Forecasting of vertical displacements based on a time series

Abstract

Before research, a graphical analysis of time series is important to carry out because the configuration of empirical points in a proper Cartesian coordinate system enables one to make a decision which class the researched trend function belongs to. When verifying the model it should be checked whether received values of structural parameters estimation are reasonable. The method of extrapolation of time series can be used to forecast only in case when the mechanism of development of the researched effect does not change in time considerably or in case if the mechanism of development of the researched effect is not known and we cannot recognize it. The forecast horizon can be dependent on inertia of researched variables. For variables with a big inertia the forecast horizon can be considerably longer. Longer forecast horizon corresponds with less probability of occurrence of the provided state and simultaneously certainty of the forecast is less. Another question is a stability of the model. It does not mean that the model will be stable after the period the model was estimated, i.e. it will be stable in future. Adaptive models are useful in case of lack of stability in the researched period. Forecast procedures based on those models assume that the effect intensification in time can be segmental, i.e. "smooth", only in some intervals of time. Such models are particularly important for short-term forecasts. Taking one of the following models into account depends on: - clear interpretation of model's parameters, - possibility of a simple estimation of the model's parameters, - the level of accuracy that the model describes the effect's development in time. It should be noticed that building a "good" model describing the given effect on the base of data from the past not always can be proper in future. To enlarge forecast certainty (especially for short time series) several forecasting methods should be used and their results should be compared