Bivariate FIGARCH and fractional cointegration

We consider the modelling of volatility on closely related markets. Univariate fractional volatility (FIGARCH) models are now standard, as are multivariate GARCH models. In this paper, we adopt a combination of the two methodologies. There is as yet little consensus on the methodology for testing for fractional cointegration. The contribution of this paper is to demonstrate the feasibility of estimating and testing cointegrated bivariate FIGARCH models. We apply these methods to volatility on the NYMEX and IPE crude oil markets. We find a common order of fractional integration for the two volatility processes and confirm that they are fractionally cointegrated. An estimated error correction FIGARCH model indicates that the preponderant adjustment is of the IPE towards NYMEX.     

Fractional cointegration and real exchange rates

This paper uses fractional integration and cointegration to model the DM-US dollar and the yen-US dollar real exchange rates in terms of both monetary and real factors, more specifically real interest rate and labour productivity differentials. We find that whilst the individual series may be integrated of order 1, their long-run relationship might have a fractionally cointegrated structure. This means that mean reversion occurs, consistently with the findings of other studies. However, it also indicates, in contrast to such studies, that the cointegrating relationship possesses long memory. In other words, the error correction term responds slowly to shocks, implying that deviations from equilibrium are long-lived. It appears that only a combination of real and monetary variables can accurately track down the movements of real exchange rates.     

Comovements of earnings, dividends, and stock prices

We investigate the comovements of the log of earnings, dividends, and stock prices by testing for the number of common stochastic trends among these series. We find that the three series are cointegrated with a single cointegrating vector. Our findings collectively imply that (i) there is an equilibrium force that tends to keep these series together over time, (ii) changes in dividends are primarily influenced by changes in some measure of permanent earnings, and (iii) a substantial fraction of stock price movement is driven by neither earnings changes nor dividend changes. When we take into account the cointegration relationship, we find that the dynamic relationship between these variables is significantly affected. We present a common stochastic trends model of earnings, dividends, and stock prices, whose implications are broadly consistent with these findings.     

Asymmetric dynamic relations between stock prices and mutual fund units in Japan. An application of hidden cointegration technique

This paper examines “causality” effects between mutual fund flows and stock index prices in Japan. In particular, both the short and long run dynamics between stock prices and fund units are investigated. The novelty of our paper is the use of the hidden cointegration technique which attempts to capture heterogeneous fund flow reactions when stock index prices move up or down. Moreover, we employ the crouching error correction model (CECM) to assess the relationship between stock market movements and fund flow changes. The results show that stock prices and mutual fund units are cointegrated. In the case of positive movements there is a bi-directional effect interconnecting them, whereas for negative movements, causality runs only from fund flows to stock prices. The dynamics structure provides evidence that market microstructure, taxation and investors' sentiment affect stock price and unit formation.     

DYNAMIC RELATIONS BETWEEN MACROECONOMIC VARIABLES AND THE JAPANESE STOCK MARKET: AN APPLICATION OF A VECTOR ERROR CORRECTION MODEL

By employing the vector error correction model (VECM) in a system of seven equations, we find that the Japanese stock market is cointegrated with a group of six macroeconomic variables. The signs of the long-term elasticity coefficients of the macroeconomic variables on stock prices generally support the hypothesized equilibrium relations. Our findings are robust to different combinations of macroeconomic variables in six-dimension systems and two subperiods. Also, the VECM consistently outperforms the vector autoregressive model in forecasting ability.     

Stock prices and demand for money in China: New evidence

This paper investigates the relationship between stock prices and the real money demands for China within a cointegrated framework. This study reports two important results. First, test results reveal that a stable long-term relationship exists between broad money (M2) and its determinants including real income, foreign interest rate, and stock prices. Second, stock prices have a significant substitute (positive) effect on long-run broad-money (M2) demand and its omission can lead to serious misspecification in the money demand function in both the short- and long-run. Finally, we demonstrate that long-run income elasticity is not significantly different from unity with the inclusion of stock prices in the money demand equation.     

High and low prices and the range in the European stock markets: A long-memory approach

This paper uses fractional integration techniques to examine the stochastic behaviour of high and low stock prices in Europe and then to test for the possible existence of long-run linkages between them by looking at the range, i.e., the difference between the two logged series. Specifically, monthly, weekly and daily data on the following five European stock market indices are analysed: DAX30 (Germany), FTSE100 (UK), CAC40 (France), FTSE MIB40 (Italy) and IBEX35 (Spain). In all cases, the order of integration of the range is lower than that of the original series, which implies the existence of a long-run equilibrium relationship between high and low prices. Further, multiple breaks are found in the high and low-price series but no breaks in the range, and the estimated fractional differencing parameter is positive in all cases, which represents evidence of long memory.     

