Serial Correlation Structure Research Articles

Characterizing the phytoplankton and zooplankton communities in Kootenay Lake: a time series analysis of 24 years of nutrient addition

Large-scale seasonal addition of limiting nutrients has been used for restoration in Kootenay Lake, British Columbia, since 1992 to mitigate cultural oligotrophication resulting from upstream hydropower development, river channelization, mysid shrimp introduction, and extensive tributary floodplain loss. Historical (1949) in-lake nutrient levels were targeted to stimulate bottom-up carbon transfer from native plankton communities to planktivorous and piscivorous fish populations that support popular fisheries. Analysis of 24 years of monitoring data assessed the effects of nutrient addition on the phytoplankton and zooplankton communities. Assessment involved comparisons of plankton community metric data from North Arm (1992–2003) and North + South arms (2004–2015) nutrient addition periods. A before–after, control–impact (BACI) analysis adjusted for these effects involved a series of phytoplankton and zooplankton metrics across the two lake arms. Time series analyses revealed significant serial correlation structure, significant increases in phytoplankton and zooplankton abundance and biomass, and increased stability within the phytoplankton and zooplankton communities. Results confirmed that adaptively managed nutrient restoration can effectively restore biological productivity and community structure in a large culturally oligotrophic lake.

DCCA and DMCA correlations of cryptocurrency markets

We examine the serial correlation structure of six liquid cryptocurrencies with a long data record – Bitcoin, DASH, Stellar, Litecoin, Monero, and Ripple – with a use of the detrended cross-correlation (DCCA) and detrending moving-average cross-correlation (DMCA) correlation coefficients. We find that these cryptocurrencies behave differently from the stock markets which are much closer to the random walk (efficient) dynamics. We further discuss issues connected to strong statements about cryptocurrency markets practical inefficiency.

Power and Design Issues in Crossover-Based N-Of-1 Clinical Trials with Fixed Data Collection Periods.

“N-of-1,” or single subject, clinical trials seek to determine if an intervention strategy is more efficacious for an individual than an alternative based on an objective, empirical, and controlled study. The design of such trials is typically rooted in a simple crossover strategy with multiple intervention response evaluation periods. The effect of serial correlation between measurements, the number of evaluation periods, the use of washout periods, heteroscedasticity (i.e., unequal variances among responses to the interventions) and intervention-associated carry-over phenomena on the power of such studies is crucially important for putting the yield and feasibility of N-of-1 trial designs into context. We evaluated the effect of these phenomena on the power of different designs for N-of-1 trials using analytical theory based on standard likelihood principles assuming an autoregressive lag 1, i.e., AR(1), serial correlation structure among the measurements as well as simulation studies. By evaluating the power to detect effects in many different settings, we show that the influence of serial correlation and heteroscedasticity on power can be substantial, but can also be mitigated to some degree through the use of appropriate multiple evaluation periods. We also show that the detection of certain types of carry-over effects can be heavily influenced by design considerations as well.

Generation of synthetic solar datasets for risk analysis

In this paper, we present a method for the synthetic generation of long-term time series of coupled 1-min global horizontal solar irradiance (GHI) and direct normal solar irradiance (DNI). This method requires an input of 10–15 annual time series of hourly DNI and GHI values that can be retrieved from satellite-based irradiance databases, and produces 100 years of 1-min solar radiation values that can be used for risk analysis or as input for solar plants performance simulation in a wide range of scenarios.The method consists of the conjunction of three steps. The first one, based on a stochastic procedure, is used to generate 100 years of monthly DNI and GHI values. The second step consists of the subsequent generation of daily irradiation values. To that end we have used a bootstrapping technique. The synthetic daily sequences have the same serial correlation structure as the observed data. The last step consists of the generation of 100 years of 1-min solar irradiance data out of the daily values based on the non-dimensionalization of the daily profiles by the clear sky envelope approach. The method has been applied for the location of Seville showing satisfactory results in terms of cumulative distribution functions (CDFs) of the synthetic data. We obtain an average monthly KSI (Kolmogorov-Smirnov test integral) index of 0.11 kWh/m2 for GHI and 0.26 kWh/m2 for DNI. The minimum KSI value is 0.07 kWh/m2 for GHI and 0.15 kWh/m2 for DNI obtained in January. The maximum KSI value is 0.19 kWh/m2 for GHI and 0.34 kWh/m2 for DNI obtained in June and August respectively.

