Statistical time-series analysis has the potential to improve our understanding of human-environment interaction in deep time. However, radiocarbon dating—the most common chronometric technique in archaeological and palaeoenvironmental research—creates challenges for established statistical methods.
The methods assume that observations in a time-series are precisely dated, but this assumption is often violated when calibrated radiocarbon dates are used because they usually have highly irregular uncertainties.
As a result, it is unclear whether the methods can be reliably used on radiocarbon-dated time-series. With "Radiometric dating pictures rose" in mind, we conducted a large simulation study to investigate the impact of chronological uncertainty on a potentially useful time-series method. It is designed for use with Radiometric dating pictures rose time-series data, which makes it applicable to a wide range of questions about human-environment interaction in deep time.
Our simulations Radiometric dating pictures rose that the PEWMA method can often correctly identify relationships between time-series despite chronological uncertainty. When two time-series are correlated with a coefficient of 0. With correlations of around 0. While further testing is desirable, these findings indicate that the method can be used to test hypotheses about long-term human-environment interaction with a reasonable degree of confidence.
Time-series regression analysis is an important tool for testing hypotheses about human-environment interaction over the long term. The primary sources of information about human behaviour and environmental conditions in deep time are the archaeological and palaeoenvironmental records, respectively. These records contain observations with an inherent Radiometric dating pictures rose ordering and are thus time-series.
This means time-series regression methods could be used to quantitatively test hypotheses about the impact of climate change on humans and other hominins, or conversely the impact of hominin societies on their environments. However, there is reason to think that chronological uncertainty may complicate the use of such methods.
In particular, the chronological uncertainty associated with the most common chronometric method used in the dating of both records—radiocarbon dating—could undermine our ability to confidently identify statistical relationships between the records. This is because calibrated radiocarbon dates have highly irregular uncertainties associated with them, and uncertainties of this type are not in line with the assumptions of many standard statistical methods, including time-series analysis [ 1 — 5 ].
To investigate this possibility, we conducted a simulation study in which we investigated the impact of radiocarbon dating uncertainty on a time-series regression method that is well-suited for archaeological and palaeoenvironmental research—the Poisson Exponentially-Weighted Moving Average PEWMA method [ 6 ]. Time-series "Radiometric dating pictures rose" have to be analyzed carefully because the order in the sequence of observations matters.
There are two traits a time-series can have that make temporal ordering important. One is non-stationaritywhich describes time-series with statistical properties that vary through time—e. The other troublesome trait is autocorrelationwhich means the observations in the series correlate with themselves at a given lag [ 7 ]. Autocorrelation leads to dependence among the observations in a time-series, which violates another common statistical assumption, namely that observations are independent.
Archaeological and palaeoenvironmental time-series typically have both traits [ 389 ].
They will usually be non-stationary, because almost all environmental or cultural phenomena change over time—e. They will also typically contain temporal autocorrelation. Thus, archaeological and palaeoenvironmental data can be expected to violate the assumptions of many statistical methods.
Consequently, we need special methods to find correlations between past human and environmental conditions. Fortunately, these methods already because statisticians, mathematicians, and engineers have been working with non-stationary, autocorrelated time-series for a long time [ 10 ]. As a result, many established time-series methods are designed specifically to handle non-stationary, autocorrelated data [ 7811 ].
However, time-series of archaeological and palaeoenvironmental observations are idiosyncratic in another way that potentially undermines even these established methods—often we are uncertain about the precise times associated with the observations [ 12 — 14 ].
That is, the time-series contain chronological uncertainty. Contemporary time-series, such as stock prices or daily temperatures, are usually recorded at precisely known times, but looking into the deep past entails significant chronological uncertainty. Archaeologists and palaeoenvironmental scientists usually make chronometric estimations by proxy using radiometric methods that rely on measuring isotopes of unstable elements that decay at a constant rate [ 15 ].
