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PubMed1997

Time series analysis and its relationship with longitudinal analysis.

This paper discusses the relationship between longitudinal analysis of inter-individual (co-)variation and time series analysis of intra-individual (co-)variation. To set the stage for this discussion, first a tutorial overview of modern techniques of multivariate time series analysis is given which highlights the central role of rate-space modeling. Some increasingly general instances of the state-spuce model are presented, followed by a concise description of two recent applications involving nonlinear state-space modeling of oscillatory finger motion and nonlinear growth, respectively. We then consider the question under which conditions longitudinal factor analysis of inter-individual covariation will yield the same results as dynamic factor analysis of single-subject time series data. The conditions concerned can be derived from ergodicity theory and turn out to be very restrictive. This implies that the results obtained in analyses of inter-individual variation (like the construction and validation of measurement scales) cannot be generalized to the assessment and prediction of individual developmental processes (e.g., in single-subject counseling). A simple illustration with simulated data is given, to the best of our knowledge for the first time, in which a factor analysis of inter-individual covariation yields a satisfactorily fitting solution that has no relationship whatsoever to the factor structures characterizing the intra-individual covariation of each subject in the sample.

Epidemiologic Methods↗

PubMed1985

Time series analysis of plasma LH and FSH concentrations as a method of assessing episodic secretion.

Time series analysis was used to detect LH and FSH episodes in untreated seasonally anoestrous ewes and prepubertal heifers, and in these animals when treated with low doses of GnRH. For comparison, these profiles were also assessed for episodic secretion by subjective, visual appraisal methods and by cycle detection-an objective threshold method. In untreated animals, time series analysis detected recurring events in the LH and FSH profiles, the period lengths of which varied between individual animals. When GnRH was injected at 2-h intervals, cycles in LH secretion with period lengths of 120 min were recorded in all animals, of 60 min in all ewes and 11/12 heifers, and of 40.5 min in 22/24 ewes and 10/12 heifers. The cycles with period lengths of 60 and 40.5 min are probably artefacts of this method of analysis. No consistent cycles in FSH release were detected in GnRH-injected anoestrous ewes, but 120-min cycles were recorded in 8/12 GnRH-injected heifers. When GnRH was administered to seasonally anoestrous ewes by continuous infusion, recurring cycles in both LH and FSH secretion were evident. However, there was no consistency in their period lengths and the mean number and frequency of cycles were similar to pretreatment values. The number of episodes detected by visual appraisal was influenced by the choice of episode definition. Both methods identified LH, but not FSH, episodes in response to each injection in all GnRH-injected animals. Cycle detection, which does not identify individual episodes, recorded LH and FSH episode frequencies similar to those detected by the more stringent method of visual appraisal. Time series analysis detected an FSH response to GnRH injections in prepubertal heifers that was not identified by the other methods of analysis. However, because of the asymmetric nature of LH episodes, it also detected cycles in LH profiles that were probably spurious. Subjective decisions influenced the frequencies of LH and FSH episodes recorded by visual appraisal, and the variation in episode amplitude in these profiles made cycle detection inappropriate. Each of these methods can contribute to the interpretation of hormone profiles, but their constraints and limitations must be recognized.

Anestrus↗

PubMed2001

Time-series analysis of delta13C from tree rings. I. Time trends and autocorrelation.