Dynamic Regression Model for Hourly River Level Forecasting Under Risk Situations: an Application to the Ebro River

This work proposes a new statistical modelling approach to forecast the hourly river level at a gauging station, under potential flood risk situations and over a medium-term prediction horizon (around three days). For that aim we introduce a new model, the switching regression model with ARMA errors, which takes into account the serial correlation structure of the hourly level series, and the changing time delay between them. A whole modelling approach is developed, including a two-step estimation, which improves the medium-term prediction performance of the model, and uncertainty measures of the predictions. The proposed model not only provides predictions for longer periods than other statistical models, but also helps to understand the physics of the river, by characterizing the relationship between the river level in a gauging station and its influential factors. This approach is applied to forecast the Ebro River level at Zaragoza (Spain), using as input the series at Tudela. The approach has shown to be useful and the resulting model provides satisfactory hourly predictions, which can be fast and easily updated, together with their confidence intervals. The fitted model outperforms the predictions from other statistical and numerical models, specially in long prediction horizons.

Statistical models for evaluating suspected artefacts in long-term environmental monitoring data

Long-term water quality monitoring is of high value for environmental management as well as for research. Artificial level shifts in time series due to method improvements, flaws in laboratory practices or changes in laboratory are a common limitation for analysis, which, however, are often ignored. Statistical estimation of such artefacts is complicated by the simultaneous existence of trends, seasonal variation and effects of other influencing factors, such as weather conditions. Here, we investigate the performance of generalised additive mixed models (GAMM) to simultaneously identify one or more artefacts associated with artificial level shifts, longitudinal effects related to temporal trends and seasonal variation, as well as to model the serial correlation structure of the data. In the same model, it is possible to estimate separate residual variances for different periods so as to identify if artefacts not only influence the mean level but also the dispersion of a series. Even with an appropriate statistical methodology, it is difficult to quantify artificial level shifts and make appropriate adjustments to the time series. The underlying temporal structure of the series is especially important. As long as there is no prominent underlying trend in the series, the shift estimates are rather stable and show less variation. If an artificial shift occurs during a slower downward or upward tendency, it is difficult to separate these two effects and shift estimates can be both biased and have large variation. In the case of a change in method or laboratory, we show that conducting the analyses with both methods in parallel strongly improves estimates of artefact effects on the time series, even if certain problems remain. Due to the difficulties of estimating artificial level shifts, posterior adjustment is problematic and can lead to time series that no longer can be used for trend analysis or other analysis based on the longitudinal structure of the series. Before carrying out a change in analytic method or laboratory, it should be considered if this is absolutely necessary. If changes cannot be avoided, the analysis of the two methods considered, or the two laboratories contracted, should be run in parallel for a considerable period of time so as to enable a good assessment of changes introduced to the data series.

Generating synthetic sequences of global horizontal irradiation

When designing renewable energy systems it is common practice to use a short period of historical weather data or Typical Meteorological Year (TMY) data to evaluate the performance of a renewable energy system for a particular location. However, short periods of historical data or TMY data do not capture enough of the variation required to design a reliable renewable energy system. Longer data sequences are necessary to include a greater variety of sequences; synthetic sequences are useful because they can include sequences that have not occurred in the recorded data but are nonetheless as likely to occur as the observed data.We propose a method to generate synthetic sequences of daily and hourly global horizontal irradiation (GHI) by developing a model to deal with the deterministic component of GHI, and then adding a stochastic component using a nonparametric bootstrapping technique. We use our synthetic daily and hourly models separately and reconcile them to match afterwards, unlike other studies that generate synthetic GHI data downscaled/interpolated from observed data. This is a fundamental difference to the literature.The synthetic daily and hourly GHI sequences can be used, for example, as input for testing the performance and operation of a solar energy system for a wider range of scenarios than previously observed data. Further, one could incorporate synthetic GHI with other synthetic renewable energy data, such as synthetic wind farm electricity output. Both of these approaches would be useful when designing a reliable renewable energy system.The synthetic sequences of daily and hourly GHI exhibit the same statistical properties as the real data. The two-sample Kolmogorov-Smirnov (KS) test shows that the distribution of the synthetic sequences of daily and hourly GHI match the distribution of the observed daily and hourly GHI respectively. The synthetic sequences of daily GHI have the same serial correlation structure as the observed data, an autoregressive model of order 1, AR(1), with similar AR(1) coefficients. Also, the synthetic sequences of hourly GHI have the same serial correlation structure as the observed data, an autoregressive model of order 3, AR(3), with similar AR(3) coefficients.

