7.1 Properties of time-series

1. Time-series data have autoregressive dynamics (AR) implied by it’s autocorrelation, i.e. the current value depends on the past values

• Classical estimation method OLS usually produces a spurious results when ignoring AR dynamics

2. Time-series data have time-varying moments (such as mean or variance), e.g. mean or variance of a time-series increases over time

• This property of time-series is called nonstationarity

• Time-varying variance is commonly referred to as conditional heteroscedasticity in the context of time-series analysis

• If two independent, nonstationary time-series are regressed on each other, the chance for finding a spurious relationship is very high!

3. Unexpected events in a time-series can cause structural breaks in the data

• We can capture these changes with regime switching model (RSM)

4. Many time-series are in an equilibrium or steady state, what we call cointegration (time-series are related both in a short-term and in a long-term)

• We can describe a cointegration with error correction model (ECM)

5. Many time-series are endogenously related, which can be described with a system of equations, such as vector autoregression model (VAR)

6. Economic time-series usually exhibit trends and/or seasonal variations, particular in industrial production, construction activity, trade and tourism (number of tourist arrivals, airline prices, \(\dots\))