This paper explores weak identiﬁcation issues arising in commonly used models of economic and ﬁnancial time series. Two highly popular conﬁgurations are shown to be asymptotically observationally equivalent: one with long memory and weak autoregressive dynamics, the other with antipersistent shocks and a near-unit autoregressive root. We develop a data-driven semiparametric and identiﬁcation-robust approach to inference that reveals such ambiguities and documents the prevalence of weak identiﬁcation in many realized volatility and trading volume series. The identiﬁcation-robust empirical evidence generally favors long memory dynamics in volatility and volume, a conclusion that is corroborated using social-media news flow data.
Price bubbles in multiple assets are sometimes nearly coincident in occurrence. Such near-coincidence is strongly suggestive of co-movement in the associated asset prices and likely driven by certain factors that are latent in the ﬁnancial or economic system with common eﬀects across several markets. Can we detect the presence of such common factors at the early stages of their emergence? To answer this question, we build a factor model that includes I(1), mildly explosive, and stationary factors to capture normal, exuberant, and collapsing phases in such phenomena. The I(1) factor models the primary driving force of market fundamentals. The explosive and stationary factors model latent forces that underlie the formation and destruction of asset price bubbles, which typically exist only for subperiods of the sample. The paper provides an algorithm for testing the presence of and date-stamping the origination and termination of price bubbles determined by latent factors in a large-dimensional system embodying many markets. Asymptotics of the bubble test statistic are given under the null of no common bubbles and the alternative of a common bubble across these markets. We prove consistency of a factor bubble detection process for the origination and termination dates of the common bubble. Simulations show good ﬁnite sample performance of the testing algorithm in terms of its successful detection rates. Our methods are applied to real estate markets covering 89 major cities in China over the period January 2003 to March 2013. Results suggest the presence of three common bubble episodes in what are known as China’s Tier 1 and Tier 2 cities over the sample period. There appears to be little evidence of a common bubble in Tier 3 cities.
While each ﬁnancial crisis has its own characteristics, there is now widespread recognition that crises arising from sources such as ﬁnancial speculation and excessive credit creation do inflict harm on the real economy. Detecting speculative market conditions and ballooning credit risk in real time is therefore of prime importance in the complex exercises of market surveillance, risk management, and policy action. This chapter provides an R implementation of the popular real-time monitoring strategy proposed by Phillips, Shi and Yu in the International Economic Review (2015), along with a new bootstrap procedure designed to mitigate the potential impact of heteroskedasticity and to eﬀect family-wise size control in recursive testing algorithms. This methodology has been shown eﬀective for bubble and crisis detection and is now widely used by academic researchers, central bank economists, and ﬁscal regulators. We illustrate the eﬀectiveness of this procedure with applications to the S&P ﬁnancial market and the European sovereign debt sector using the psymonitor R package developed in conjunction with this chapter.
Causal relationships in econometrics are typically based on the concept of predictability and are established in terms of tests for Granger causality. These causal relationships are susceptible to change, especially during times of ﬁnancial turbulence, making the real-time detection of instability an important practical issue. This paper develops a test for detecting changes in causal relationships based on a recursive rolling window, which is analogous to the procedure used in recent work on ﬁnancial bubble detection. The limiting distribution of the test takes a simple form under the null hypothesis and is easy to implement in conditions of homoskedasticity, conditional heteroskedasticity and unconditional heteroskedasticity. Simulation experiments compare the eﬀicacy of the proposed test with two other commonly used tests, the forward recursive and the rolling window tests. The results indicate that both the rolling and the recursive rolling approaches oﬀer good ﬁnite sample performance in situations where there are one or two changes in the causal relationship over the sample period, although the performance of the rolling window algorithm seems to be the best. The testing strategies are illustrated in an empirical application that explores the causal impact of the slope of the yield curve on real economic activity in the United States over the period 1985–2013.
Expansion and collapse are two key features of a ﬁnancial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several diﬀerent forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper develops analytics and studies the performance characteristics of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2014b,c, PSY) under alternative forms of bubble implosion that can be represented in terms of mildly integrated processes which capture various return paths to market normalcy. We propose a new reverse sample use of the PSY procedure for detecting crises and estimating the date of market recovery. Consistency of the dating estimators is established and the limit theory addresses new complications arising from the alternative forms of bubble implosion and the endogeneity eﬀects present in the reverse regression. Simulations explore the ﬁnite sample performance of the strategy for dating market recovery and an illustration to the Nasdaq stock market is provided. A real-time version of the strategy is provided that is suited for practical implementation.
This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right tailed unit root tests (each with a diﬀerent recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure and the CUSUM procedure.
Right-tailed unit root tests have proved promising for detecting exuberance in economic and ﬁnancial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model speciﬁcation used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under diﬀerent hypotheses and model speciﬁcations. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. Empirical applications to the Nasdaq and to Australian and New Zealand housing data illustrate these speciﬁcation issues and reveal their practical importance in testing.
Identifying and dating explosive bbles when there is periodically collapsing behavior over time has been a major concern in the economics literature and is of great importance for practitioners. The complexity of the nonlinear structure inherent in multiple bubble phenomena within the same sample period makes econometric analysis particularly diﬀicult. The present paper develops new recursive procedures for practical implementation and surveillance strategies that may be employed by central banks and ﬁscal regulators. We show how the testing procedure and dating algorithm of Phillips, Wu and Yu (2011, PWY) are aﬀected by multiple bubbles and may fail to be consistent. The present paper proposes a generalized version of the sup ADF test of PWY to address this diﬀiculty, derives its asymptotic distribution, introduces a new date-stamping strategy for the origination and termination of multiple bubbles, and proves consistency of this dating procedure. Simulations show that the test signiﬁcantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. Empirical applications are conducted to S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach identiﬁes many key historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and the CUSUM procedure locate far fewer episodes in the same sample range.