Equity market integration in the NAFTA region: Evidence from unit root and cointegration tests

This study examines integration of the three participating equity markets before and after the 1993 passage of NAFTA based on daily, weekly, and monthly data. As expected, unit root tests for the overall period 1988-2001 and the two subperiods, 1988-1993 (pre-NAFTA) and 1994-2001 (post-NAFTA), indicate that stock prices are non-stationary but stock returns are generally stationary for all three markets for all three periods. However, daily, weekly, and monthly equity prices in the three NAFTA countries are cointegrated only for the post-NAFTA period. Similarly, US stock prices are more integrated with both Canadian and Mexican stock prices after the passage of NAFTA. This evidence of increased financial integration and co-movement in NAFTA equity markets after the passage of NAFTA has important implications for policymakers and managers.     

Long-run equilibrium, short-term adjustment, and spillover effects across Chinese segmented stock markets and the Hong Kong stock market

This paper adopts a novel FIVECM-BEKK GARCH approach to examine the bilateral relationships among the A-share and B-share stock markets in China and the Hong Kong stock market. The evidence shows that these stock markets are fractionally cointegrated. Analyses of the spillover effects across these markets indicate that the A-share markets are most influential. The relaxation of government restrictions on the purchase of B shares by domestic residents accelerates the market integration process of A-share markets with the B-share and Hong Kong markets. The effects of the Asian crisis on the stock-return dynamic correlations vary across these markets.     

STOCK PRICES AND EXCESSIVE VOLATILITY: SOME EVIDENCE FOR THE FT ORDINARY SHARE INDEX

In this paper the efficiency of the UK stock market is examined using the FT Ordinary share price and dividend indices for the period January 1947 to June 1987. In particular, we examine the validity of the present value model of stock prices using a vector error correction model (VECM). Amongst the findings reported in the paper are that stock prices and dividends are cointegrated and the cross-equation restrictions imposed on the VECM are strongly rejected.     

Risk and return: Long-run relations,fractional cointegration,and return predictability

Univariate dependencies in market volatility, both objective and risk neutral, are best described by long-memory fractionally integrated processes. Meanwhile, the ex post difference, or the variance swap payoff reflecting the reward for bearing volatility risk, displays far less persistent dynamics. Using intraday data for the Standard & Poor's 500 and the volatility index (VIX), coupled with frequency domain methods, we separate the series into various components. We find that the coherence between volatility and the volatility-risk reward is the strongest at long-run frequencies. Our results are consistent with generalized long-run risk models and help explain why classical efforts of establishing a naïve return-volatility relation fail. We also estimate a fractionally cointegrated vector autoregression (CFVAR). The model-implied long-run equilibrium relation between the two variance variables results in nontrivial return predictability over interdaily and monthly horizons, supporting the idea that the cointegrating relation between the two variance measures proxies for the economic uncertainty rewarded by the market.     

A note on cointegration of international stock market indices

Cointegration is frequently used to assess the degree of interdependence of financial markets. We show that if a stock's price follows a stock specific random walk, market indices cannot be cointegrated. Indices are a mere combination of n different random walks which itself is non-stationary by construction. We substantiate the theoretical propositions using a sample of 28 stock indices as well as a simulation study. In the latter we simulate stock prices, construct indices and test whether these indices are cointegrated. We show that while heteroscedasticity misleads cointegration tests, it is not sufficient to explain the high correlation between stock market index returns. A common random walk component and correlated price innovations are necessary to reproduce this feature.     

On the relationship between concentration of prospect theory/mental accounting investors,cointegration, and momentum

We examine the role of cointegration between stock prices and their estimated fundamental values in return momentum. We find that the positive relationship between capital gains overhang and future stock returns in Grinblatt and Han (2005) is significantly stronger among the “non-cointegrated” group of stocks as compared with the “cointegrated” group of stocks. Further, for the cointegrated stocks, the slower the speed of adjustment to the cointegrating equilibrium, the greater (smaller) is the future return of stocks with unrealized capital gains (losses). These findings are robust to various firm characteristics including firm size, book-to-market ratio, past returns, idiosyncratic volatility, dispersion in analysts’ earnings forecasts, turnover, individual investor ownership, and industry returns.     

Determining the contributions to price discovery for Chinese cross-listed stocks

We study the price-discovery process for a number of Chinese cross-listed stocks. For the stocks cross-listed on the New York Stock Exchange (NYSE) and the Stock Exchange of Hong Kong (SEHK), we find that the stock prices of these two exchanges are cointegrated and mutually adjusting, and that the SEHK makes more contributions than the NYSE to the price-discovery process. The SEHK contributions are 81.6% and 89.4%, computed from Gonzalo and Granger [Gonzalo, J., Granger, C., 1995. Estimation of common long-memory components in cointegrated systems. Journal of Business and Economics Statistics 13, 27–35] permanent–transitory (PT) and Hasbrouck [Hasbrouck, J., 1995. One security, many markets: Determining the contributions to price discovery. Journal of Finance 50, 1175–1119] information share (IS) models respectively.     