Univariate time-series analyses were conducted on stable carbon isotope ratios obtained from tree-ring cellulose. We looked for the presence and structure of autocorrelation. Significant autocorrelation violates the statistical independence assumption and biases hypothesis tests. Its presence would indicate the existence of lagged physiological effects that persist for longer than the current year. We analyzed data from 28 trees (60-85 years old; mean = 73 years) of western white pine (Pinus monticola Dougl.), ponderosa pine (Pinus ponderosa Laws.), and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. glauca) growing in northern Idaho. Material was obtained by the stem analysis method from rings laid down in the upper portion of the crown throughout each tree's life. The sampling protocol minimized variation caused by changing light regimes within each tree. Autoregressive moving average (ARMA) models were used to describe the autocorrelation structure over time. Three time series were analyzed for each tree: the stable carbon isotope ratio (delta(13)C); discrimination (delta); and the difference between ambient and internal CO(2) concentrations (c(a) - c(i)). The effect of converting from ring cellulose to whole-leaf tissue did not affect the analysis because it was almost completely removed by the detrending that precedes time-series analysis. A simple linear or quadratic model adequately described the time trend. The residuals from the trend had a constant mean and variance, thus ensuring stationarity, a requirement for autocorrelation analysis. The trend over time for c(a) - c(i) was particularly strong (R(2) = 0.29-0.84). Autoregressive moving average analyses of the residuals from these trends indicated that two-thirds of the individual tree series contained significant autocorrelation, whereas the remaining third were random (white noise) over time. We were unable to distinguish between individuals with and without significant autocorrelation beforehand. Significant ARMA models were all of low order, with either first- or second-order (i.e., lagged 1 or 2 years, respectively) models performing well. A simple autoregressive (AR(1)), model was the most common. The most useful generalization was that the same ARMA model holds for each of the three series (delta(13)C, delta, c(a) - c(i)) for an individual tree, if the time trend has been properly removed for each series. The mean series for the two pine species were described by first-order ARMA models (1-year lags), whereas the Douglas-fir mean series were described by second-order models (2-year lags) with negligible first-order effects. Apparently, the process of constructing a mean time series for a species preserves an underlying signal related to delta(13)C while canceling some of the random individual tree variation. Furthermore, the best model for the overall mean series (e.g., for a species) cannot be inferred from a consensus of the individual tree model forms, nor can its parameters be estimated reliably from the mean of the individual tree parameters. Because two-thirds of the individual tree time series contained significant autocorrelation, the normal assumption of a random structure over time is unwarranted, even after accounting for the time trend. The residuals of an appropriate ARMA model satisfy the independence assumption, and can be used to make hypothesis tests.

Carbon Isotopes↗

PubMedDate not supplied

Interrupted time series analysis in clinical research.

OBJECTIVE: To demonstrate the usefulness of interrupted time series analysis in clinical trial design. METHODS: A safety data set of electrocardiographic (ECG) information was simulated from actual data that had been collected in a Phase I study. Simulated data on 18 healthy volunteers based on a study performed in a contract research facility were collected based on single doses of an experimental medication that may affect ECG parameters. Serial ECGs were collected before and during treatment with the experimental medication. Data from 7 real subjects receiving placebo were used to simulate the pretreatment phase of time series; data from 18 real subjects receiving active treatment were used to simulate the treatment phase of the time series. Visual inspection of data was performed, followed by tests for trend, seasonality, and autocorrelation by use of SAS. RESULTS: There was no evidence of trend, seasonality, or autocorrelation. In 11 of 18 simulated individuals, statistically significant changes in QTc intervals were observed following treatment with the experimental medication. A significant time of day and treatment interaction was observed in 4 simulated patients. CONCLUSIONS: Interrupted time series analysis techniques offer an additional tool for the study of clinical situations in which patients must act as their own controls and where serial data can be collected at evenly distributed intervals.

Algorithms↗

PubMed1995

Application of time series analysis in the clinical setting.

A growth curve time series model is characterized by a biological growth pattern with random deviations added to this basic pattern. Various types are reviewed including the homeostatic model which is a special and simple type characterized by zero growth. The limitations to the use of time series analysis in the clinical setting include lack of initial baseline values and difficulties in specifying in quantitative terms a relevant hypothesis alternative to the one postulated by the time series model. Some ongoing research addressing these problems is discussed.

Biomarkers, Tumor↗

PubMed2006

The effects of the irregular sample and missing data in time series analysis.

