Canonical correlation analysis of stochastic trends via functional approximation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911158571630592 |
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| author | Franchi, Massimo Georgiev, Iliyan Paruolo, Paolo |
| author_facet | Franchi, Massimo Georgiev, Iliyan Paruolo, Paolo |
| contents | This paper proposes a novel approach for semiparametric inference on the number $s$ of common trends and their loading matrix $ψ$ in $I(1)/I(0)$ systems. It combines functional approximation of limits of random walks and canonical correlations analysis, performed between the $p$ observed time series of length $T$ and the first $K$ discretized elements of an $L^2$ basis. Tests and selection criteria on $s$, and estimators and tests on $ψ$ are proposed; their properties are discussed as $T$ and $K$ diverge sequentially for fixed $p$ and $s$. It is found that tests on $s$ are asymptotically pivotal, selection criteria of $s$ are consistent, estimators of $ψ$ are $T$-consistent, mixed-Gaussian and efficient, so that Wald tests on $ψ$ are asymptotically Normal or $χ^2$. The paper also discusses asymptotically pivotal misspecification tests for checking model assumptions. The approach can be coherently applied to subsets or aggregations of variables in a given panel. Monte Carlo simulations show that these tools have reasonable performance for $T\geq 10 p$ and $p\leq 300$. An empirical analysis of 20 exchange rates illustrates the methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical correlation analysis of stochastic trends via functional approximation Franchi, Massimo Georgiev, Iliyan Paruolo, Paolo Econometrics Methodology This paper proposes a novel approach for semiparametric inference on the number $s$ of common trends and their loading matrix $ψ$ in $I(1)/I(0)$ systems. It combines functional approximation of limits of random walks and canonical correlations analysis, performed between the $p$ observed time series of length $T$ and the first $K$ discretized elements of an $L^2$ basis. Tests and selection criteria on $s$, and estimators and tests on $ψ$ are proposed; their properties are discussed as $T$ and $K$ diverge sequentially for fixed $p$ and $s$. It is found that tests on $s$ are asymptotically pivotal, selection criteria of $s$ are consistent, estimators of $ψ$ are $T$-consistent, mixed-Gaussian and efficient, so that Wald tests on $ψ$ are asymptotically Normal or $χ^2$. The paper also discusses asymptotically pivotal misspecification tests for checking model assumptions. The approach can be coherently applied to subsets or aggregations of variables in a given panel. Monte Carlo simulations show that these tools have reasonable performance for $T\geq 10 p$ and $p\leq 300$. An empirical analysis of 20 exchange rates illustrates the methods. |
| title | Canonical correlation analysis of stochastic trends via functional approximation |
| topic | Econometrics Methodology |
| url | https://arxiv.org/abs/2411.19572 |