Chaos and nonlinear dynamical approaches to predicting exchange rates in Kenya
The liberalization of the foreign exchange rate market in Kenya was meant to increase market efficiency. However, this does not seem to be the case as evidence by high and persistent volatility in the market. Excess volatility increases the cost of doing business and the prices of essential goods and services to consumers. This reduces allocation efficiency of economic resources and consequently affects economic growth and development in Kenya. Thus it becomes necessary for the Central Bank of Kenya (CBK) to intervene in the foreign exchange market. Attempts by the Central Bank of Kenya (CBK) to intervene in the market to reduce excessive volatility have either been too little or too late. Often such interventions have even contributed to increased market volatility. For effective intervention the CBK must understand the data generating process (d.g.p.) for the observed exchange rates and volatility clusters. However, no such model is currently available and CBK interventions more often than not fail to meet expectations of market participants and citizens in general. This study contributed to the filling of this gap by examining the data generating process for exchange rates and volatility in the KSHlUS$ market. The study used data for daily, weekly and monthly closing prices of the KSHlUS$ exchange rates; the l-rnonth, 3-, 6- and 12- months forward and risk premia; the daily, weekly and monthly Government of Kenya (GoK) and the USA government Treasury Bills rate. The study covered the period starting January 1995 to June 2007. Therefore, the objectives of this study were to analyze market efficiency, volatility, and chaos in the foreign exchange market in Kenya for the period starting January 1995 to June 2007. As a matter of procedure, firstly, the study employed the normality test, the serial' correlation test, the unit root test, the information content of the term structure of the risk premiums and analysis of seasonality to examine market efficiency. Secondly, the study analyzed volatility clustering in the market. Lastly, the study analyzed the presence, occurrence, distribution and duration of chaos in the market. The objective was to determine the data generating process for the observed returns and volatility clusters in the market. There are five major findings from this study. Firstly, the results from the data analysis strongly suggest that the foreign exchange market is not efficient in the weak form. The spot Market is characterized by returns that are not normally distributed. The returns are positively serially correlated implying that the exchange rate has been depreciating most of the time. , Returns are also mean- reverting. The results also showed the existence of a time varying risk premium. The term structure of the risk premia contains significant information that can be used to predict the future spot exchange rate. Secondly, the results strongly suggest that the foreign exchange market is highly volatile. Both extremely low and extremely high volatility are clustered and are well described by the GARCH model. Thus, volatility in the foreign exchange market is predictable, at least in the short run. Also, the distribution of extreme returns and extreme volatility over thresholds at particular time intervals strongly suggests that they are well described by the same distribution - the Generalized Extreme Value (GEV) distribution. Further, the results strongly suggest that the distribution of volatility cluster members follows the inverse power law, irrespective ofthe scale at which these are examined. Thirdly, there are seasonal patterns in returns and volatility in the foreign exchange market. Foreign exchange returns display seasonal patterns around holidays, in April, May, June, July and August. Volatility also revealed significant seasonal patterns in March to June, and September to December. Seasonality may reflect the economy-wide events such as reading of the government budget and the tourism season, as well as the institutional arrangements within the market. Fourthly, the results show that the term structure of the risk premiums rises with the investment horizon. Thus, as the investment horizon rises from one month to twelve month, the risk premiums demanded also increases to reflect the increasing exposure to risk at longer maturities. This suggests that the yield curve is upward sloping. Short-term (1- and 3- months) and long-term (6- and 12-months) risk premiums also appear to move pro-cyclically, rising during economic expansions and falling during economic recessions. However, shortterm risk premiums displayed greater amplitude than longer-term premiums over time. Also when short-term risk premiums are falling, the 6-months and 12-months risk premiums are also declining. When short-term risk premiums are rising, longer-term risk premiums are alsorising. Therefore, the yield curve typically shifts upward or downward each week or month instead of twisting or rotating about some point along the yield curve. Fifthly, the evidence strongly indicates that the foreign exchange rate market is nonlinear and chaotic. The results of the BDS test and the Lyapunov exponent test strongly suggests the presence of nonlinearity and chaos in the returns; the forward premia and the risk premia. The maximum duration of volatility and chaos in the market is six months. Chaos is ascribed to either risk-aversion or speculation in the foreign exchange market. The results of this study have a number of implications for the theory, practice and policy of Finance. For the theory of Finance, the results show that using the Theory of Point Processes enriches the repertoire of models available for the study of market volatility. This model captures well the time dependency in the distribution of volatility magnitudes. For the practice of Finance, the findings indicate that investors cannot earn abnormal profits in the market only in the long run. Market fundamentals influence the behavior of exchange rates in the long run. Two key policy implications are worthy noting. First, to be effective, CBK intervention in the market should be no later than five days after the start of excessive volatility in the market. Second, the CBK should among other things focus on reducing speculation in the foreign exchange market since this is what increases volatility.