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# Standard Error Of Autocorrelation

comparison of convolution, cross-correlation and autocorrelation. Autocorrelation, also known as serial correlation, is the correlation of a signal with itself at different points in time. Informally, it is the similarity between observations as autocorrelation function a function of the time lag between them. It is a mathematical tool

## Autocorrelation Example

for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency autocorrelation matlab in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Unit root processes, trend stationary processes, autoregressive how to calculate autocorrelation processes, and moving average processes are specific forms of processes with autocorrelation. Contents 1 Definitions 1.1 Statistics 1.2 Signal processing 2 Properties 3 Efficient computation 4 Estimation 5 Regression analysis 6 Applications 7 Serial dependence 8 See also 9 References 10 Further reading 11 External links Definitions Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is

## Autocorrelation Statistics

used interchangeably with autocovariance. Statistics In statistics, the autocorrelation of a random process is the correlation between values of the process at different times, as a function of the two times or of the time lag. Let X be a stochastic process, and t be any point in time. (t may be an integer for a discrete-time process or a real number for a continuous-time process.) Then Xt is the value (or realization) produced by a given run of the process at time t. Suppose that the process has mean μt and variance σt2 at time t, for each t. Then the definition of the autocorrelation between times s and t is R ( s , t ) = E ⁡ [ ( X t − μ t ) ( X s − μ s ) ] σ t σ s , {\displaystyle R(s,t)={\frac {\operatorname {E} [(X_{t}-\mu _{t})(X_{s}-\mu _{s})]}{\sigma _{t}\sigma _{s}}}\,,} where "E" is the expected value operator. Note that this expression is not well-defined for all time series or processes, because the mean may not exist, or the variance may be zero (for a constant process) or infinite (for processes with distribution lacking well-behaved moments, such as certain types of power

## Autocorrelation Test

in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers https://en.wikipedia.org/wiki/Autocorrelation are voted up and rise to the top Why autocorrelation affects OLS coefficient standard errors? up vote 3 down vote favorite 1 It seems that OLS residuals autocorrelation is not always an issue, depending on the problem at hand. But why residuals autocorrelation would affect the coefficient standard errors? From the Wikipedia article on autocorrelation: While it does not bias the OLS coefficient estimates, the standard errors tend to be underestimated http://stats.stackexchange.com/questions/114564/why-autocorrelation-affects-ols-coefficient-standard-errors (and the t-scores overestimated) when the autocorrelations of the errors at low lags are positive. regression standard-error autocorrelation share|improve this question edited Sep 6 '14 at 22:45 Glen_b♦ 151k20250519 asked Sep 6 '14 at 22:34 Robert Kubrick 1,27041937 Consider an extreme case of correlation. Suppose all the errors were perfectly positively correlated. In other words, somebody had generated a single random number and added it to all the response values. How certain would you be of (say) the intercept in the regression? Would you have any clues at all concerning the size of the random value that was added? –whuber♦ Sep 6 '14 at 22:55 Yes, but that is true of any missing predictor that could explain 99% of the variance and we just ignore. Why are making a specific case for $Y_{t-1}$? –Robert Kubrick Sep 6 '14 at 22:59 My example is not missing any predictors at all: it is only positing an extreme case of autocorrelation among the residuals. –whuber♦ Sep 7 '14 at 13:34 ok, but how is this different than the case where we don't have any residuals autocorrelation, but we're not including another critical predictor? We can draw the same confidence conclusions because of that other critical predictor. T