Parameter-tying approximate factor model for high-dimensional time series with different lengths

This study will propose a new factor model --- a parameter-tying approximate factor (PTAF) model --- by introducing a parameter tying technology from machine learning into the classical approximate factor (AF) model to analyze a type of irregular high-dimensional time series data where most time series have long sample periods, whereas the rest have considerably short sample periods (in other words, high-dimensional time series with different lengths). Nowadays, more and more economic or finance data series collected have different lengths (e.g., the monthly macroeconomic indices: real personal income and new orders for consumer goods in the FRED-MD database from McCracken and Ng, 2016).

The proposed PTAF model includes both observed explanatory variables and unobserved common factors. The main idea of the PTAF model is to tie the parameters of the long time series with those of the short time series together by exerting some restrictions on parameters so that some useful information can be transferred from the long series to the short series, this can help improve the estimation accuracy of the tied parameters.

I propose to investigate estimation strategies and theory for such models, before applying them to new applications in macroeconomics and finance.