Permanent-transitory Decomposition Research Articles

Fractional cointegration and price discovery in Canadian commodities

Using as a unifying theme commodities important to the Canadian economy, recently developed tools are applied to studying price discovery in the spot and futures markets. For each commodity the fractionally cointegrated vector autoregression (FCVAR) model of Johansen and Neilsen is estimated and tested against the special case of the conventional cointegrated vector autoregression (CVAR). These models characterize the fundamental value of a commodity as the common stochastic trend shared by its cointegrated spot and futures prices, and so price discovery can be analyzed using the permanent-transitory decomposition of Gonzalo and Granger. Model forecasts are evaluated and compared using a distributional result due to Clark and West. The generalization to fractional cointegration is found to be statistically significant. However the economic significance of this generalization—in terms of forecast accuracy and the profitability of mean–variance dynamic trading strategies—is more fragile than may have been appreciated.

Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices

Summary We propose a cointegration-based Permanent-Transitory decomposition for nonstationary dynamic factor models (DFMs). Our methodology exploits the cointegration relations among the observable variables and assumes they are driven by a common and an idiosyncratic component. The common component is further split into a long-term nonstationary and a short-term stationary part. A Monte Carlo experiment shows that incorporating the cointegration structure into the DFM leads to a better reconstruction of the space spanned by the factors, compared to the most standard technique of applying a factor model in differenced systems. We apply our procedure to a set of commodity prices to analyse the co-movement among different markets and find that commodity prices move together mostly due to long-term common forces; while the trend for the prices of most primary goods is declining, metals and energy exhibit an upward or at least stable pattern since the 2000s.

Determination of the Number of Common Stochastic Trends under Conditional Heteroskedasticity

Permanent-transitory decompositions and the analysis of the time series properties of economic variables at the business cycle frequencies strongly rely on the correct detection of the number of common stochastic trends (co-integration). Standard techniques for the determination of the number of common trends, such as the well-known sequential procedure proposed in Johansen (1996), are based on the assumption that shocks are homoskedastic. This contrasts with empirical evidence which documents that many of the key macro-economic and financial variables are driven by heteroskedastic shocks. In a recent paper, Cavaliere et al., (2010, Econometric Theory) demonstrate that Johansen's (LR) trace statistic for co-integration rank and both its i.i.d. and wild bootstrap analogues are asymptotically valid in non-stationary systems driven by heteroskedastic (martingale difference) innovations, but that the wild bootstrap performs substantially better than the other two tests in finite samples. In this paper we analyse the behaviour of sequential procedures to determine the number of common stochastic trends present based on these tests. Numerical evidence suggests that the procedure based on the wild bootstrap tests performs best in small samples under a variety of heteroskedastic innovation processes.

The trend and cycle components of China’s housing prices: a new decomposition method

ABSTRACT The paper proposes a novel hybrid method that extends previous work incorporating the fractionally cointegrated vector autoregressive and the permanent-transitory decomposition model. Using the hybrid method, we investigate whether the rapid rise in China’s housing prices is a trend or cyclical fluctuation as well as whether there exists a housing price bubble. The findings indicate there exists a fractional cointegration relationship between housing prices and macroeconomic fundamentals in China, and that the fundamental value of housing prices is determined by macroeconomic factors. In particular, the upward trend in China’s housing prices has shifted and decelerated since 2012, in line with GDP and money supply. Moreover, we provide evidence of the existence of a housing price bubble in China since 2012, particularly during the 2015–2018 period. We demonstrate that the hybrid model has a superior forecasting performance and decomposes the trend and cycle components more accurately than the conventional methods when estimating a system of possibly fractional cointegration relationship.

