Konsumentprisindex för kläder och skor 1986-2005 - Dekomponering och prognostisering
KPITidsserieanalysSäsongsrensningStatisticsOperations researchProgrammingActuarial mathematicsStatistikOperationsanalysProgrammeringAktuariematematikMathematics and Statistics
The essay initially intends to find adequate models to describe and forecast monthly data for the Swedish Consumer Price Index sub group Clothes and Shoes 1986-2005. The time series observations during 2006 are considered ?out of sample period? which is used to evaluate the forecasts. The purpose is to perform time series decomposition and to investigate and analyzethe seasonal pattern. The Box-Jenkins approach is used to find adequate ARIMA models. Further the investigation assumes the approach of SCB for seasonal decomposition and the so called likelihood principal. The statistical program package TRAMO/SEATS is used throughout the investigation. The formulation of adequate ARIMA models is carried out through the automatic function of TRAMO and seasonal decomposition is performed by SEATS. On the basis of different pre-transformations four ARIMA-models are composed. Based on the assumed criteria?s one of the models proves to be adequate. Non-adequate models are rejected and the adequate model is used for predictions and seasonal decomposition. It shows that a Box-Cox transformation using? = ?1 produces a stationary time-series and further anARIMA-model by the form (0,1,1) (0,1,1). It shows that 9 out 12 monthly predictions made for 2006 are within a 95%-prediction interval. Decomposition of the time-series shows that CPI for Clothes and Shoes is initially characterised by a relatively even positive trend, which however declines and gradually passes into a negative trend during the latest years. The seasonally decomposed series further shows an evidently reduced variance which indicates a well adapted model. A closer analysis of the seasonal pattern indicates that the time series is increasingly influenced by seasonal effects. Further, the results indicate that the seasonal pattern is changing by affecting more months. The investigation of the seasonal component shows that the last months of the year have the highest CPI and the largest positive seasonal component. In a corresponding way the early months and the months during summer are characterised by low prices. The investigation suggests that this is an increasing process. The analysis of the seasonal patterns shows thus far a price level increasingly related to season.