High Serial Correlation Research Articles

A note on the effects of serial cross correlation

Given a large sample of properties with time series returns extending over a number of periods it can be shown that the average cross correlation coefficient between the properties increases with the reporting interval. This paper offers an explanation for why this phenomenon exists and shows that, in addition to the contemporaneous cross correlation, the impact of serial cross correlation plays an important role. By contrast, smoothing has little impact. It is further shown that at the portfolio level the distribution of cross correlation coefficients is positively skewed for monthly returns. As the reporting interval increases the distribution becomes more normal. This has important implications at two levels. First, behavioural effects are likely to be more pervasive at the monthly level so that a large proportion of monthly valued properties will exhibit high serial cross correlation. Second, high serial cross correlation will induce high serial correlation in an index of returns. As the reporting interval increases this effect diminishes

Market Efficiency and Return Statistics: Evidence from Real Estate and Stock Markets Using a Present-Value Approach

This paper develops a methodology to identify asset price response to news in the framework of Campbell-Shiller log-linear present-value equation. We show that slow price adjustment not only induces high serial auto correlation in real estate excess returns, but also dampens their volatility and correlation with other asset returns. Using Hong Kong real estate and stock market data, we find that the quarterly real estate price assimilates only about half the effect of market news, whereas the quarterly stock price incorporates the news fully. Our analysis identifies a cumulative price adjustment that recovers lost information in real estate returns due to market inefficiency and thereby restores real estate return volatility and correlation with the stock market.

A cumulative sum type of method for environmental monitoring

We describe a graphical approach for detecting changes in the distribution of the variable over a number of monitoring sites between two or more sample times, with associated randomization tests. This method was derived from the cumulative sum (CUSUM) method that was developed initially for industrial process control, but our use differs in some fundamental ways. In particular, the standard CUSUM procedure is used to detect changes with time in the mean of a variable at one location, whereas our concern is with detecting changes with time in the distribution of a variable measured at a number of different locations. We compare our randomization test for any changes in distribution with the Mann–Kendall test and analysis of covariance in terms of the power for detecting a systematic time trend affecting all sites, with and without serial correlation in time. We also compare these different tests in the situation where trend occurs, but it is not the same at all sites, again with and without serial correlation in time. All tests were adversely affected by high serial correlation, so we repeated the comparisons with the CUSUM and analysis of covariance tests modified to take this into account. We conclude that although our randomization test sometimes has less power than the Mann–Kendall test and analysis of covariance for detecting trends, it does have reasonable power and also has the ability to detect other types of change with time. The modified randomization test is very robust to serial correlation. Copyright © 2000 John Wiley & Sons, Ltd.

Climate change and the detection of trends in annual runoff

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 08:129-134 (1997) - DOI: https://doi.org/10.3354/cr008129 Climate change and the detection of trends in annual runoff McCabe GJ Jr, Wolock DM This study examines the statistical likelihood of detecting a trend in annual runoff given an assumed change in mean annual runoff, the underlying year-to-year variability in runoff, and serial correlation of annual runoff. Means, standard deviations, and lag-1 serial correlations of annual runoff were computed for 585 stream gages in the conterminous United States, and these statistics were used to compute the probability of detecting a prescribed trend in annual runoff. Assuming a linear 20% change in mean annual runoff over a 100 yr period and a significance level of 95%, the average probability of detecting a significant trend was 28% among the 585 stream gages. The largest probability of detecting a trend was in the northwestern U.S., the Great Lakes region, the northeastern U.S., the Appalachian Mountains, and parts of the northern Rocky Mountains. The smallest probability of trend detection was in the central and southwestern U.S., and in Florida. Low probabilities of trend detection were associated with low ratios of mean annual runoff to the standard deviation of annual runoff and with high lag-1 serial correlation in the data. Runoff · Climate change · Trends · United States Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 08, No. 2. Publication date: May 08, 1997 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 1997 Inter-Research.

Reexamination of the relation between depth of the Antarctic Ozone Hole, and equatorial QBO and SST, 1962–1992

The relation between depth of the Antarctic ozone hole, and equatorial QBO and SST, is reexamined for the interval 1962–1992, using Dobson total‐ozone data at the South Pole, Singapore 50 mb zonal wind, and average SST in the El Nino region 12S–2N, 180–90W. During this interval the correlation between October–November values of South Pole total ozone, and south polar 100 mb temperature from radiosondes, is 0.93. In 23 of 27 cases, South Pole springtime (October–November) total ozone decreased from one year to the next when the Singapore 50 mb zonal wind averaged from the east during the intervening 3 seasons and increased when this wind averaged from the west. Owing to the high serial correlation of the wind and total‐ozone data, this distribution is only significant at the 5% level according to the Chi‐square test, but basically supports the conclusions of Garcia and Solomon (1987) and Lait et al. (1989) regarding the relation between equatorial QBO and depth of the ozone hole. The tendency for a deeper ozone hole when equatorial SST warms (El Nino) yields a relation between depth of the Antarctic ozone hole, and equatorial QBO and SST, significant at the 1% level only by the subjective drawing of a smooth line which separates springtime total‐ozone increases and decreases from one year to the next in 24 of 25 cases with 2 cases on the line of separation. The Singapore 50 mb wind has been from the west during the first half of 1993, suggesting a less deep ozone hole in 1993 than in 1992, especially if the current prolonged El Nino finally abates in mid 1993.

More on the Speed of Adjustment in Inventory Models

When empirical stock-adjustment models of manufacturers' inventories of finished goods are estimated, there appear to be two local minima in the sum of squared residuals functions. At one local minimum, the estimated adjustment speed is typically quite high; at the other, it is typically quite low. Furthermore, finding two sets of estimates that fit the data almost equally well does not appear to be a quirk of this particular application. Rather, it stems from a fundamental identification problem that afflicts partial adjustment models of all kinds. In the specific context of manufacturers' inventories of finished goods, the estimation procedure employed by Maccini and Rossana seems to pick out the solution with rapid adjustment (and high serial correlation in the disturbances) whereas the solution with slow adjustment (and little serial correlation) is more often the global minimum.

Holocene secular variation in western North America: Paleomagnetic record from Fish Lake, Harney County, Oregon

An 8.9‐m composite section of lake sediment from Fish Lake, Steens Mountain, southeastern Oregon, has provided a high‐resolution record of Holocene geomagnetic secular variation in western North America. The section is composed of overlapping core segments with stratigraphic control based on six tephra layers and other thin, distinct bands and with age control from 37 radiocarbon dates. The 455 paleomagnetic samples possess a strong and stable magnetic remanence which is carried by pseudo‐single‐domain magnetite. Paleomagnetic records for individual core segments show low scatter and high serial correlation, and where the segments overlap, there is excellent agreement between records. The azimuthal orientation of the composite section was recovered from the known direction of the geomagnetic field at the time of the climactic eruption of Mount Mazama tephra which is present in Fish Lake. Both internal and external evidence, including the correspondence with an archaeomagnetic record from the southwestern United States, support the conclusion that the Fish Lake record represents the history of geomagnetic field behavior during at least the last 10,000 years B.P. Analysis of that record reveals that the average geomagnetic direction can not be distinguished from that of a geocentric axial dipole field and that the overall circularity of the field was clockwise but the detailed behavior was quite complex. Angular standard deviations of both field directions and virtual geomagnetic poles differ significantly from the values predicted from theoretical models of secular variation but are consistent with those of other Holocene records. When the record from Fish Lake is compared to the proposed type curve for east central North America, there is excellent agreement for the past 6000 years, provided the curves are offset by about 400 years. This offset corresponds to a rate of westward drift of about 0.062°/yr. Beyond about 6000 radiocarbon years ago, good agreement between the two curves occurs when there is no offset, suggesting that the field was standing rather than drifting during this time.

Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables

Since dynamic regression equations are often obtained from rational distributed lag models and include several lagged values of the dependent variable as regressors, high order serial correlation in the disturbances is frequently a more plausible alternative to the assumption of serial independence than the usual first order autoregressive error model. The purpose of this paper is to examine the problem of testing against general autoregressive and moving average error processes. The Lagrange multiplier approach is adopted and it is shown that the test against the nth order autoregressive error model is exactly the same as the test against the nth order moving average alternative. Some comments are made on the treatment of serial correlation.

