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The Moving Median is a more robust alternative to the Moving Average when it comes to estimating the underlying trend in a time series. While the Moving Average is optimal for recovering the trend if the fluctuations around the trend are normally distributed, it is susceptible to the impact of rare events such as rapid shocks or anomalies.
Trend-stationary process. In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. [1] The trend does not have to be linear.
For example, time series are usually decomposed into: , the trend component at time t, which reflects the long-term progression of the series (secular variation). A trend exists when there is a persistent increasing or decreasing direction in the data. The trend component does not have to be linear. [1]
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered, tends to increase or decrease over time, or is influenced by changes in an external factor. Linear trend estimation essentially creates a straight line on a graph of data that models the general ...
The notation ARMA(p, q) refers to the model with p autoregressive terms and q moving-average terms.This model contains the AR(p) and MA(q) models, [5]= + = + =. The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference.
Autoregressive integrated moving average. In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average ( ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. To better comprehend the data or to forecast upcoming series points, both of these models are fitted ...
In Fourier analysis, such as the Fourier transform and discrete Fourier transform, the sinusoids fitted to data are all mutually orthogonal, so there is no distinction between the simple out-of-context dot-product-based projection onto basis functions versus an in-context simultaneous least-squares fit; that is, no matrix inversion is required ...
e. In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables ). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear ...