Explanation

Regression coefficient estimates in time-series models can change substantially due to changes in both the length and the starting point of the sample period.

Why both factors matter:

1. Length of sample period:

   • Longer time periods may capture different economic regimes or structural breaks
   • Shorter periods may be affected by temporary anomalies or specific market conditions
   • Different sample sizes affect statistical precision and coefficient stability

2. Starting point of sample period:

   • Different starting points may capture different phases of business cycles
   • Economic relationships can vary across different time periods
   • Structural changes in the economy can make relationships time-dependent

Time Series Characteristics:

• Time series data often exhibit non-stationarity, where statistical properties change over time
• Parameter instability is common in time series models due to changing economic relationships
• This sensitivity to sample selection is particularly problematic for forecasting and inference

Therefore, both the length and starting point of the sample period can significantly impact regression coefficient estimates in time-series analysis.