Hiro Y. Toda

Overview

Hiro Y. Toda is an econometrician at the Institute of Socio-Economic Planning, University of Tsukuba, Japan. Known for foundational work on the asymptotic theory of Granger causality tests in non-stationary VAR systems, in collaboration with Peter C. B. Phillips.

Key Contributions / Features

• Toda and Phillips (1993) — "Vector Autoregressions and Causality" (Econometrica 61): derived the full limit theory for Wald causality tests in levels VARs and Johansen ECMs with $I(1)$ variables; showed standard $\chi^2$ asymptotics fail in general; established rank conditions for validity (Theorems 1–3).
• Toda and Phillips (1991b) — companion simulation study proposing and evaluating a sequential ECM-based causality testing procedure; established favorable performance for small systems ($n \leq 4$) at $T > 100$.
• Toda and Yamamoto (1995) — "Statistical Inference in Vector Autoregressions with Possibly Integrated Processes" (Journal of Econometrics 66): proposed the lag-augmentation trick — estimate VAR($k + d_{\max}$) and apply standard Wald test on first $k$ lags — which gives $\chi^2$ inference regardless of integration order without requiring rank pretests.

Related

• Peter C. B. Phillips
• Granger Causality
• Cointegration
• Vector Autoregression