Abstract
Time series, i.e. data collected at various times. The data collection segments may differ de-pending on the task. Time series are used for decision making. Time series analysis allows you to get some result that will determine the format of the decision. Time series analysis was carried out in very ancient times, for example, various calendars became a consequence of the analysis. Later, time series analysis was applied to study and forecast economic, social and other systems. Time se-ries appeared a long time ago. Once upon a time, ancient Babylonian astronomers, studying the po-sition of the stars, discovered the frequency of eclipses, which allowed them to predict their appearance in the future. Later, the analysis of time series, in a similar way, led to the creation of various calen-dars, for example, harvest calendars. In the future, in addition to natural areas, social and economic ones were added. Aim. Search for classification patterns of time series, allowing to understand whether it is possible to apply the ARIMA model for their short-term (3 counts) forecast. Materials and methods. Special software with ARIMA implementation and all need services is made. We examined 59 data sets with a short length and step equal a year, less than 20 values in the paper. The data was processed using Python libraries: Statsmodels and Pandas. The Dickey – Fuller test was used to de-termine the stationarity of the series. The stationarity of the time series allows for better forecasting. The Akaike information criterion was used to select the best model. Recommendations for a rea-sonable selection of parameters for adjusting ARIMA models are obtained. The dependence of the settings on the category of annual data set is shown. Conclusion. After processing the data, four categories (patterns) of year data sets were identified. Depending on the category ranges of parame-ters were selected for tuning ARIMA models. The suggested ranges will allow to determine the starting parameters for exploring similar datasets. Recommendations for improving the quality of post-forecast and forecast using the ARIMA model by adjusting the settings are given.
Highlights
Введение Временные ряды появляются в результате измерения неких показаний, полученных от технических, природных, социальных, экономических и других систем [1, 2,3,4,5,6,7]
Исследование влияния изменения параметров модели Autoregressive Integrated Moving Average (ARIMA) на качество прогноза для коротких наборов данных позволяет работать с нестационарными временными рядами, которые можно сделать стационарными, используя разность некоторого порядка от исходного ряда [1, 8, 9]
We examined 59 data sets with a short length and step equal a year, less than 20 values in the paper
Summary
Что после первого лага происходит резкое снижение значений функции. По обработанным данным были получены четыре категории графиков и найдены диапазоны значений параметров для настройки модели ARIMA для каждой категории: 1) график похож на прямую и имеет четкий тренд: = 1, ∈ [1, 3], ∈ [1, 3], прогнозируются без каких-либо проблем; 2) график с четким трендом: ∈ [2, 3], ∈ [1, 3], ∈ [1, 3] прогнозируются без каких-либо проблем; 3) график сложно оценить и имеет слабый тренд: ∈ [1, 5], ∈ [1, 2], ∈ [1, 2], качество прогноза может быть плохим, автор предполагает, что в данном случае на ухудшении качества прогноза сказывается малая длина набора данных; 4) график сложно оценить, тренд отсутствует или сложно определить наглядно: ∈ [1, 2], ∈ [0, 2], ∈ [0, 2], может возникнуть ситуация, при которой ряд окажется стационарным, в применении модели ARIMA не будет смысла, однако если ей воспользоваться, то при нулевых AR и MA можно получить качественные прогнозы.
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