Estimating labor force joiners and leavers using a heterogeneity augmented two-tier stochastic frontier

In a seminal paper, Basmann (1985) introduced a serial correlation structure based on an intertemporal adjustment mechanism. Basmann’s 1985 paper of course was built on his previous pioneering work on estimation and identifiability in structural equations leading to 2SLS (Basmann, 1957, 1960). In this paper, we follow a similar path. We derive a non-standard unit root serial correlation formulation for intertemporal adjustments in the labor force participation rate. This leads to a tractable three-error component model, which in contrast to other models embeds heterogeneity into the error structure. Unlike in the typical i.i.d. three-error component two-tier stochastic frontier model, our equation’s error components are independent but not identically distributed. This leads to a complex nonlinear likelihood function requiring identification through a two-step estimation procedure, which we estimate using Current Population Survey (CPS) data. By transforming the basic equation linking labor force participation to the working age population, this paper devises a new method which can be used to identify labor market joiners and leavers. The method’s advantage is its parsimonious data requirements, especially alleviating the need for survey based longitudinal data.

Pupil-linked arousal is driven by decision uncertainty and alters serial choice bias

While judging their sensory environments, decision-makers seem to use the uncertainty about their choices to guide adjustments of their subsequent behaviour. One possible source of these behavioural adjustments is arousal: decision uncertainty might drive the brain’s arousal systems, which control global brain state and might thereby shape subsequent decision-making. Here, we measure pupil diameter, a proxy for central arousal state, in human observers performing a perceptual choice task of varying difficulty. Pupil dilation, after choice but before external feedback, reflects three hallmark signatures of decision uncertainty derived from a computational model. This increase in pupil-linked arousal boosts observers’ tendency to alternate their choice on the subsequent trial. We conclude that decision uncertainty drives rapid changes in pupil-linked arousal state, which shape the serial correlation structure of ongoing choice behaviour.

Innovative Trend Methodology Applications to Precipitation Records in Turkey

There are trend identification methodologies in the literature but they have three crucial points that should be cared with great attention in practical applications. These points are that the available time series should have independent serial correlation structure, Gaussian (normal) distribution and monotonic trend fitting to whole time series through the least square technique. The existing methods consider the whole duration of the time series and try to identify a monotonic trend in increasing or decreasing forms. This paper presents partial trend methodology as an innovative and simple trend identification method, which yields low, medium and high cluster trends separately. It provides the opportunity to segregate between the low, high and medium flow trends and their relative intensities, durations as well as magnitudes. The application of the partial trend methodology is presented for 7 precipitation stations from 7 different sub-climatic regions of Turkey leading to spatial and temporal trend interpretations.

Spatial and temporal patterns of climate variables in Iraq

Temporal and spatial changes in Iraq total precipitations, maximum and minimum temperatures in the period of 1980–2011 are analyzed using 28 meteorological stations data distributed throughout the country. The Mann–Kendall and Spearman’s Rho test statistics for annual and seasonal Kendall and Sen’s T tests for monthly total precipitation and temperature series are calculated and plotted on maps to display any spatial trend patterns. Serial correlation structure in the data series and homogeneity of trends in monthly series were tested before applying the methods. Non-parametric methods using annual and monthly data over 32 years show almost same temporal and spatial patterns in trends of precipitation (P), maximum and minimum temperature (Tmax, Tmin) but some are not statistically significant at the 5 % level. While observation shows decreasing trends in precipitation except for two stations when using monthly data, increasing trend is detected in both temperature series. The Sen’s and seasonal Kendall slope estimator are also used to estimate linear trend magnitudes for annual and monthly data to determine the change per unit time in a time series, respectively. The six tests provide the same results about trend in most cases. As a conclusion, all of the study results show that there are not differences in the geographic location of trends (statistically significant or not) in the meteorological variables implying that climatic impacts are spatially uniform in this region. The effect of the North Atlantic Oscillation (NAO) on temporal patterns of climate data in Iraq is also investigated, since it has been suggested that it affects the northern hemisphere climate system. Our study shows that NAO has no detectable influences on climate of this region. This paper is the first comprehensive studies for evidence of climate change with applying tests in this region.