Permanent-Transitory decomposition of cointegrated time series via Dynamic Factor Models, with an application to commodity prices

Permanent-Transitory decomposition of cointegrated time series via Dynamic Factor Models, with an application to commodity prices

Common integrating factor in softwood log exports from the United States

Softwood logs comprise a large portion of forest product exports from the United States. Most of these exports have occurred between the Pacific Northwest region of the United States and several Asian countries. In this study, the extent and degree of market integration of softwood log exports from 1996 to 2018 are examined by co-integration analyses and permanent–transitory decomposition. Softwood log exports to Japan and South Korea appear to be in the same economic market and show a high degree of integration, while trade between the United States and China has evolved more independently. A detailed analysis is conducted on five prices related to Japan and South Korea with full-time coverage, and one common integrating factor is found and estimated. The price of export from the Columbia-Snake Customs District to Japan is identified as the driving force. Price responses to market shocks usually occur within four months. These findings have implications for government agencies and participants in the market of softwood log trade.

Common shocks, common transmission mechanisms and time-varying connectedness among Dow Jones Islamic stock market indices and global risk factors

The purpose of this paper is twofold. First, we examine the importance of permanent versus transitory shocks as well as their domestic and foreign components in explaining the business cycle fluctuations of seven Dow Jones Islamic stock markets (DJIM), namely U.S., U.K., Canada, Europe, Asia-Pacific, Japan and GCC, over the period from April 2003 to November 2018, using the permanent-transitory (P-T) decompositions approach of Centoni et al. (2007). Second, we investigate the spillover mechanisms of these shocks across Islamic stock markets and a set of global risk factors, using the Diebold and Yilmaz (DY) (2012) approach. The P-T decomposition results show that the DJIM U.S., U.K., Europe and GCC indices are sensitive to both domestic and foreign shocks, while the DJIM Canada, Japan and Asia-Pacific are most sensitive to domestic shocks. The empirical results of the DY approach indicate that: (i) the return and volatility spillover intensity increase during financial turmoil, supporting evidence of the contagion phenomenon, (ii) the DJIM U.S. is the main transmitter of return and volatility spillovers, while the DJIM GCC is identified as the main receiver of both return and volatility spillovers, (iii) the seven Dow Jones Islamic stock indices are weakly linked to movements of global risk factors, and (iv) there is evidence of possible portfolio diversification between the selected Islamic stock markets and the oil commodity market.

Analysis of Bitcoin Prices Using Market and Sentiment Variables

This paper proposes an empirical model for analyzing the dynamics of Bitcoin prices. To do this, we consider a vector error correction model over two overlapping periods: 2010-2017 and 2010-2019. Price discovery is achieved through the Gonzalo-Granger permanent-transitory decomposition. The pricing factors are endogenous linear combinations of the S&P 500 index, gold price, a Google search variable associated to Bitcoin, and a fear index proxied by the FED Financial Stress Index. Our empirical analysis shows that during the first period a linear combination of four pricing factors describes the efficient Bitcoin price. The S&P 500 index and Google searches have a positive effect whereas gold prices and the fear index have a negative effect. In contrast, during the second period, the efficient price behaves idiosyncratically and can be only rationalized by individuals’ search for information on the cryptocurrency. These findings provide empirical evidence on the presence of a correction in Bitcoin prices during the period 2018-2019 uncorrelated to market fundamentals. We also show that standard empirical asset pricing models perform poorly for explaining Bitcoin prices.

The role of Eonia in the dynamics of short-term interbank rates

To signal monetary policies and market expectations, we apply a fractionally cointegrated vector autoregressive (FCVAR) model, aiming to analyse the expectations hypothesis of term structure (EHTS), persistence in the Euro OverNight Index Average (Eonia) spread and permanent-transitory decomposition using a novel approach. We use a monthly frequency sample for the 3- month Euribor rate and Eonia rate, covering the period from January 1999 to February 2019. The results obtained confirm the EHTS and show evidence of a high persistence of the spread, which means that shocks may impede effectiveness in monetary policy and that the European Central Bank (ECB) loses control over interest rates. Additionally, according to permanent-transitory decomposition, we determine that the Eonia rate has a permanent component and thus dominates the common trend in the cointegration system. In sum, if the ECB wants to keep the interbank market interest rates under control, it must contemplate the evolution of the Eonia rate.

A new way of measuring the WTI – Brent spread. Globalization, shock persistence and common trends.

