Can I use non-stationary variables in forecasting problem I want to build survival analysis model (Cox PH) with time-varying covariates. Time-varying covariates are macroeconomic variables. Therefore, they are same for each individual at the same calendar date. The aim of this model is to predict probability of some event occurrence during following 3 years. I have only 17 calendric time periods with quarterly frequency. The interval period from from state to end state is also 3 month. The time-dependent covariates and even their first difference are not stationary. I wonder if I could to involve the non-stationary time-dependent variables into survival analysis model? and, which kind of problems does it induced? Does it decline forecast accuracy or make it models less stable?
I update the question according to the @Edm's comment.
 A: One big problem you face is the way that Cox PH models incorporate the effects of time-varying covariates. Those models assume that the current hazard of an event is related to the current covariate values. On that basis it doesn't really matter if the external covariates are stationary or not: what matters is the current value facing someone at risk.
That, however, is often a risky assumption in this type of study. It's possible that the current hazard is related to some earlier value of a covariate, or to some integrated exposure. For a Cox model to work, you need to translate those types of covariates into some type of current value to associate with current hazard. You need to think about that carefully, applying your knowledge of the subject matter.
Another problem is the limited number of time periods. Cox models implicitly assume continuous time, with special handling of tied event times. Data such as yours might better be modeled with discrete-time survival models, which are effectively sets of binary regressions. Tutz & Schmid cover that subject in "Modeling Discrete Time-to-Event Data" (2016). This web page has references to several publications by Singer and Willett on the topic. The R discSurv package provides tools to help set up these models.
I think that the issue of stationarity in your predictors has more to do with your ability to extrapolate their values reliably for 3 years into the future. That's not an issue for the Cox modeling per se, provided that you have identified the correct way to associate covariate values over time (whether current covariate values directly, or current values of functions of earlier covariate values) with current hazards.
