Time-varying linear regression via flexible least squares. (English) Zbl 0666.62065
Suppose noisy observations obtained on a process are assumed to have been generated by a linear regression model with coefficients which evolve only slowly over time, if at all. Do the estimated time-paths for the coefficients display any systematic time-variation, or is time-constancy a reasonable satisfactory approximation? A “flexible least squares” (FLS) solution is proposed for this problem, consisting of all coefficient sequence estimates which yield vector-minimal sums of squared residual measurement and dynamic errors conditional on the given observations. A procedure with FORTRAN implementation is developed for the exact sequential updating of the FLS estimates as the process length increases and new observations are obtained. Simulation experiments demonstrating the ability of FLS to track linear, quadratic, sinusoidal, and regime shift motions in the true coefficients, despite noisy observations, are reported. An empirical money demand application is also summarized.
MSC:
| 62J05 | Linear regression; mixed models |
| 62P20 | Applications of statistics to economics |
| 65C99 | Probabilistic methods, stochastic differential equations |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62-04 | Software, source code, etc. for problems pertaining to statistics |
Keywords:
flexible least squares; vector-minimal sums of squared residual measurement; FORTRAN implementationReferences:
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