Stock market prices in China. Efficiency, mean reversion, long memory volatility and other implicit dynamics

This paper analyzes the long-term dynamics of Chinese stock market prices, using the data series of daily closing spot price indices from Shanghai and Shenzhen stock markets, two major stock exchange markets in China. Both autoregressive and fractional models have been employed: in the former case, we implement standard unit root tests to determine the nonstationarity; while for the fractional I(d) models, we use a parametric testing procedure developed by Robinson (1994) and a semiparametric estimation method based on a “local” Whittle estimate of d (Robinson, 1995). The results show strong evidence in favour of unit roots and thus lack of mean reverting behaviour for the log-prices series, when using both the classical methods based on integer degrees of differentiation but also when applying fractionally integrated techniques. On the other hand, when examining the volatility processes by means of studying the absolute and the squared returns series, the results strongly support the view of fractional integration in all cases, with the orders of integration fluctuating in the range (0, 0.5). This implies stationary long memory in volatility

The PPP hypothesis in the US/China relationship. Fractional integration, time variation and data frequency

This paper deals with the analysis of the Purchasing Power Parity (PPP) hypothesis in China by means of fractional integration or I(d) techniques. Using real exchange rates data between the Chinese Yuan and the US dollar, the results indicate that the estimated integration order d is generally larger than 1, which means that the PPP hypothesis in China does not hold in the long run over the sample period 1994M01 to 2010M11. Moreover, to check the stability of d across the sample period, we re-estimate it recursively over different subsample periods with 5-year and 10-year data frequencies respectively. The recursive estimated results show that after the structural change at the beginning of the sample period, the fractional differencing parameter d remains stable and generally larger than 1

Investigating long range dependence in temperatures in Siberia

In this paper we examine monthly mean temperatures in 40 selected stations in Siberia for the time period January 1937–December 2020 using long range dependence techniques. In particular, we use a fractionally integrated model that incorporates a linear time trend along with a seasonal structure. Our results show first that long memory is present in all stations with significantly positive values for the differencing parameter, though, at the same time the seasonal component seems to be important in all cases. Performing seasonal unit root tests, the results support nonstationary seasonality and working with the seasonal differenced data, the results differ depending on the structure of the error term: if the errors are uncorrelated, long memory is present; however, allowing autocorrelation, this feature disappears in favor of a short memory pattern

Testing the Fisher hypothesis in the G-7 countries using I(d) techniques

This paper revisits the Fisher hypothesis concerning the determination of real rates by estimating fractional integration and cointegration models for nominal interest rates and expected inflation in the G7 countries. Two sets of results are obtained under the alternative assumptions of white noise and Bloomfield (1973) autocorrelated errors respectively. The univariate analysis suggests that the differencing parameter is higher than 1 for most series in the former case, whilst the unit root null cannot be rejected for the majority of them in the latter case. The multivariate results imply that there exists a positive relationship, linking nominal interest rates to inflation; however, there is no evidence of the full adjustment of the former to the latter required by the Fisher hypothesis

U.S. house prices by census division: persistence, trends and structural breaks

This paper uses fractional integration methods to examine persistence, trends and structural breaks in United States house prices, more specifically the monthly Federal Housing Finance Agency House Price Index for census divisions, and the United States as a whole over the period from January 1991 to August 2022. The full sample estimates imply that the order of integration of the series is above one in all cases, and is particularly high for the aggregate series, implying high levels of persistence. However, when the possibility of structural breaks is taken into account, segmented trends are detected. The subsample estimates of the fractional differencing parameter tend to be lower, with mean reversion occurring in a number of cases. This means that shocks in the series are expected to be transitory in these subsamples, disappearing in the long run by themselves. In addition, the time trend coefficient is at its highest in the last subsample, which in most cases starts around May 2020 coincident with the beginning of the coronavirus pandemic. The results provide clear evidence of differences between census divisions, which implies that appropriate housing policies should be designed at the local (rather than at the federal) level

Fractional Integration and the Persistence of UK Inflation, 1210–2016*

This note examines the degree of persistence of UK inflation by applying fractional integration methods to historical data spanning the period 1210–2016; the chosen approach is more general than the popular ARMA models based on the classical I(0) vs. I(1) dichotomy. The full-sample results do not suggest that UK inflation is a persistent process; however, the recursive analysis indicates an increase in the degree of persistence in the 16th century and more recently after WWI and in the last quarter of the 20th century. On the whole, monetary and exchange rate regime changes do not appear to have had a significant impact on the stochastic behaviour of inflation if one takes a longrun, historical perspective

Oil Prices: Persistence and Breaks

The rise of oil prices is a main issue in contemporary economics. This study examines the monthly, weekly and daily structure in several oil prices series using a modeling approach based on fractional integration and long range dependence. The results indicate that oil prices series are highly persistent, with orders of integration equal to or higher than 1. Breaks in the series do not alter the main conclusions of this study. That means that shocks have a permanent nature and strong policy measures must be implemented to return the series to their original long term projections

Prospects for a monetary union in the East Africa community: Some empirical evidence

This paper examines generalised purchasing power parity (G-PPP) and business cycle synchronisation in the East Africa Community with the aim of assessing the prospects for a monetary union. The univariate fractional integration analysis shows that the individual series exhibit unit roots and are highly persistent. The fractional bivariate cointegration tests suggest that there exist bivariate fractional cointegrating relationships between the exchange rate of the Tanzanian shilling and those of the other EAC countries, and also between the exchange rates of the Rwandan franc, the Burundian franc and the Ugandan shilling. The Fractionally Cointegrated Vector AutoRegressive (FCVAR) results imply the existence of a single cointegrating relationship between the exchange rates of the EAC countries. On the whole, there is evidence in favour of G-PPP. In addition, there appears to be a high degree of business cycle synchronisation between these economies. On both grounds, one can argue that a monetary union should be feasible

Long memory and data frequency in financial markets

This paper investigates persistence in financial time series at three different frequencies (daily, weekly and monthly). The analysis is carried out for various financial markets (stock markets, FOREX, commodity markets) over the period from 2000 to 2016 using two different long memory approaches (R/S analysis and fractional integration) for robustness purposes. The results indicate that persistence is higher at lower frequencies, for both returns and their volatility. This is true of the stock markets (both developed and emerging) and partially of the FOREX and commodity markets examined. Such evidence against the random walk behaviour implies predictability and is inconsistent with the Efficient Market Hypothesis (EMH), since abnormal profits can be made using trading strategies based on trend analysis