Human self-report time series data are typically marked by irregularities in sampling rates; furthermore, these irregularities are typically natural outcomes of the data generation process. Relatively little has been published to assist the analysis of irregularly sampled data. We report the results of a series of computational experiments on synthetic data sets designed to assess the utility of techniques for handling irregular time series data. The behavior of a conservative quasiperiodic, a dissipative chaotic, and a self-organized critical dynamics were sampled regularly in time and the regular sampling was disrupted by data point removal or by stochastic shifts in time. Missing data segments were then patched by means of segment concatenation, by segment filling with average data values, or by local interpolation in phase space. We compared results of nonlinear analytical tools such as autocorrelations and correlation dimensions using complete and patched sets, as well as power spectra with Lomb periodograms of the decimated sets. Local interpolation in phase space was particularly successful at preserving key features of the original data, but required potentially impractical quantities of intact data as a primer. While the other patching methods are not limited by the need for intact data, they distort results relative to the intact series. We conclude that irregularly sampled data sets with as much as 15 percent missing data can potentially be re-sampled or repaired for analysis with techniques that assume regular sampling without introducing substantial errors.

Journal Article↗

PubMed1989

Time series analysis of injuries.

We used time series models in the exploratory and confirmatory analysis of selected fatal injuries in the United States from 1972 to 1983. We built autoregressive integrated moving average (ARIMA) models for monthly, weekly, and daily series of deaths and used these models to generate hypotheses. These deaths resulted from six causes of injuries: motor vehicles, suicides, homicides, falls, drownings, and residential fires. For each cause of injury, we estimated calendar effects on the monthly death counts. We confirmed the significant effect of vehicle miles travelled on motor vehicle fatalities with a transfer function model. Finally, we applied intervention analysis to deaths due to motor vehicles.

Accidents, Traffic↗

PubMed1997

New technique for time series analysis combining the maximum entropy method and non-linear least squares method: its value in heart rate variability analysis.

A new technique for time series analysis, which is a combination of the maximum entropy method (MEM) for spectral analysis and the non-linear least squares method (LSM) for fitting analysis, is described. In this technique, the MEM power spectral density (MEMPSD) is calculated using a very large lag that could diminish the lag dependence of dominant periods estimated by the MEM analysis. The validity of this large lag is confirmed by the LSM, given that the ten dominant MEM periods are known quantities. To validate the MEM plus LSM technique, it is compared with autoregressive (AR) modelling, by analysing heart rate variability under pharmacological interventions (phenylephrine and trinitroglycerine), using 16 young males. The results indicate that the MEMPSD, when compared with the ARPSD, has numerous periods that could reproduce the original time series much more accurately, as revealed by the LSM analysis. However, both the low- and high-frequency powers with MEMPSD and ARPSDs shift in the expected directions in accordance with the pharmacological effects on the cardiovascular system. The implications of these results are discussed from the theoretical and practical standpoints of the MEM plus LSM technique, compared with AR modelling.

Adolescent↗

PubMed1995

Temporal coding in the guinea-pig auditory cortex as revealed by optical imaging and its pattern-time-series analysis.

The neural network structure of a guinea-pig's primary auditory cortex is estimated by applying pattern-time-series analysis to the auditory evoked responses. Spatiotemporal patterns in click-evoked responses, observed by optical recording with voltage-sensitive dye, are analyzed by time series analysis using a multivariable autoregressive (MAR) model. Oscillatory neural activities with a distribution of about 10 approximately 40 Hz in the click-induced evoked responses are found in the cortical response field. The cortical regions where the distributed neural oscillations are generated are identified by pattern-time-series analysis. In addition, two types of cortico-cortical connections, unilateral and bilateral connections between the cortical points, are speculated to be the causes of oscillatory neural activity transfer. It can be said that the so-called synchronized neural oscillation, in the sense of coherency or correlation between the two evoked responses at the oscillatory frequency, does not necessarily represent real cortico-cortical neural connections at the evoked response points.

Animals↗

PubMed2004

Time series analysis of long-term data sets of atmospheric mercury concentrations.