Investigating Trends in Streamflow and Precipitation in Huangfuchuan Basin with Wavelet Analysis and the Mann-Kendall Test

This study aims to investigate trends in streamflow and precipitation in the period 1954–2010 in a semiarid region of the Yellow River watershed, Huangfuchuan basin, China. The combination of the wavelet transform and different Mann-Kendall (MK) tests were employed to figure out the basic trends structure in streamflow and precipitation and what time scales are affecting the observed trends. The comparative analysis with five MK test methods showed that the modified MK tests with full serial correlation structure performed better when significant autocorrelations exhibited for more than one lag. Three criteria were used to determine the optimal smooth mother wavelet, the decomposition level and the extension mode used in the discrete wavelet transform (DWT) procedure. The first criteria referred to the relative error of the wavelet approximated component and the original series. The second one was the relative error of MK Z-values of approximation component and the original series. Additionally, a new criterion (Er), based on the relative error of energy between the approximate component and the original series, was proposed in this study, with better performance than the previous two criteria. Further, a new powerful index, the energy of the hydrological time series, was proposed to verify the dominant periodic components for the observed trends. The analysis indicated that all monthly, seasonal and annual streamflow showed significant decreasing trends, while no significant trends were found in precipitation. Results from the DWT and MK tests revealed that the main factors influencing the trends in the monthly and seasonal series in Huangfuchuan watershed are intra-annual cycles, while the leading factors affecting the trends in the annual series are decadal events. Different driving factors (e.g., seasonal cycles, solar activities, etc.) related to the periodicities identified in these data types resulted in this discrepancy.

Connection between uniform and serial correlation structure in the growth curve model

We introduce a special correlation structure in the growth curve model, which can be viewed as a transition between the serial and the uniform correlation structure. Estimators of unknown variance parameters are derived.

A Comparative Study of Observation- and Parameter-driven Zero-inflated Poisson Models for Longitudinal Count Data

Longitudinal count data with excessive zeros frequently occur in social, biological, medical, and health research. To model such data, zero-inflated Poisson (ZIP) models are commonly used, after separating zero and positive responses. As longitudinal count responses are likely to be serially correlated, such separation may destroy the underlying serial correlation structure. To overcome this problem recently observation- and parameter-driven modelling approaches have been proposed. In the observation-driven model, the response at a specific time point is modelled through the responses at previous time points after incorporating serial correlation. One limitation of the observation-driven model is that it fails to accommodate the presence of any possible over-dispersion, which frequently occurs in the count responses. This limitation is overcome in a parameter-driven model, where the serial correlation is captured through the latent process using random effects. We compare the results obtained by the two models. A quasi-likelihood approach has been developed to estimate the model parameters. The methodology is illustrated with analysis of two real life datasets. To examine model performance the models are also compared through a simulation study.

Modeling sheep pox disease from the 1994–1998 epidemic in Evros Prefecture, Greece

Sheep pox is a highly transmissible disease which can cause serious loss of livestock and can therefore have major economic impact. We present data from sheep pox epidemics which occurred between 1994 and 1998. The data include weekly records of infected farms as well as a number of covariates. We implement Bayesian stochastic regression models which, in addition to various explanatory variables like seasonal and environmental/meteorological factors, also contain serial correlation structure based on variants of the Ornstein–Uhlenbeck process. We take a predictive view in model selection by utilizing deviance-based measures. The results indicate that seasonality and the number of infected farms are important predictors for sheep pox incidence.

