Essays on univariate long memory models

Sammanfattning: This thesis consists of five papers dealing with univariate long memory modelsin time series analysis.The first paper examines the performance of information criteria when usedto determine the lag order of a long memory process. The results indicate thatinformation criteria cannot be used successfully for small sample sizes. For largersample sizes the probability of successfully identifying the lag order is substantially higher.The covariance matrix of ARMA errors is the subject of the second paper.We generalise the matrix expression of the covariance matrix for ARIMA errorsto involve ARFIMA errors. In practise, it is necessary to truncate the orders ofthe matrices. The truncation only has a mild effect for small and medium valuesof the long memory parameter, but for large values, very large matrices must beused.A matrix representation of the moving average representation is given in thethird paper. The first two coefficients of the moving average representation of anARFIMA (1, d, 1) are presented as an example.The fourth paper examines the consequences of using forecasts from an ARIMA model when the process is an ARFIMA. Ignoring long memory increases the meansquared error of prediction substantially for long memory processes with high longmemory. Using information criteria to choose lag lengths does not improve theperformance of the forecasts. Further, the parameters of the misspecified modelare evaluated by maximising the expected likelihood.The existence of long memory in the Swedish OMX index and in the Swedish stock market is investigited in the fifth paper. We find no long memory, but do identify short memory and conditional heteroscedasticity.

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