Time series - jikeiretsu (English spelling) time series

Japanese: 時系列 - じけいれつ（英語表記）time series

A time series is a sequence of values that are observed over time (days, months, years, etc.) and arranged in that order. The statistical analysis of such values is called time series analysis. Mathematically, the values at each point in time are considered to be the realized values of random variables, since they contain quantities that are determined by chance, and the sequence of values observed at each point in time is considered to be a sample of a stochastic process. There are various models for such time series, and statistical research is also progressing. For example, for stationary processes in which the probability distribution and correlation between values at each point in time are invariant over time, the characteristics of the time series can be captured by knowing the autocorrelation coefficient, which shows the correlation between values at two points in time, and the spectral density function, which shows what frequency waves are strongly contained. There are theories of detailed properties and inference for normal processes, in which the joint distributions at several points in time all follow a normal distribution; Markov processes, in which it is sufficient to know the current state to know the probability distribution that shows what the next value will be, and it is not necessary to know all of the past; and autoregressive and moving average processes, which represent the relationship with values at past points in time as a single model. There are also theories of inferring the coefficients of trend lines (trends, mean value functions) in time series, and theories by N. Wiener and AN Kolmogorov regarding predicting future values.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

時間 (日，月，年など) の経過とともに変化していく量を観測し，得られた値をその順序に従って整理，配列したもの。このような量を統計的に分析することを時系列解析という。数学的には各時点の値には偶然的に定まる量が含まれるものとして確率変数の実現値と考え，時点ごとに観測されていく値の列を確率過程の一標本と考える。このような時系列には種々のモデルが考えられ，統計学上の研究も進んでいる。たとえば確率分布や各時点の値の間の相関が時間の推移に関して不変であるような定常過程については，2つの時点の値の相関を示す自己相関係数やどのような周波数の波が強く含まれるかを示すスペクトル密度関数を知ることによってその時系列の特徴がとらえられる。いくつかの時点の同時分布がすべて正規分布に従う正規過程，この次の値の取り方を示す確率分布を知るには現時点の状態がわかっていれば十分で，過去をすべて知る必要のないマルコフ過程，過去の時点の値との関係を一つのモデルとして表わす自己回帰・移動平均過程などに関しては詳しい性質や推測のための理論があり，また時系列の傾向線 (トレンド，平均値関数) の係数の推測の理論，将来の値の予測に関しての N.ウイナーや A.N.コルモゴロフの理論などがある。

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