Abstract: This study proposes a tying maximum likelihood estimation (TMLE) method to improve the performance of estimation of statistical and econometric models in which most time series have long sample periods, whereas the other time series are very short. The main idea of the TMLE is to tie the parameters of the long time series with those of the short time series together so that some useful information in the long time series which is related to the short time series can be transferred to the short time series. The information transferred from the long series can help improve the estimation accuracy of the parameters related to the short series. We first provide asymptotic properties of the TMLE and show its finite-sample risk bound with a fixed tuning parameter which determines the strength of tying. Further, we provide a method for selecting the tuning parameter based on a bootstrap procedure. A finite sample theory about this method is derived, which tells us how to conduct the bootstrap procedure effectively. Extensive artificial simulations and empirical applications show that the TMLE has an outstanding performance in point estimate and forecast.

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