Even the most precise of these methods, however, yield uncertain dates, some with decadal error "Radiometric dating pictures rose" and others with centennial or millennial error ranges. Consequently, many palaeoenvironmental and archaeological time-series contain temporal uncertainty. The most common chronometric method, radiocarbon dating, is particularly problematic. Radiocarbon dates have to be calibrated to account for changes in isotope ratios through time.
The calibration process results in chronometric errors that are often highly irregular, yielding ranges of potential dates spanning many decades or even centuries [ 451617 ]. Radiometric dating pictures rose statistical methods are, therefore, undermined by calibrated radiocarbon dating because most methods rely, at least to some extent, on point estimates. Time-series methods are no different, raising concerns about our ability to use them for identifying correlations between archaeological and palaeoenvironmental time-series.
In the study reported here, we explored the impact of chronological uncertainty on a time-series regression method called the Poisson Exponentially Weighted Moving Average PEWMA method [ 6 ].
Classified as a state-space time-series method, the PEWMA method models physical and natural systems as a set of input and output variables. It can be thought of as a mathematical filter that takes input variables and produces outputs by estimating the relationships among the variables. Importantly, the method accounts for autocorrelation and non-stationarity in the Poisson process. It is potentially useful for many archaeological and palaeoenvironmental applications because count data is common in these fields—e.
The first is called the measurement equation. The measurement equations represent the observed Radiometric dating pictures rose data as outcomes of a sequence of Poisson random variables. The previous mean is not merely a lagged value, though, which is why the asterisk is used. These equations characterize the change in the unobserved mean through time. The first equation defines the mean at "Radiometric dating pictures rose" given time, and has three terms.
The first of these, e r tdescribes the base rate of the mean process and ensures that the mean is always positive, which is necessary for Poisson processes. To be consistent with the measurement equations, we added an asterisk to the term, making it slightly different from Brandt et al. The parameters that appear in the Gamma and Beta distributions are also estimated from the data.
To the best of our knowledge, the PEWMA method has only been used to analyze past human-environment interaction in one study [ 18 ]. In that study, we tested the prominent hypothesis that climate change exacerbates conflict within and between human societies over the long term e.
To test the hypothesis, we compared a time-series of Classic Maya conflict levels to several palaeoenvironmental proxies. The time-series of interest was a historical record of conflict events inscribed into monuments along with Classic Maya Long Count calendar dates.
The conflict events include mentions of violent attacks, captive taking, human sacrifices, deliberate destruction of monuments, and Radiometric dating pictures rose coordinated attacks timed to coincide "Radiometric dating pictures rose" astronomical events [ 2122 ]. Classic Maya elites had these events inscribed on monuments like door lintels in temples, stairways on pyramids, and most importantly large stone stelae [ 23 ].
The inscriptions describing these events generally include the date of the event in question, information about the nature of the event—e. Though not necessarily indicative of warfare in the modern sense, changes in the number of these events throughout the Classic Period likely indicates changes in the overall level of conflict among polities [ 18 ]. Radiometric dating pictures rose create a time-series of these events, we counted the number of conflicts per year period from — CE.
The size of the interval was chosen to be consistent with earlier research, but we explored changing the size of the interval in subsequent analyses and obtained results that were consistent with those yielded Radiometric dating pictures rose the main analyses see the supplementary material associated with [ 18 ]. Using the PEWMA method, we compared the conflict record with five palaeoenvironmental records including two temperature and three rainfall proxies.
The temperature proxies are sea surface temperature SST reconstructions for the summer and winter seasons in the Cariaco Basin [ 24 ]. These records show an increase in SST over the Classic Maya period that correlate with other circum-Caribbean records over the same period. They also positively correlate with air temperature readings in the central Maya region during the 20 th century see the supplementary material associated with [ 18 ]. The rainfall proxies included a titanium concentration record from the Cariaco Basin [ 25 ], an oxygen isotope record from a speleothem in southern Belize [ 21 ], and the Radiometric dating pictures rose sediment density record from Lake Chichancanab located in the center of the Yucatan Peninsula [ 26 ].
In contrast to previous research on Classic Maya conflict [ 21 ], we found that temperature was the only variable that correlated significantly with conflict levels.