and series. These articles turn research, lecture material, and project learning into durable explanations.
From Observations to a Modelable Time Series
Why stationarity matters, how transformations remove changing structure, and what differencing does to the information in a series.
Understanding Dependence in Time Series
How autocovariance, autocorrelation, and linear filters reveal what the past contributes to the present.
ARMA Models as Dynamic Filters
How autoregressive feedback and moving-average innovations create memory, persistence, oscillation, and finite shock effects.
From Correlation Patterns to a Fitted Time-Series Model
How linear projection, PACF, and Yule-Walker equations turn lag relationships into candidate models and forecasts.
Diagnosing and Selecting Time-Series Models
How residual evidence, Ljung-Box testing, AIC, and AICc distinguish useful structure from overfitting.
ARIMA, SARIMA, and Multi-Step Forecasting
How differencing, seasonal structure, and innovation recursions turn persistent time series into forecasts with explicit uncertainty.
Exponential Smoothing as a State-Space Model
How recursive level, trend, and seasonal updates create adaptive forecasts and probabilistic uncertainty.
Daily Moment
Choose one photograph each day as the special moment worth remembering. The constraint of choosing one image forces attention, curation, and reflection. A photo becomes more meaningful when it is attached to a specific day, place, and st...