Different aspects and techniques of time series analysis were used to investigate long-term data sets of atmospheric mercury in the Northern Hemisphere. Two perennial time series from different latitudes with different seasonal behaviour were chosen: first, Mace Head on the west coast of Ireland (53 degrees 20'N, 9 degrees 54'W), representing Northern Hemispherical background conditions in Europe with no indications for so-called atmospheric mercury depletion events (AMDEs); and second, Alert, Canada (82 degrees 28'N, 62 degrees 30'W), showing strong AMDEs during Arctic springtime. Possible trends were extracted and forecasts were performed by using seasonal decomposition procedures, autoregressive integrated moving average (ARIMA) methods and exponential smoothing (ES) techniques. The application of time series analysis to environmental data is shown in respect of atmospheric long-term data sets, and selected advantages are discussed. Both time series have not shown any statistically significant temporal trend in the gaseous elemental mercury (GEM) concentrations since 1995, representing low Northern Hemispherical background concentrations of 1.72+/-0.09 ng m(-3) (Mace Head) and 1.55+/-0.18 ng m(-3) (Alert), respectively. The annual forecasts for the GEM concentrations in 2001 at Alert by two different techniques were in good agreement with the measured concentrations for this year.

Journal Article↗

PubMed2000

To smooth or not to smooth? Bias and efficiency in fMRI time-series analysis.

This paper concerns temporal filtering in fMRI time-series analysis. Whitening serially correlated data is the most efficient approach to parameter estimation. However, if there is a discrepancy between the assumed and the actual correlations, whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates. This bias, although not expressed in terms of the estimated responses, has profound effects on any statistic used for inference. The special constraints of fMRI analysis ensure that there will always be a misspecification of the assumed serial correlations. One resolution of this problem is to filter the data to minimize bias, while maintaining a reasonable degree of efficiency. In this paper we present expressions for efficiency (of parameter estimation) and bias (in estimating standard error) in terms of assumed and actual correlation structures in the context of the general linear model. We show that: (i) Whitening strategies can result in profound bias and are therefore probably precluded in parametric fMRI data analyses. (ii) Band-pass filtering, and implicitly smoothing, has an important role in protecting against inferential bias.

Algorithms↗

PubMed2001

Surrogate for nonlinear time series analysis.

We present a surrogate for use in nonlinear time series analysis. This surrogate algorithm has significant advantages over the most commonly used surrogates, in that it provides a more robust statistical test by producing an entire population of surrogates that are consistent with the null hypothesis. We will show that for the currently used surrogate algorithms, although individual surrogate files are consistent with the null hypothesis the population of surrogates generated is not. The surrogate is tested on a linear stochastic process and a continuous nonlinear system.

Journal Article↗

PubMed1992

Time series analysis of glottal airflow in normal and pathological phonation.

Time series analysis of glottal airflow was carried out on 26 normal controls and 40 patients with voice disorders, using a modification of Isshiki's original technique which uses a hot-wire flowmeter, taking cycle-by-cycle fluctuations into consideration. The mean flow rate and mean AC/DC were shown to have significant differences among normal and patient groups. The standard deviations of AC/DC and AC/DC perturbation were calculated from the AC/DC value of 50 cycles and shown not to vary significantly among the normal and patient groups. The relationship between AC/DC and perceptual impression of voice was also studied among 20 selected patients with breathy voices. Using Spearman's rank correlation coefficient, this relationship was found to have statistical significance (P < .05).

Glottis↗

PubMed1999

New methods of time series analysis of non-stationary EEG data: eigenstructure decompositions of time varying autoregressions.

OBJECTIVE: Those who analyze EEG data require quantitative techniques that can be validly applied to time series exhibiting ranges of non-stationary behavior. Our objective is to introduce a new analysis technique based on formal non-stationary time series models. This novel method provides a decomposition of the time series into a set of 'latent' components with time-varying frequency content. The identification of these components can lead to practical insights and quantitative comparisons of changes in frequency structure over time in EEG time series. METHODS: The technique begins with the development of time-varying autoregressive models of the EEG time series. Such models have been previously used in EEG analysis but we extend their utility by the introduction of eigenstructure decomposition methods. We review the basis and implementation of this method and report on the analysis of two channel EEG data recorded during 3 generalized tonic-clonic seizures induced in an individual as part of a course of electroconvulsive therapy for major depression. RESULTS: This technique identified EEG patterns consistent with prior reports. In addition, it quantified a decrease in dominant frequency content over the seizures and suggested for the first time that this decrease is continuous across the end of the seizures. The analysis also suggested that the seizure EEG may be best modeled by the combination of multiple processes, whereas post-ictally there appears to be one dominant process. There was also preliminary evidence that these features may differ as a function of ECT therapeutic effectiveness. CONCLUSIONS: Eigenanalysis of time-varying autoregressive models has promise for improving the analysis of EEG time series.

