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Time series. In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily ...
Decomposition of time series. The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns. [1] There are two principal types of decomposition, which are outlined below.
Given a time series of data x t, the STAR model is a tool for understanding and, perhaps, predicting future values in this series, assuming that the behaviour of the series changes depending on the value of the transition variable. The transition might depend on the past values of the x series (similar to the SETAR models), or exogenous variables.
First, regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Second, in some situations regression analysis can be used to infer causal relationships between the independent and dependent variables.
Autoregressive moving-average model. In the statistical analysis of time series, autoregressive–moving-average (ARMA) models are a way to describe of a (weakly) stationary stochastic process using autoregression (AR) and a moving average (MA), each with a polynomial. They are a tool for understanding a series and predicting future values.
The first to introduce and analyse the concept of spurious—or nonsense—regression was Udny Yule in 1926. [2] Before the 1980s, many economists used linear regressions on non-stationary time series data, which Nobel laureate Clive Granger and Paul Newbold showed to be a dangerous approach that could produce spurious correlation, [3] since standard detrending techniques can result in data ...
[1] [2] Given two completely unrelated but integrated (non-stationary) time series, the regression analysis of one on the other will tend to produce an apparently statistically significant relationship and thus a researcher might falsely believe to have found evidence of a true relationship between these variables.
Exponential smoothing. Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.