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Autocorrelation (serial correlation) is the correlation of a series of data with itself at some lag. This is an important topic in time series analysis.

16 votes
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PACF manual calculation

As you said "The PACF values are the coefficients of an autoregression of the series of interest on lagged values of the series" and I add where the PACF(K) is the coefficient of the last (kth) lag. T …
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15 votes

How to test the autocorrelation of the residuals?

The DW Test or the Linear Regression test are not robust to anomalies in the data. If you have Pulses, Seasonal Pulses , Level Shifts or Local Time Trends these tests are useless as these untreated co …
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6 votes
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Autocorrelation and trends

The autocorrelation(acf) function summarizes the correlation of different lags and is a descriptive statistic. If there is a "trend" in the data then the acf will suggest non-stationarity. …
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6 votes
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When was the autocorrelation function invented? And what was the motivation for it?

The earliest reference for autocorrelation that I can find relates to Udney Yule, a British Statistician who among other notable accomplishments developed the Yule-Walker procedure to approximate the Partial …
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5 votes

Can I trust a regression if variables are autocorrelated?

The t-statistics are un-reliable in the presence of autocorrelation of the errors. …
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5 votes

Reasons for autocorrelation in time-series residuals

Residuals can be autocorrelated due to a number of factors. Possible causes are: insufficient ARIMA structure, omitted lags of one or more of the user-specified causal variables, omitted deter …
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5 votes
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Multiple ARIMA models fit data well. How to determine order? Correct approach?

1)Can you still describe the ACF of the time series as cutting of despite the spikes around lag 26? 26 and 27 suggest to me that the data is weekly some sort of annual cycle pf order 26 or 52 Are th …
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4 votes
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What to do with very low Durbin-Watson?

The Durbin-Watson test may suggest the need for an ARIMA model to render the error term free of structure IFF there are no outliers/inliers/pulses AND no unspecified evel/step shifts AND no unspecifie …
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4 votes

Outlier detection for generic time series

You are quite right that the ARIMA Model you are using (first differences) may not be appropriate to detect outliers. Outliers can be Pulses, Level Shifts, Seasonal Pulses or Local Time Trends. You mi …
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4 votes
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How to perform pooled cross-sectional time series analysis?

For each of the 86 companies , identify an appropriate ARMAX model which should incorporate the effects ( both contemporaneous and lag ) of the two user-suggested predictor variables and any necessary …
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4 votes
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How to build ARIMA model from my time series?

You originally had 500,000 readings, 128 per second for 3,907 seconds. After taking the readings at 1 second interval (N=3907) the plot is here . AUTOBOX identified a break point in parameters at per …
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3 votes

Why is the ACF diagram showing seasonal patterns when they should have been removed by `deco...

q1. The decomposition assumes 11 deterministic seasonal factors ... if the data has an autoregesssive structure seasonal dummies are inadequate. On the other hand if the data is correctly modelled …
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3 votes
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What to read from the autocorrelation function of a time series?

this acf suggests non-stationarity which might be remedied by incorporating a daily effect as it appears to evidence structure at lag 24. The daily effect could be either auto-regressive of order 24 o …
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3 votes

Autocorrelation and auto regressive

Yes that is correct auto-correlation is a sequence of correlations taken at fixed intervals. If the auto-correlation decays while the partial correlation (conditional correlation ) cuts off after k va …
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3 votes

Does autocorrelation cause bias in the regression parameters in piecewise regression?

Thanks for sharing your data. It raises some interesting answers. To begin with a potentially useful model between y and x is which suggests a strong relationship between y and two previous y's and bo …
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