The thesis deal with long-memory processes which are defined by several ways. The main concern is dedicated to ARFIMA model, to its basic properties and its application. Next, graphical, semiparametric and parametric estimation methods of ARFIMA parameters are described in detail. Five selected R packages are introduced that are suitable for modeling long-memory processes. We discuss their basic functions with description of input arguments and output. Finally, the application of the packages on real data is discussed according to results of~each function. Data sample comes from the Nile River and represents its yearly minimal water levels. Powered by TCPDF (www.tcpdf.org)

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / Using the ARFIMA (autoregressive and fractionally integrated moving aver age) model extended with sGARCH (standard generalised autoregressive con ditional heteroscedasticity) and ’gjrGARCH (Glosten-Jagannathan-Runkle gen eralised autoregressive conditional heteroscedascity) innovations, fractional in tegration approach and state space model, this study has empirically examined persistency of inflation dynamics of Ghana and South Africa, the only two coun tries in Sub-Saharan Africa with Inflation Targeting (IT) monetary policy. The first part of the analysis employed monthly CPI (Consumer Price Index) in flation series for the period January 1971 to October 2014 obtained from the Bank of Ghana (BoG), and for the period January 1995 to December 2014 ob tained from Statistics South Africa. The second part involves the estimation of threshold effect of inflation on economic growth using annual data obtained from the IMF (International Monetary Fund) database for the period 1981 to 2014, for both countries. Results from the study showed that structural breaks, long memory and non linearities (or regime shifts) are largely responsible for inflation persistence, hence the ever-changing nature of inflation rates of Ghana and South Africa. ARFIMA(3,0.35,1)-‘gjrGARCH(1,1) under Generalised Error Distribution (GED) and ARFIMA(3,0.50,1)-‘gjrGARCH(1,1) under Student-t Distribution (STD) mod els provided the best fit for persistence in the conditional mean (or level) of CPI for Ghana and South Africa, respectively. The results from these models pro vided evidence of time-varying conditional mean and volatility in CPI inflation rates of both countries. The two models also revealed an asymmetric effect of inflationary shocks, where negative shocks appear to have greater impact than positive shocks, in terms of persistence on the conditional mean with time varying volatility. This thesis proposes a model that combines fractional integration with non linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa. We tested for non-linear deterministic terms in the context of fractional integration and esti mated the fractional differencing parameters, d to be 1.11 and 1.32 respectively, for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. New ev idence from this thesis depicts that inflation rate of Ghana is highly persistent and non-mean reverting, with an estimated fractional differencing parameter, d > 1.0, and will therefore require some policy action to steer inflation back to stability. However, the South African inflation series was found to be a cyclical process with an order of integration estimated to be d = 0.7, depicting mean reversion, with the length of the cycles approximated to last for 80 months. Finally, the thesis incorporated structural breaks, long memory, non-linearity, and some explanatory variables into a state space model and estimated the threshold effect of inflation on economic growth. The empirical results suggest that inflation below the estimated levels of 9% and 6% for Ghana and South Africa respectively, will be conducive for economic growth. The policy implications of these results for both countries are as follows. First, both series had similar properties responsible for inducing inflation persistence such as structural breaks, non-linearities, long memory and asymmetric re sponse to negatives shocks - but with varied degrees of magnitude. For both countries, the conditional mean and unobserved components such as volatility for both countries were found to be time-varying. This thesis, therefore, recom mends to the BoG and the South African Reserve Bank (SARB) - responsible for monetary policies, and the Finance Ministers of both governments - respon sible for fiscal policies, to take the above-mentioned properties into account in the formulation of their monetary policies. Second, the thesis recommends that the BoG and the SARB consolidate the IT policy, since keeping inflation below the targets set of 9% and 6%, respectively for Ghana and South Africa, will boost economic growth. Third, policymakers could also design measures (monetary and fiscal policies) such as increase in interest rates, credit control, and reduction of unnecessary expenditure, among others, to control inflation due to its adverse effects on market volatility. Even though an increase in interest rates could assist in curtailing the recent and anticipated increase in inflation rates in both countries, where targets have been missed by Ghana and South Africa, it will also be prudent to legislate monetary policies around demand-supply side since the problem of both coun tries appears to be more of a structuralist than a monetarist. It is, therefore, recommended that both countries tighten the IT monetary policy in order to re duce inflation persistence. This will eventually impact on poverty and income distribution with ramifications for economic growth and/or development. The fourth implication of these results is that governments and central banks should be mindful of the actions and decisions they take, in the sense that unguarded decisions and unnecessary alarms could raise uncertainties in the economy, which could, in turn, affect the future trajectory of inflation. Finally, the thesis recommends that governments of both countries strengthen the pri vate sector, which is the engine of growth. For small and open economies such as Ghana and South Africa, this will grow the economy through job creation and restore investor confidence. / National Research Foundation (NRF), Department of Science and Technology (DST), Telkom’s Tertiary Education Support Programme (TESP) and the NRF-DST Centre of Excellence for Mathematical and Statistical Sciences (CoE-MaSS)