The standard cointegration and the persistence of the spread of the Brent-WTI price have been widely analyzed. However, no studies have been able to present evidence of both issues jointly so far. A novel focus is presented in this paper from the application of the fractionally cointegrated vector autoregressive (FCVAR) approach, which allows the rigidity of the standard cointegration to be solved. As result of the application of the FCVAR model, we identify several degrees of globalization by analyzing the order of integration of the error correction term. Indeed, by using Permanent-Transitory decomposition analysis, we present what drives the relationship between both oil crude prices’ information. The findings shown here reveal that the Brent-WTI market is strongly globalized. Nevertheless, the Brent–WTI price spread follows a long memory process, and the Brent drives the Brent-WTI price structure. These results sustain some corollaries on economic policies for economic agents, policy makers and business operators.

Financial integration in the United Arab Emirates Stock Markets

This paper examines the integration of financial markets using data from the Dubai Financial Market Stock Exchange, Abu Dhabi Stock Exchange and the FTSE Nasdaq Dubai UAE 20 index. To do this, we apply a vector error correction model and a permanent-transitory decomposition of the series of prices. Our results reveal the existence of a long-run equilibrium relationship between the three financial indices suggesting that UAE stock markets are integrated. Shocks to any of these markets affect the other markets in the long and the short run through the equilibrium condition. We uncover a major role of the FTSE Nasdaq Dubai UAE 20 index in this equilibrium relationship. Our analysis of market integration also allows us to obtain a permanent-transitory decomposition given by two common factors that drive the three financial indices. Whereas the first factor is defined as a weighted combination of the two major financial indices the second factor is mainly determined by the FTSE Nasdaq Dubai. As a byproduct of our analysis, we find empirical evidence of short-run and long-run predictability running from the Dubai financial indices to the Abu Dhabi index.

The volatility linkage between energy and agricultural futures markets with external shocks

This paper investigates the volatility linkage between energy and agricultural futures returns and how this linkage responds to external macroeconomic shocks. A framework combining the VARMA-BEKK-GARCH model and the Permanent-Transitory decomposition technology is employed to detect the volatility transmission, to decompose the volatility linkage into permanent and transitory components, and to examine the underlying determinants of the transitory volatility linkage. We have the following findings. A bidirectional volatility linkage between energy and agricultural futures returns exists and becomes more pronounced in recent years. The bidirectional linkage results from the co-movement effect induced by external shocks rather than from the substitution effect induced by the biofuel industry, and is not weakened by the shale gas revolution. Serving as proxies for external shocks from the world economy, trade, and financial markets, the CRB, BDI, and USDX indices provide strong explanatory power for the transitory volatility linkage, and the futures of these indices can be used to effectively and inexpensively hedge against the risks of the portfolios involving energy and agricultural futures.

Modelling the Dynamics of Fuel and EU Allowance Prices during Phase 3 of the EU ETS

This article studies the relationship between the prices of fuel and EU Allowances (EUA) for carbon emissions during Phase 3 of the European Union Emissions Trading System. We find that the forward prices of EUA, coal, gas and Brent oil are jointly determined in equilibrium. The existence of such a long-run relationship entails a permanent-transitory decomposition for the series of EUA and fuel prices that reveals the short- and long-term causal influence of the EUA market in shaping the joint dynamics of fuel prices. This result complements the literature that suggests that EUA prices are driven by the dynamics of fuel prices. Interestingly, we do not find an equilibrium relationship in the spot market. EUA and fuel spot prices are driven by independent unit root processes. The differences between spot and forward markets are attributed to the tradability of forward prices that are used for speculation and hedging in financial markets. In contrast, spot prices are mainly driven by supply and demand in energy markets.

