This note analyzes the empirical size of the augmented Dickey and Fuller (ADF) statistic proposedby Perron and Rodríguez (2003) when the errors are fractional. This ADF is based on a searching procedure for additive outliers based on first-differences of the data named td. Simulations show that empirical size of the ADF is not affected by fractional errors confirming the claim of Perron and Rodríguez (2003) that the procedure td is robust to departures of the unit root framework. In particular the results show low sensitivity of the size of the ADF statistic respect to the fractional parameter (d). However, as expected, when there is strong negative moving average autocorrelation or negative autoregressive autocorrelation, the ADF statistic is oversized. These difficulties are fixed when sample increases (from T = 100 to T = 200). Empirical application to eight quarterly Latin American inflation series is also provided showing the importance of taking into account dummy variables for the detected additive outliers. / En esta nota se analiza el tamaño empírico del estadístico Dickey y Fuller aumentado (ADF), propuesto por Perron y Rodríguez (2003), cuando los errores son fraccionales. Este estadístico se basa en un procedimiento de búsqueda de valores atípicos aditivos basado en las primeras diferencias de los datos denominado td. Las simulaciones muestran que el tamaño empírico del estadístico ADF no es afectado por los errores fraccionales confirmando el argumento de Perron y Rodríguez (2003) que el procedimiento td es robusto a las desviaciones del marco de raíz unitaria. En particular, los resultados muestran una baja sensibilidad del tamaño del estadístico ADF respecto al parámetro fraccional (d). Sin embargo, como es de esperar, cuando hay una fuerte autocorrelación negativa de tipo promedio móvil o autocorrelación autorregresiva negativa, el estadístico ADF tiene un tamaño exacto mayor que el nominal. Estas dificultades desaparecen cuando aumenta la muestra (a partir de T = 100 a T = 200). La aplicación empírica a ocho series de inflación latinoamericana trimestral proporciona evidencia de la importancia de tener en cuenta las variables ficticias para controlar por los outliers aditivos detectados.

Thesis (M. Com.(Economics)) -- University of Limpopo, 2017 / The relationship between unemployment, exchange rate and inflation has been a subject of debate for many years. Given the fact that South Africa is faced with a very low economic growth rate, inflation rate which is likely to go beyond the upper band of 6 percent and a high level of unemployment, policy makers are often faced with the trade-off between unemployment and inflation rate in the country. The purpose of this study is to determine the relationship between exchange rate, unemployment and inflation in South Africa. The study employed Johansen cointegration procedures and the vector error correction model (VECM) to capture the relationship between the variables. The Engle-Granger causality test was also employed to analyse causality amongst the variables. The results of Johansen cointegration test indicate that there is a long-run equilibrium relationship between the variables. The VECM also confirmed the existence of short-run equilibrium relationship between the variables. The nature of the relationship indicates that there is a significant negative relationship between unemployment and inflation in South Africa. This implies that policy makers are been faced with the trade-off between these two variables. The results further indicate that inflation is positively related to exchange rate, meaning a depreciation of the Rand (South African currency) in the foreign exchange market will feed to inflation in the home country. Furthermore, it is also indicated that unemployment is positively related to exchange rate. Meaning, a depreciation of the Rand in the foreign exchange market increases the level of unemployment in South Africa. All the results appeared to be significant. Policies aimed at lowering unemployment and inflation rate are recommended. It is also recommended that policy makers in South Africa take measures to improve the quality of education, skills training and steps to increase the labour intensity of production.