periodically stationary process (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/pɪəˈrɪədɪkli ˌsteɪʃəˈnɛri ˈprəʊsɛs/

Meaning and Usage

A periodically stationary process refers to a type of stochastic process (a statistical process that involves randomness) that exhibits properties that are stationary within certain intervals or periods but may vary when observed over a larger timescale. In simpler terms, the statistical properties (such as mean and variance) of the process remain consistent during certain periods but can change after those periods.

This term is primarily used in mathematics, statistics, and fields such as signal processing and time series analysis. It tends to appear more in written contexts, particularly in academic and technical literature.

Example Sentences

1. The researchers concluded that the data collected over three years exhibited traits of a periodically stationary process.

2. Исследователи пришли к выводу, что данные, собранные за три года, проявили черты периодически стационарного процесса.

3. Understanding a periodically stationary process is essential for accurately modeling seasonal variations in economic data.

4. Понимание периодически стационарного процесса имеет важное значение для точного моделирования сезонных колебаний в экономических данных.

5. In this study, we analyze the implications of a periodically stationary process in climate modeling.

6. В этом исследовании мы анализируем последствия периодически стационарного процесса в моделировании климата.

Idiomatic Expressions

The term "periodically stationary process" does not frequently occur in idiomatic expressions since it is a niche concept primarily used in technical fields. Nonetheless, the term "stationary" is used in various expressions:

1. Stationary phase: In research, scientists often say, "During the stationary phase, the parameters of our experiment remained constant."

2. В фазе стационарности параметры нашего эксперимента оставались неизменными.

3. Stationary target: In the context of accuracy, one might say, "Hitting a stationary target requires focus and precision."

4. Попадание в стационарную цель требует сосредоточенности и точности.

5. Stationary point: In mathematics, it is common to state, "Finding the stationary point of the function helps us determine its maximum or minimum."

6. Нахождение стационарной точки функции помогает нам определить ее максимум или минимум.

Etymology

The term "periodically" derives from the late Middle English term "periodic," which comes from the Greek "periodos," meaning "a going around" or "cycle." "Stationary" comes from the Latin "stationarius," meaning "a standing" or "fixed." "Process" is borrowed from Latin "processus," meaning "a going forward."

Synonyms and Antonyms

Synonyms: - Stochastic process - Time series model (when considering specific contexts)

Antonyms: - Non-stationary process - Fluctuating process

This detailed examination of "periodically stationary process" illustrates its significance in statistical contexts and highlights its specialized use, especially in written academic discourse.