About
Least Square Method provides parameter estimates by minimizing the sum of squared residuals, with two main variants that differ in how they handle initial observations.
Conditional vs Unconditional
Method Initial Values Information Used Complexity Conditional LS Fixed at observed Y 1 Only Y 2 , … , Y n Simpler, explicit for AR Unconditional LS Marginal distribution includes Y 1 All observations More complex, numerical
When to Use Each
Conditional Least Squares
Large samples (initial value impact negligible)
Simple AR models
Quick preliminary estimates
Software default for many time series packages
Unconditional Least Squares
Short time series
Seasonal models
When precision for early observations matters
Compromise between conditional LS and full MLE
Comparison with Maximum Likelihood
Aspect Conditional LS Unconditional LS MLE Uses all data No (Y 1 Yes Yes Distributional assumption None required Normal errors Normal errors Efficiency Good for large n Better Best (large n