This file contains
the sample autocorrelation function (ACF) and sample partial autocorrelation function (PACF) for the proportion of New Zealand male stillbirths from 1929 - 2009.
This file contains
the sample autocorrelation function (ACF) and sample partial autocorrelation function (PACF) for the proportion of males born in New Zealand from 1876 - 2009.
In Exhibit 2,
the sample autocorrelation function shows significant autocorrelation in the squared residual series, calculated by the square of daily total return of the S&P 500 subtracted by the long - term average daily return.
Not exact matches
Arguably the simplest is to just to compute the (lower) effective
sample size based on the actual size and the estimated
autocorrelation, and use that value to determine your probability (p).
Note that the range of simulated
autocorrelation values is entirely due to
sampling fluctuations associated with a short record: none are significantly different from zero.
For continuously
sampled processes, the ACS and ACVS are known as the
autocorrelation function (ACF) and autocovariance function (ACVF) respectively.
We adjusted both the
sample size and the degrees of freedom for indexing of the critical t - value according to the lag - 1
autocorrelation of the regression residuals.
The simplest, a chain of length one month («AR (1)» in the plot), doesn't do it, but one of just two months length («AR (2)») works pretty well (subtracting it from the
sample noise moves most of the
autocorrelations into the zero uncertainty range).
However, we find the estimation of statistical significance ascribed to these results to be in error: MS00 based this calculation on 12 - month smoothed data, from a calculation of the effective
sample size (taking into account
autocorrelation effects).
Yeah, I'd prefer more
samples but I think in this case the
autocorrelation can help us get the edges right if we wanted to plot credible intervals (I'd smooth the edges with the same filter I used on the data).
Honestly, the p - values should be generated by constructing a Monte Carlo ensemble of model results, per model, and looking at the actual distribution of (and variance of,
autocorrelation of, etc) the ensemble of outcomes where the outcomes ARE iid
samples drawn from a distribution of model results, and then use a correctly generated mean / sd to determinea p - value on the null hypothesis.
I am somewhat surprised, given your PhD and your list of programs you use (Mathematica, Excel, etc.) that you seem to be so woefully unaware of even these rudimentary issues of
sample size and
autocorrelation when analyzing climate data... truly, you have demonstrated beyond question that are out of your depth here.