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### Modelling volatity of time series data containing outliers observations with ARCH effect DOI:10.15199/48.2019.01.10

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Modeling and forecasting the volatility of time series has become a popular research area. Currently, this topic attracts the attention of scientists, researchers and economists who are focused on creating models, analytical tools to describe mathematically changes in real world. Process of data gathering is very complicated and exposed to many distortions. Nevertheless, modelling of data becomes more and more popular. It is worth mentioning that government, economic and engineering data are usually published as time series. Time series are the measurements of variable taken at regular intervals over time. Observations are made sequentially over time at regular intervals, such as daily, weekly, monthly, quarterly or hourly. Some time series data are incomplete, contain many missing observations, which may affect the estimation of the model and the result of its estimation. Commonly dataset has missing values that impacts on the model correctness. What is more, data is susceptible to change due to noise and exceptions. Statistical noise is an unexplained variability within a given data sample, which impairs the model’s correctness. An outlier is an observation that is inconsistent with the remainder of the given data set. Another definition says that an outlier is an important kind of deviation, which occurs in the data set as a result of measurement error. Outliers existence also in case of heavy-tailed distribution of population. [2] An outlier can be perceived as a valid data point or a representative of a noise. Identification of the outlier’s nature positively impacts on the process of fitting the best model to the given sample. Using the visualization methods is the best solution to discover outliers as these observations lie outside the overall pattern of distribution. Usually the distribution of observations differs from the normal distribution, which is perceived as one of the characteristics of the ti[...]

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