Serial correlation refers to the relationship between consecutive or neighboring data points in a sequence. It shows whether there is a pattern or trend in how the values change over time. For example, if one value is high, the next value is also likely to be high, indicating positive
serial correlation. On the other hand, if one value is high, and the next value is low, it suggests negative
serial correlation. Serial correlation helps us understand the predictability or randomness of data points in a sequence.
Full definition
A richer analysis could exploit additional information, such as the temporal ordering of the classrooms for a given teacher, where patterns
of serial correlation could emerge.
The model result (s) were already quite insignificant without the adjustment
for serial correlation with the errors.
To summarize, the Mann - Kendall has essentially the same lack of robustness wrt
serial correlation as the parametric estimator.
Having some sense of
serial correlations by quintile, however, provides useful perspective for investors building company models.
Is it possible to
predict serial correlation (autocorrelation) of stock returns, and thereby enhance reversal and momentum strategies.
As a statistical question, answering would require
considering serial correlation in the data as well as specifying what time range you consider to be «the pause» and specify «statistically significant compared to what»?
Now maybe you don't want to give equal weighting to years (technical aside: Herndon - Ash - Pollin bring up
serial correlation as a possibility).
Trading Volume and
Serial Correlation in Stock Returns: John Y. Campbell, Sanford J.Grossman, Jiang Wang
The second issue is
serial correlation, the probability a company stays in the same ROIC quintile from year to year.
An adjustment for
the serial correlation of returns accomplishes much the same thing.
[5] Andrew Lo et al., An Econometric Model of
Serial Correlation and Illiquidity in Hedge Fund Returns, Journal of Financial Economics, 2003.
Value is based on long - term mean reversion, while momentum relies on intermediate (usually 3 to 12 months)
serial correlation.
Using block bootstrapping selects a random sequence of annual returns and better captures
the serial correlation and mean reversion of assets.
In the January 2014 version of his paper entitled «The Information Content of Option Prices Regarding Future Stock Return
Serial Correlation», Scott Murray investigates the relationship between the variance ratio (the ratio of realized to implied stock return variance, a measure of the variance risk premium) to stock return serial correlation.
An appreciation of the degree of
serial correlations in ROICs provides perspective on how much ROICs are likely to improve or deteriorate.
[1] M. Getmansky, A. W. Lo & I. Makarov, An Econometric Model of
Serial Correlation and Illiquidity in Hedge Fund Returns, Journal of Financial Economics, 2004.
Global maps of
serial correlation in non-linearly detrended monthly time - series for boreal summer (top) and austral summer (bottom).
Simulation experiments demonstrated that the existence of
serial correlation alters the variance of the estimate of the Mann - Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation.
These results indicate that the commonly used pre-whitening procedure for eliminating the effect of
serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test.
By the way, the trend uncertainty when the trend is calculated this way is + / - 0.32, and, if one corrects for
the serial correlation in the residuals, it jumps to + / - 0.86.
When calculated properly, the 50 - year Byrd trend is 0.25 + / - 0.2 (corrected for
serial correlation).
What would seem so simple statistically is complicated by the degrees of freedom in the various time series which is related to
the serial correlation in the data (e.g., next year's value is highly dependent on this year's value).
In the absence of
serial correlation the standard deviation of this trend estimate is the standard deviation of the period - to - period changes in temperature divided by the square root of the number of periods in the interval.