Brain↗

PubMed2005

Time series analysis of ion dynamics in glassy ionic conductors obtained by a molecular dynamics simulation.

We present several characteristics of ionic motion in glassy ionic conductors brought out by time series analysis of molecular dynamics (MD) simulation data. Time series analysis of data obtained by MD simulation can provide crucial information to describe, understand and predict the dynamics in many systems. The data have been treated by the singular spectrum analysis (SSA), which is a method to extract information from noisy short time series and thus provide insight into the unknown or partially unknown dynamics of the underlying system that generated the time series. Phase-space plot reconstructed using the principal components of SSA exhibited complex but clear structures, suggesting the deterministic nature of the dynamics.

Journal Article↗

PubMed1998

Multivariate time series analysis in nosocomial infection surveillance: a case study.

BACKGROUND: The present study describes the use of time series analysis in the evaluation of the incidence of nosocomial infection. The main hypothesis analysed was that monthly occurrence of nosocomial infection in a hospital may be related to work-related factors such as the control and training of personnel imposed by a surveillance system, strikes supported by medical personnel and movement of personnel. Time series analysis was used to quantify, model and statistically evaluate these interventions. METHODS: The data employed (March 1982-December 1990) were supplied by the nosocomial infection surveillance system of a primary-care general hospital. The monthly time series incidence of nosocomial infections (measured as percentage cumulative incidence) was analysed by curve fitting, autoregressive, integrated and moving average (ARIMA) modelling (Box-Jenkins) and intervention and dynamic regression analysis. RESULTS: The imposed control and training of personnel by the surveillance system was associated with a 3.63% decrease in the accumulated monthly incidence of nosocomial infection from 7.82% to a baseline level of 4.19%. There was a strong indication that an increase of infection incidence of 4.34% corresponded to a medical strike. This increase was maintained over the following months raising the baseline level to 4.84%. An increase of 0.18% was associated with each new nursing contract. Evidence was obtained for the possible relationship between incidence of nosocomial infection and vacation periods. CONCLUSIONS: The results suggest the need for strict control of the activities of hospital personnel and for the adoption of certain preventative measures during vacation periods to avoid an undesirable increase in the incidence of nosocomial infections.

Case-Control Studies↗

PubMed1977

Time-series analysis in operant research.

A time-series method is presented, nontechnically, for analysis of data generated in individual-subject operant studies, and is recommended as a supplement to visual analysis of behavior change in reversal or multiple-baseline experiments. The method can be used to identify three kinds of statistically significant behavior change: (a) changes in score levels from one experimental phase to another, (b) reliable upward or downward trends in scores, and (c) changes in trends between phases. The detection of, and reliance on, serial dependency (autocorrelation among temporally adjacent scores) in individual-subject behavioral scores is emphasized. Examples of published data from the operant literature are used to illustrate the time-series method.

Journal Article↗

PubMed2003

A lengthy look at the daily grind: time series analysis of events, mood, stress, and satisfaction.

The present study investigated processes by which job stress and satisfaction unfold over time by examining the relations between daily stressful events, mood, and these variables. Using a Web-based daily survey of stressor events, perceived strain, mood, and job satisfaction completed by 14 university workers, 1,060 occasions of data were collected. Transfer function analysis, a multivariate version of time series analysis, was used to examine the data for relationships among the measured variables after factoring out the contaminating influences of serial dependency. Results revealed a contrast effect in which a stressful event associated positively with higher strain on the same day and associated negatively with strain on the following day. Perceived strain increased over the course of a semester for a majority of participants, suggesting that effects of stress build over time. Finally, the data were consistent with the notion that job satisfaction is a distal outcome that is mediated by perceived strain.

Affect↗