# computeEffectiveNumObs: Compute the effective number of observations taking into... In lognorm: Functions for the Lognormal Distribution

## Description

Compute the effective number of observations taking into account autocorrelation

## Usage

 ```1 2 3 4 5 6``` ```computeEffectiveNumObs( res, effAcf = computeEffectiveAutoCorr(res), na.rm = FALSE, exact.na = TRUE ) ```

## Arguments

 `res` numeric of autocorrelated numbers, usually observation - model residuals `effAcf` autocorrelation coefficients. The first entry is fixed at 1 for zero distance. `na.rm` if not set to TRUE will return NA in there are missings in the series `exact.na` if set to FALSE then do not count and correct for missing in the sum of autocorrelation terms. This is faster, but results are increasingly biased high with increasing number of missings.

## Details

Assumes records of all times present. DO NOT REMOVE OR FILTER NA records before. The length of the time series is used.

Handling of NA values: The formula from Zieba 2011 is extended to subtract the number of missing pairs in the count of correlation terms. If 'exact.na=false' the original formula is used (after trimming edge-NAs).

## Value

integer scalar: effective number of observations

## References

```Zieba & Ramza (2011) Standard Deviation of the Mean of Autocorrelated Observations Estimated with the Use of the Autocorrelation Function Estimated From the Data. Metrology and Measurement Systems, Walter de Gruyter GmbH, 18 10.2478/v10178-011-0052-x```

```Bayley & Hammersley (1946) The "effective" number of independent observations in an autocorrelated time series. Supplement to the Journal of the Royal Statistical Society, JSTOR,8,184-197```

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# generate autocorrelated time series res <- stats::filter(rnorm(1000), filter = rep(1,5), circular = TRUE) res[100:120] <- NA # plot the series of autocorrelated random variables plot(res) # plot their empirical autocorrelation function acf(res, na.action = na.pass) #effAcf <- computeEffectiveAutoCorr(res) # the effective number of parameters is less than number of 1000 samples (nEff <- computeEffectiveNumObs(res, na.rm = TRUE)) ```

lognorm documentation built on Nov. 22, 2021, 1:07 a.m.