A General Multiple Distributed Lag Framework for Estimating the Dynamic Effects of Promotions

Game attendance resulting from ticket sales is the single largest revenue stream for Major League Baseball (MLB) teams. We propose a general multiple distributed lag framework following the Koyck family of models for estimating MLB attendance drivers and focus specifically on the differential direct and carryover effects of in-game promotions. By setting various model constraints, the proposed framework incorporates different forms of serial correlation and promotion-specific dynamic effects. Using information model-selection heuristics, we select an optimal model of attendance drivers for the Pittsburgh Pirates' 2010–2012 MLB seasons. We demonstrate that our newly proposed model with an unrestricted serial correlation structure performs best. We find that although kids promotions have the highest direct effect on attendance, giveaway and entertainment promotions have substantial carryover effects and the largest total effects. We use our results to optimize the Pirates' promotional schedule and find that a reallocation of resources across promotional categories can increase profits between 39% and 88%. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1856 . This paper was accepted by Eric Bradlow, special issue on business analytics.

Estimating Regional Trends of Temperature in Bangladesh

This study aims to determine trends in the long-term monthly total data series using non-parametric methods like Mann-Kendall and Sen's T test. The change per unit time in a time series having a linear trend is estimated by applying a simple non-parametric procedure, namely Sen's estimator of slope. Serial correlation structure in the data is accounted for determining the significance level of the results of the Mann-Kendall test. The data used in this study, consists of seven divisional meteorological stations across Bangladesh. Station basis trend analysis has been performed for temperature data. For temperature data most of the stations show significant trend. There are rising rates of temperature in some months and decreasing trend in some other months obtained by these statistical tests suggesting overall significant changes in the area.

Estimating the Reliability of Aggregated and Within-Person Centered Scores in Ecological Momentary Assessment

A procedure for estimating the reliability of test scores in the context of ecological momentary assessment (EMA) was proposed to take into account the characteristics of EMA measures. Two commonly used test scores in EMA were considered: the aggregated score (AGGS) and the within-person centered score (WPCS). Conceptually, AGGS and WPCS represent the interindividual differences and the intraindividual differences, respectively. The reliability coefficients for AGGS and WPCS were derived using a multilevel factor model with a serial correlation structure framework. Point estimates and confidence intervals of these coefficients were obtained using Mx (Neale, Boker, Xie, & Maes, 2004). A simulation study showed that the proposed procedure performed well empirically. Diary data from Huang (2009), which recorded daily joy level of 110 undergraduate students for 8 days, was used to illustrate the applicability of the proposed method.

Disentangling stability, variability and adaptability in human performance: Focus on the interplay between local variance and serial correlation.

We address the complex relationship between the stability, variability, and adaptability of psychological systems by decomposing the global variance of serial performance into two independent parts: the local variance (LV) and the serial correlation structure. For two time series with equal LV, the presence of persistent long-range correlations (or 1/ƒ β noise) increases the global variance. We hypothesized that a coadjustment between these two determinants of variability constitutes a resource for adaptive systems whose appropriate functioning under critical conditions requires the outcome variance to be limited. To test this hypothesis, we looked at the bimanual coordination dynamics at comfortable (stable) and critical (close to phase transition) frequencies. Results showed that a negative correlation appeared gradually as the theoretical stability of coordination modes decreased and reached significance only in the critical condition. We propose that the emergence of a mutual adjustment between LV and serial correlations might be an indicator of effective adaptation to stabilize behavior.

TESTING FOR A SHIFT IN TREND AT AN UNKNOWN DATE: A FIXED-BANALYSIS OF HETEROSKEDASTICITY AUTOCORRELATION ROBUST OLS-BASED TESTS

This paper analyzes tests for a shift in the trend function of a time series at an unknown date based on ordinary least squares (OLS) estimates of the trend function. Inference about the trend parameters depends on the serial correlation structure of the data through the long-run variance (zero frequency spectral density) of the errors. Asymptotically pivotal tests can be obtained by the use of serial correlation robust standard errors that require an estimate of the long-run variance. The focus is on the class of nonparametric kernel estimators of the long-run variance. Tests based on these estimators present two problems for practitioners. The first is the choice of kernel and bandwidth. The second is the well-known overrejection problem caused by strong serial correlation (or a possible unit root) in the errors.We provide solutions to both problems by using the fixed-basymptotic framework of Kiefer and Vogelsang (2005,Econometric Theory, 21, 1130–1164) in conjunction with the scaling factor approach of Vogelsang (1998,Econometrica65, 123–148). Our results provide practitioners with a family of OLS-based trend function structural change tests that are size robust to the presence of strong serial correlation or a unit root. Specific recommendations are provided for the tuning parameters (kernel and bandwidth) in a way that maximizes asymptotic integrated power.