A new class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si116.svg" display="inline" id="d1e810"><mml:mi mathvariant="double-struck">Z</mml:mi></mml:math>-valued INAR(1) models with application to mutual fund flows

Z -valued time series , which have discrete and quantitative observations on the set Z = { . . . , − 2 , − 1 , 0 , 1 , 2 , … } , are commonly observed in economics and finance . Z -valued versions of integer-valued autoregressive (INAR) models are frequently employed to fit Z -valued time series. However, the existing Z -valued INAR models encounter difficulties in data generation mechanism and statistical inference. To enhance the modeling and prediction of Z -valued time series, this article constructs a class of Z -valued INAR(1) models from a new perspective and studies the related statistical inference problem. Empirically, an application to mutual fund flows demonstrates that our model offers satisfactory performance in economics and finance. • Z -valued time series are not formally used to analyze mutual fund flows. • Our model is the first Z -valued INAR(1) model based on zero-inflated modeling method. • The forward algorithm is used to obtain the maximum likelihood estimate. • The proposed model outperforms others in fitting and predicting mutual fund flows.