Price Discovery Study of Chinese ADRs on Global Markets

This paper analyzes the price discovery mechanism between the Chinese American Depository Receipts (ADRs) listed on the New York Stock Exchange (NYSE) and their underlying H shares on the Hong Kong Stock Exchange (HKEX). It employs the Permanent-Transitory decomposition in vector autoregression (VAR) model, and finds that the New York stock market makes the principal contribution to the price discovery, and the proportion of contribution is 84.84%; while the Hong Kong market makes only subsidiary contribution of 15.16%. In addition, it confirms the existence of the long-term cointegration relationship between ADRs and H shares, which implies that portfolio diversification among Chinese ADRs is consistent with Global Center Hypothesis and efficient for international investors.

Long-run and short-run relationships between oil prices, producer prices, and consumer prices: What can we learn from a permanent-transitory decomposition?

We use a permanent-transitory decomposition to provide new econometric evidence on long-run and short-run relationships between oil prices, producer prices and consumer prices. Results support cointegration and suggest a single common I(1) factor driving all three variables. Impulse responses to a permanent shock to the common factor indicate an important long-run relationship between oil prices, producer prices, and consumer prices. Impulse responses to a transitory oil price shock show no consumer price index response and only weak evidence of a short-run response in the producer price index. Hence, the conclusion is that oil price shocks have to be perceived as permanent before there is a strong link to consumer prices. Policy focused on ameliorating the effects of oil price shocks should pay close attention to whether shocks are permanent or transitory. Conclusions are robust to alternative measures of consumer prices and over different sub-samples of the data, although there is some evidence that the cointegration relationships disappear in the latter part of the sample.

Nonparametric Stochastic Discount Factor Decomposition

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron-Frobenius eigenfunction problem of Hansen and Scheinkman (2009). Our empirical framework allows researchers to (i) recover the time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron-Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.

The estimation uncertainty of permanent-transitory decompositions in co-integrated systems

ABSTRACTThe topic of this article is the estimation uncertainty of the Stock–Watson and Gonzalo–Granger permanent-transitory decompositions in the framework of the co-integrated vector autoregression. We suggest an approach to construct the confidence interval of the transitory component estimate in a given period (e.g., the latest observation) by conditioning on the observed data in that period. To calculate asymptotically valid confidence intervals, we use the delta method and two bootstrap variants. As an illustration, we analyze the uncertainty of (U.S.) output gap estimates in a system of output, consumption, and investment.

Dissecting Exchange Rates and Fundamentals in the Modern Floating Era: The Role of Permanent and Transitory Shocks

AbstractIn this paper, we apply a permanent–transitory decomposition method to analyze the link between nominal exchange rates and fundamentals in the modern floating era. The results suggest that transitory shocks dominate nominal exchange rate fluctuations, while permanent shocks dominate the variations in fundamentals. Therefore, the findings suggest that the nominal exchange rate should not be approximated by a pure random walk. Moreover, we find that unobserved fundamentals in the Taylor rule model can explain the transitory components in exchange rates.

Revisiting the relationship between exchange rates and fundamentals

In this paper, we apply the permanent–transitory decomposition method to analyze the role of permanent and transitory shocks in explaining the apparent weak link between nominal exchange rates and economic fundamentals. The results suggest that for most of the countries we investigate, including Finland, Italy, Portugal, France and Switzerland, transitory shocks dominate exchange rate fluctuations, while permanent shocks dominate the variations in economic fundamentals. The findings therefore provide an alternative interpretation of the “exchange rate disconnect puzzle”. Moreover, the results also suggest that comprehensive modeling of transitory components in empirical models should not be neglected in studies of the dynamics of exchange rates.

Revisiting the Exchange Rate - Fundamental Nexus

In this paper, we apply the permanent–transitory decomposition method to analyze the role of permanent and transitory shocks in explaining the apparent weak link between nominal exchange rates and economic fundamentals. The results suggest that for most of the countries we investigate, including Finland, Italy, Portugal, France and Switzerland, transitory shocks dominate exchange rate fluctuations, while permanent shocks dominate the variations in economic fundamentals. The findings therefore provide an alternative interpretation of the “exchange rate disconnect puzzle”. Moreover, the results also suggest that comprehensive modeling of transitory components in empirical models should not be neglected in studies of the dynamics of exchange rates.