Lecture 2 : time series analysis

Time series data

Observations collected from the same unit repeatedly over time (e.g., daily, monthly, yearly).

Stationarity

A time series is (weakly) stationary if its behavior does not change over time.

Autocovariance

The autocovariance only depends on the distance (lag) and not on time.

Forecasting

The process of predicting future values based on current and past information.

Point forecast

Predicting a single value for a future observation.

Prediction interval

A range that gives a measure of uncertainty around a forecast.

AR(1) model

A time series model where the current value depends on its previous value plus an error term.

MA(q) model

A moving average model where the current value depends on current and past error terms.

ARMA(p,q) model

A model that combines autoregressive (AR) and moving average (MA) components.

Serial correlation

When the error terms of observations are correlated, violating the assumption of independence in OLS regression.

Newey-West standard errors

A method to correct standard errors in the presence of serial correlation and heteroskedasticity.

Out-of-sample R^2

Measures whether the forecasting model performs better than using the historical mean as a predictor.

Ljung-Box test

A statistical test used to check if residuals (errors) of a time series model are white noise.

Mean reversion

The tendency of a time series to return to its long-term mean over time.

Residual analysis

The examination of the difference between predicted and observed values to check if residuals behave like white noise.

Overfitting

A modeling error that occurs when a model is too complex, capturing noise instead of the underlying pattern.