Limit Theory for Moderate Deviations from a Unit Root

By Peter C. B. Phillips, Tassos Magdalinos. 2007

73 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aecb1c10f47e32ba2972c47d4d8d9fb36fe8e10d

Citations in the corpus

• Bubbles in food commodity markets: Four decades of evidence ☆ (2014, unknown): “…autoregressive processes as the central limit theory does not apply (White 1958; Anderson 1959), the asymptotic behavior of mildly explosive processes is more regular and a least squares regression theory can be established to construct confidence intervals (Phillips and Magdalinos 2007a,b).”
• Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors (2009, unknown): “t=1 ˆ̇ u 2 1,t p −→ ω11 2c (22) where ˆ̇ u1,t is the regression residual of yt on zt, as previously mentioned, we need to consistently estimate ω11, the long-run variance of u1,t.”
• LIMIT THEORY FOR COINTEGRATED SYSTEMS WITH MODERATELY INTEGRATED AND MODERATELY EXPLOSIVE REGRESSORS (2009, unknown): “In the moderately explosive case (where ci > 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, Journal of Econometrics 136, 115–130).”
• Mildly explosive autoregression under weak and strong dependence (2012, unknown): “As a result, the Cauchy regression theory of Phillips and Magdalinos (2007a) is invariant to the dependence structure of the innovation sequence even in the long memory case.”
• Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500 (2015, unknown): “Whatever its origins, explosive or mildly explosive (Phillips and Magdalinos, 2007) behavior in asset prices is a primary indicator of market exuberance during the inflationary phase of a bubble and it is this time series manifestation that may be subjected to econometric testing using recursive…”
• Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values? (2011, unknown): “…estimator δ̂n (τ) =∑τ j=1 x̃j x̃j−1/ ∑τ j=1 x̃ 2 j−1 that n(1+α)/2δτ−τen 2c ( δ̂n (τ) − δn ) = δ −(τ−τe) n nα/2+1/2 τ∑ j=τe xj−1εj { 1 + op (1) } 2cδ−2(τ−τe)n n1+α τ∑ j=τe x2j−1 { 1 + op (1) } =⇒ C,(16) where the limit C is a Cauchy variate (cf., theorem 4.3 of Phillips and Magdalinos, 2007a).”
• Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence (2005, unknown): “Giraitis and Phillips (2004) derived related limit results for the case of martingale difference errors.”
• Datestamping the Bitcoin and Ethereum bubbles (2017, unknown): “Phillips and Magdalinos [2007] stated that no matter what unobservable fundamentals were fuelling the origins of such observed bubbles, explosive or mildly explosive behaviour in asset price can be considered a primary indicator of market exuberance during the inflationary phase of a bubble 3 .”
• Robust econometric inference for stock return predictability (2011, unknown): “…arise when predictors exhibit a lower degree of persistence relative to local-to-unity processes, as is the case with the class of “near-stationary”processes introduced by Phillips and Magdalinos (2007) as well as stationary autoregressive processes. matrix with specified persistence degree.”
• Testing for Multiple Bubbles: Limit Theory of Real Time Detectors (2015, unknown): “…(2009) for the impact of alternative initializations on the limit theory. allow the limit theory to continue to hold under the null (1), based on the functional law (2), and under mildly explosive alternatives as in (4) below, the latter based on results in Phillips and Magdalinos (2007a, 2007b).”