The behavior of equity securities on the German Stock Exchange

This is the first major empirical study of the German Stock Exchange and involves the analysis of monthly data for ninety German companies from 1960 to 1970. Whereas previous studies had suggested that German securities were peculiar, this analysis showed that, except for the high positive serial correlation of returns for the larger companies, German securities had very similar properties to securities elsewhere. Betas for German companies were fairly stationary over time, with the interperiod correlation for company betas ranging from 0.2 to 0.4. When the effect of measurement error was reduced, the perceived stationarity increased and a significant regression tendency towards the mean was observed. Further, it was found that the behaviour of German securities did not conflict with the domestic capital asset pricing model and indeed supported it during the bull market of the early 1960s.

A Simple Model for Population Dynamics in Stochastic Environments

1. A linear model for population dynamics in stochastic environments is introduced by linearizing the logistic equation in discrete time for small stochastic variations around a large average carrying capacity. The analysis of this model involves the relatively simple mathematics of time-series analysis and is not restricted to white noise (i.e., totally unpredictable) environments. 2. In this linear model the population size at any time is a reflection of many historical effects. The intrinsic rate of increase, r, is a measure of the responsiveness of the population to changes in k. A responsive population (r ≈ 1) does not retain historical effects for long, whereas a sluggish population (r ≈ 0) does. 3. The variance of the population size through time always increases with r. But the presence of much predictability in the environment, as measured by the serial correlation between consecutive values of K, reduces the influence of r. High serial correlation allows time for even a sluggish population to ac...

Effective Devaluation and Exports: Some Issues in Empirical Analysis, with Illustrations from Israel

The arguments for and against devaluation are usually based on speculation from theory or intuition, but rarely on statistical evaluations of past devaluations. The relatively frequent devaluations in many developing countries2 stress the need and provide some data for such statistical analysis. But even where data exist for at least relatively simple regression analysis, conceptual issues concerning both dependent and independent variables complicate empirical work and conftise policy discussions. This paper discusses several such issues which arose in an empirical study of Israel, and the solutions adopted. Section I considers what is the most suitable dependent variable. Sections II and III discuss explanatory variables-exchange rates and a growth factor, respectively. Conspicuous by its absence is a foreign demand variable: several attempts to introduce such a variable did not lead to significant results, mainly because of high serial correlation between foreign demand indicators and domestic growth indicators. It may also be argued that Israel's aggregated industrial exports-to which the empirical work refers-generally faced highly (if not infinitely) elastic demand curves. Thus, our main concern is with export supply functions. Some empirical results are presented in Section IV.

Correlogram Analysis Revisited

Consideration of the Hurst coefficient h offers new insight into the interpretation of observed correlograms for streamflow sequences. Autoregressive models, for which h = ½, cannot reproduce the structures of those correlograms. The structures are symptomatic of long‐term persistence as indicated by observed values of h being greater than ½. The tendency has been to test a sequence for independence, and if the hypothesis of independence is unacceptable, then (1) the generating process for the sequence is approximated by a short memory process, and (2) variations in the high lag serial correlation coefficients are ascribed to chance. If indeed the sequences are generated by long memory processes, then the powers of most independence tests are low for short records. Consequently, correlograms may be useful indicators of long‐term persistence when more formal tests give contrary results.

The instability of the incremental capital-output ratio

Although the incremental capital-output ratio (ICOR) is frequently used by policy makers for economic projections, many economists doubt its usefulness, mainly, because of its instability over time. This article considers the factors affecting the movement of the ratio on “ a priori” grounds, and its actual variation in several countries. The empirical part of this study reveals that the national incremental capital-output ratios do in fact vary from year to year over a wide range. Between five-year periods, however, the extreme variability of the annual ratios is reduced substantially. A regression analysis of annual gross domestic product on gross fixed cumulative investment for the period 1950–1965 showed a very good fit for all 24 countries considered ( R 2 > 0.960). While significant statistically, however, these results are doubtful because of the high serial correlation. The study also emphasizes that, even if the ICOR is stable, it might lead policy-makers to project investment uneconomically if the relative contribution of capital to output is not included in the calculation.