Cointegration,Fractional Cointegration,and Exchange Rate Dynamics

Multivariate tests due to Johansen (1988, 1991) as implemented by Baillie and Bollerslev (1989a) and Diebold, Gardeazabal, and Yilmaz (1994) reveal mixed evidence on whether a group of exchange rates are cointegrated. Further analysis of the deviations from the cointegrating relationship suggests that it possesses long memory and may possibly be well described as a fractionally integrated process. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons.     

Cointegration and causality between macroeconomic variables and stock market returns

The purpose of this study is to investigate whether current economic activities in Korea can explain stock market returns by using a cointegration test and a Granger causality test from a vector error correction model. This study finds that the Korean stock market reflects macroeconomic variables on stock price indices. The cointegration test and the vector error correction model illustrate that stock price indices are cointegrated with a set of macroeconomic variables—that is, the production index, exchange rate, trade balance, and money supply—which provides a direct long-run equilibrium relation with each stock price index. However, the stock price indices are not a leading indicator for economic variables, which is inconsistent with the previous findings that the stock market rationally signals changes in real activities.     

A Fractional Cointegration Approach to Testing Mean Reversion Between Spot and Forward Exchange Rates: A Case of High Frequency Data with Low Frequency Dynamics

This paper applies a relatively new but generalised concept of fractional cointegration to shed some light on the validity of a long-run relationship between high frequency daily spot and the lagged forward Australian-US dollar exchange rate. An investigation of the stochastic properties of these rates reveals that, while the relationship is not cointegrated in their logs, they appear to be fractionally cointegrated if we allow for mean reverting processes that are CI (1, d ) with 0< d <1. The paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a I (0) process, captures a much wider class of mean-reversion behaviour. This result is interpreted in the context of the speculative EMH between the spot and forward exchanges rates, as having some empirical support. Furthermore, an analysis of the short-run dynamics propelling the long-run relationship tends to imply that in both the short- and long-term, the forward rate is led by the spot rate. In the longer term, the spot rate is found to be the initial receptor of any exogenous shock to the equilibrium and it is the forward exchange rate that bears the brunt of short-run adjustment to re-establish the long-run equilibrium relationship. The approach illustrated in this paper is shown to hold enormous potential for tests of mean reversion involving hypotheses popular to financial econometrics in general, where the dynamics of high frequency data are under scrutiny.     

Identifying Permanent and Temporary Components in Daily and Monthly Japanese Stock Prices

The purpose of this study is to analyze time series of daily and monthly values for the Tokyo Stock Price Index (TOPIX) and stock price values for 15 companies listed on the Tokyo Stock Exchange, Section 1 (TSE-I), to determine the contribution of permanent and temporary components to Japanese stock prices. The existence of temporary components in the price series would imply that Japanese stock returns are partially predictable. The method of canonical correlation is used to determine components common to each series and the persistence of each component series is evaluated by estimating the amount of dependence in the series. The results suggest that Japanese stock prices contain a small temporary component. The fractionally integrated ARIMA (ARFIMA) model is used to characterize both the component series and an estimate of the temporary component for each original price series. The contribution of the temporary component to the total variation of the price series estimated. We find that, in general, the temporary component accounts for less than 8% of the variation in the daily price series and from 5% to 15% of variation in the monthly price series, indicating that there may be a small amount of predictability in Japanese stock prices.     

Stock Market Efficiency and Economic Efficiency: Is There a Connection?

In a capitalist economy, prices serve to equilibrate supply and demand for goods and services, continually changing to reallocate resources to their most efficient uses. However, secondary stock market prices, often viewed as the most “informationally efficient” prices in the economy, have no direct role in the allocation of equity capital since managers have discretion in determining the level of investment. What is the link between stock price informational efficiency and economic efficiency? We present a model of the stock market in which: (i) managers have discretion in making investments and must be given the right incentives; and (ii) stock market traders may have important information that managers do not have about the value of prospective investment opportunities. In equilibrium, information in stock prices will guide investment decisions because managers will be compensated based on informative stock prices in the future. The stock market indirectly guides investment by transferring two kinds of information: information about investment opportunities and information about managers' past decisions. However, because this role is only indirect, the link between price efficiency and economic efficiency is tenuous. We show that stock price efficiency is not sufficient for economic efficiency by showing that the model may have another equilibrium in which prices are strong-form efficient, but investment decisions are suboptimal. We also suggest that stock market efficiency is not necessary for investment efficiency by considering a banking system that can serve as an alternative institution for the efficient allocation of investment resources.     

Cointegration, Efficiency and Forecasting in the Currency Market

Existing literature on using the cointegration approach to examine the efficiency of the foreign exchange market gives mixed results. Arguments typically focus on econometric testing techniques, with fractional cointegration being the most current one. This paper tries to look at the issue from an economic perspective. It shows that the cointegrating relationship, whether cointegrated or fractionally cointegrated, is found mainly among the currencies of the European Monetary System which are set to fluctuate within a given range. Hence, there is no inconsistency with the notion of market efficiency. Yet, exploiting such a cointegrating relationship is helpful in currency forecasting. There is some evidence that restricting the forecasting model to consist of only cointegrated currencies improves forecasting efficiency.