The inability to effectively hedge against unfavourable exchange rate movements, using the current forward exchange rate as the only guideline, is a key inhibiting factor of international trade. Market participants use the current forward exchange rate quoted in the market to make decisions regarding future exchange rate changes. However, the current forward exchange rate is not solely determined by the interaction of demand and supply, but is also a mechanistic estimation, which is based on the current spot exchange rate and the carry cost of the transaction. Results of various studies, including this study, demonstrated that the current forward exchange rate differs substantially from the realized future spot exchange rate. This phenomenon is known as the exchange rate puzzle. This study contributes to the dynamics of modelling exchange rate theories by developing an exchange rate model that has the ability to explain the realized future spot exchange rate and the exchange rate puzzle. The exchange rate model is based only on current (time t) economic fundamentals and includes an alternative approach of incorporating the impact of the interaction of two international financial markets into the model. This study derived a unique exchange rate model, which proves that the exchange rate puzzle is a pseudo problem. The pseudo problem is based on the generally excepted fallacy that current non–stationary, level time series data cannot be used to model exchange rate theories, because of the incorrect assumption that all the available econometric methods yield statistically insignificant results due to spurious regressions. Empirical evidence conclusively shows that using non–stationary, level time series data of current economic fundamentals can statistically significantly explain the realized future spot exchange rate and, therefore, that the exchange rate puzzle can be solved. This model will give market participants in the foreign exchange market a better indication of expected future exchange rates, which will considerably reduce the dependence on the mechanistically derived forward points. The newly derived exchange rate model will also have an influence on the demand and supply of forward exchange, resulting in forward points that are a more accurate prediction of the realized future exchange rate. / Thesis (Ph.D. (Risk management))--North-West University, Potchefstroom Campus, 2011.

The inability to effectively hedge against unfavourable exchange rate movements, using the current forward exchange rate as the only guideline, is a key inhibiting factor of international trade. Market participants use the current forward exchange rate quoted in the market to make decisions regarding future exchange rate changes. However, the current forward exchange rate is not solely determined by the interaction of demand and supply, but is also a mechanistic estimation, which is based on the current spot exchange rate and the carry cost of the transaction. Results of various studies, including this study, demonstrated that the current forward exchange rate differs substantially from the realized future spot exchange rate. This phenomenon is known as the exchange rate puzzle. This study contributes to the dynamics of modelling exchange rate theories by developing an exchange rate model that has the ability to explain the realized future spot exchange rate and the exchange rate puzzle. The exchange rate model is based only on current (time t) economic fundamentals and includes an alternative approach of incorporating the impact of the interaction of two international financial markets into the model. This study derived a unique exchange rate model, which proves that the exchange rate puzzle is a pseudo problem. The pseudo problem is based on the generally excepted fallacy that current non–stationary, level time series data cannot be used to model exchange rate theories, because of the incorrect assumption that all the available econometric methods yield statistically insignificant results due to spurious regressions. Empirical evidence conclusively shows that using non–stationary, level time series data of current economic fundamentals can statistically significantly explain the realized future spot exchange rate and, therefore, that the exchange rate puzzle can be solved. This model will give market participants in the foreign exchange market a better indication of expected future exchange rates, which will considerably reduce the dependence on the mechanistically derived forward points. The newly derived exchange rate model will also have an influence on the demand and supply of forward exchange, resulting in forward points that are a more accurate prediction of the realized future exchange rate. / Thesis (Ph.D. (Risk management))--North-West University, Potchefstroom Campus, 2011.