Poisson regression with a periodic function. (English) Zbl 1075.62611
Summary: Let \(\{y_t\}\) be a Poisson-like process with the mean \(\mu_t\) which is a periodic function of time \(t\). We discuss how to fit this type of data set using quasi-likelihood method. Our method provides a new avenue to fit a time series data when the usual assumption of stationarity and homogeneous residual variances are invalid. We show that the estimators obtained are strongly consistent and also asymptotically normal.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M09 | Non-Markovian processes: estimation |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
Consistent estimators; Asymptotic normality; Poisson-like process; Non-stationary time seriesReferences:
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