The article discusses the increasing significance of random variables in metric spaces and introduces an autoregressive model tailored for Hadamard spaces. It focuses on estimating the parameters, including the Fréchet mean and a concentration parameter, along with proposing a test statistic for assessing serial dependence. Theoretical validation is provided through simulations, demonstrating converging estimators and their efficiency. The model's applicability is showcased through a case study on consumer inflation expectations, highlighting its relevance in practical scenarios where non-parametric methods have fallen short.
In addressing the limitations of non-parametric methods, our adaptation of the classical linear autoregressive model enables effective analysis of time series data in Hadamard spaces.
The introduction of a test statistic, along with its asymptotic normality, allows for robust hypothesis testing, enhancing the study of serial dependence in time series.
#statistical-modeling #time-series-analysis #hadamard-spaces #autoregressive-models #hypothesis-testing
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