Interest rate dynamics in Kenya : commercial banks' rates and the 91 day treasury bill rate

This paper analyses the implicit dynamics underlying the interest rate structure in Kenya. For this purpose we use data on four commercial banks’ interest rates (Deposits, Savings, Lending and Overdraft) together with the 91-Day Treasury Bill rate, for the time period July 1991 – August 2010, and apply various techniques based on long-range dependence and, in particular, on fractional integration. The results indicate that all series examined are nonstationary with orders of integration equal to or higher than 1. The analysis of various spreads suggests that they also are nonstationary I(1) variables, the only evidence of mean reversion being obtained in the case of the Deposits – Treasury Bill rate spread with autocorrelated errors

Fractional integration and cointegration in US financial time series data

This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with d < 1, which implies mean reversion. The multivariate framework exploiting recent developments in fractional cointegration allows to investigate in greater depth the relationships between financial series. We show that there exist many (fractionally) cointegrated bivariate relationships among the variables examined

Long Run and Cyclical Dynamics in the US Stock Market

This paper examines the long-run dynamics and the cyclical structure of various series related to the US stock market using fractional integration. We implement a procedure which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperforms the others in a number of cases.stock market, fractional cycles, long memory, Gegenbauer processes

Multi-Factor Gegenbauer Processes and European Inflation Rates

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest that inflation in France and Italy is nonstationary. However, while for the former country this applies both to the zero and the seasonal frequencies, in the case of Italy the nonstationarity comes exclusively from the long-run or zero frequency. In the UK, inflation seems to be stationary with a component of long memory at both the zero and the semi-annual frequencies, especially at the former.fractional integration, long memory, inflation

Multi-Factor Gegenbauer Processes and European Inflation Rates

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest that inflation in France and Italy is nonstationary. However, while for the former country this applies both to the zero and the seasonal frequencies, in the case of Italy the nonstationarity comes exclusively from the long-run or zero frequency. In the UK, inflation seems to be stationary with a component of long memory at both the zero and the semi-annual frequencies, especially at the former.Fractional Integration, Long Memory, Inflation

Long Memory and Volatility Dynamics in the US Dollar Exchange Rate

This paper focuses on nominal exchange rates, specifically the US dollar rate vis-à-vis the Euro and the Japanese Yen at a daily frequency. We model both absolute values of returns and squared returns using long-memory techniques, being particularly interested in volatility modelling and forecasting given their importance for FOREX dealers. Compared with previous studies using a standard fractional integration framework such as Granger and Ding (1996), we estimate a more general model which allows for dependence not only at the zero but also at other frequencies. The results show differences in the behaviour of the two series: a long-memory cyclical model and a standard I(d) model seem to be the most appropriate for the US dollar rate vis-à-vis the Euro and the Japanese Yen respectively.Fractional integration, Long memory, Exchange rates, Volatility

Estimating Persistence in the Volatility of Asset Returns with Signal Plus Noise Models

This paper examines the degree of persistence in the volatility of financial time series using a Long Memory Stochastic Volatility (LMSV) model. Specifically, it employs a Gaussian semiparametric (or local Whittle) estimator of the memory parameter, based on the frequency domain, proposed by Robinson (1995a), and shown by Arteche (2004) to be consistent and asymptotically normal in the context of signal plus noise models. Daily data on the NASDAQ index are analysed. The results suggest that volatility has a component of long- memory behaviour, the order of integration ranging between 0.3 and 0.5, the series being therefore stationary and mean-reverting.Fractional integration, long memory, stochastic volatility, asset returns

Persistence and Cyclical Dependence in the Monthly Euribor Rate

This paper analyses two well-known features of interest rates, namely their time dependence and their cyclical structure. Specifically, it focuses on the monthly Euribor rate, using monthly data from January 1994 to May 2011. Models based on fractional integration at the long run or zero frequency, although adequately describing the persistent behaviour of the series, do not take into account its cyclical structure. Therefore, a more general cyclical fractional model is considered. Future directions for research in this context are also discussed.Euribor rate, time dependence, cyclical behaviour

REAL EXCHANGE RATES IN LATIN AMERICA: THE PPP HYPOTHESIS AND FRACTIONAL INTEGRATION

This paper tests for PPP in a group of seventeen Latin American (LA) countries by applying fractional integration techniques to real exchange rate series. Compared to earlier studies on these economies, this approach has the advantage of allowing for non-integer values for the degree of integration, and thus for the possibility of PPP not holding continuously but as a long-run equilibrium condition. Further, breaks in the series are endogenously determined using a procedure based on the least-squares principle. This is particularly crucial in the Latin American countries, which have been affected by several exchange rate crises and policy regime changes. The results, based on different assumptions about the underlying disturbances, are in the majority of cases inconsistent with PPP, even more so when breaks are incorporated: Argentina is the only country for which clear evidence of mean reversion is found in the model including a break, albeit only in the second subsample.Real Exchange Rates, Purchasing Power Parity, Fractional Integration, Structural Breaks

US Disposable Personal Income and Housing Price Index: A Fractional Integration Analysis

This paper examines the relationship between US disposable personal income (DPI) and house price index (HPI) during the last twenty years applying fractional integration and long-range dependence techniques to monthly data from January 1991 to July 2010. The empirical findings indicate that the stochastic properties of the two series are such that cointegration cannot hold between them, as mean reversion occurs in the case of DPI but not of HPI. Also, recursive analysis shows that the estimated fractional parameter is relatively stable over time for DPI whilst it increases throughout the sample for HPI. Interestingly, the estimates tend to converge toward the unit root case after 2008 once the bubble had burst. The implications for explaining the recent financial crisis and choosing appropriate policy actions are discussed.personal disposable income, house price index, fractional integration