Time Series Analysis for Veterinary Disease Surveillance

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-11

Key Takeaways

• Time series analysis is crucial for veterinary surveillance as it formally models the temporal dependence inherent in longitudinal data (e.g., monthly case counts, weekly test positivity), which violates assumptions of ordinary regression and requires explicit modeling of autocorrelation.
• Stationarity, where statistical properties like mean and variance remain constant over time, is a prerequisite for many classical time series methods; non-stationary series, often exhibiting trend or seasonality, necessitate transformations like differencing (e.g., \(y_t - y_{t-1}\) for linear trend, \(y_t - y_{t-12}\) for annual seasonality) to achieve stationarity.
• Autocorrelation, quantified by the Autocorrelation Function (ACF), is the defining characteristic of time series data, revealing correlations between a series and its lagged values; a slowly decaying ACF indicates non-stationarity, while peaks at specific lags (e.g., lag 12 for monthly data) suggest seasonality.
• Trend analysis, whether linear or nonlinear (e.g., using splines), aims to identify long-term directional changes in disease occurrence, but requires accounting for autocorrelation to ensure valid inference; for example, a study on endoparasitic infections revealed significant downward trends in canine hookworms and upward trends in feline tapeworms.
• Seasonal patterns, driven by factors like climate (e.g., rainfall influencing leptospire survival) or management practices (e.g., calving seasons), can be identified through decomposition or harmonic regression, with the autocorrelation function providing empirical guidance on the seasonal period (commonly 12 months for annual cycles).
• Model selection for time series analysis, particularly when incorporating environmental covariates like rainfall, should utilize information criteria such as AICc to compare candidate models and ensure biological plausibility of estimated lags, as demonstrated by the association between canine leptospirosis cases and rainfall lagged by three months.

Veterinary surveillance data accumulate as sequences of observations ordered in time: monthly case counts, weekly test positivity, daily herd health events. These sequences carry structure that ordinary cross-sectional methods discard. Time series analysis provides the formal framework for extracting that structure, separating meaningful signal from noise, and quantifying patterns such as trend, seasonality, and autocorrelation. This article explains the core concepts and methods veterinary researchers need to analyze temporal surveillance data, with emphasis on detecting long-term trends and seasonal cycles in animal disease occurrence.

The intended reader is a veterinary researcher or graduate student who has completed introductory epidemiology and biostatistics and now faces longitudinal surveillance data. The article answers three questions. What properties of a time series must be understood before any modeling begins? Which methods are appropriate for describing trend and seasonality in veterinary data? How should results be interpreted and reported so that they support surveillance decisions? Spatial analysis and forecasting are excluded, the focus is on descriptive and inferential methods for patterns already present in the data.

At a Glance

The Structure of Veterinary Time Series

A time series is a sequence of observations indexed by time. In veterinary surveillance, the index is usually month or week, and the observation is a count, a proportion, or a rate. The defining feature of such data is dependence: the value at time \(t\) tends to resemble the value at time \(t-1\) more closely than it resembles a value chosen at random from the series. This autocorrelation violates the independence assumption of ordinary regression and requires methods that model the dependence explicitly.

Three components dominate veterinary surveillance series. Trend is the long-term tendency of the series to increase, decrease, or remain stable. Seasonality is a periodic fluctuation with fixed period, most commonly annual. Irregular components are the remaining random fluctuations after trend and seasonality are removed. The decomposition of a series into these components is often the first analytical step, and it guides the choice of more formal models.

The sampling interval is a decision with consequences. Monthly aggregation smooths short-term variation but can obscure outbreaks lasting days. Weekly aggregation preserves more detail but produces noisier series with more zero counts, particularly for rare diseases. The interval must match the question. A study of leptospirosis seasonality in dogs used monthly case counts aggregated across 22 veterinary teaching hospitals over 16 years, a design that captured the late summer to fall peak while keeping the series tractable for time series regression WOAH animal health surveillance standards. Finer intervals would have produced many months with zero cases and unstable estimates.

Stationarity and Autocorrelation

Stationarity means that the statistical properties of the series, mean, variance, and autocorrelation, do not change over time. Most classical time series methods assume stationarity, yet most raw surveillance series are nonstationary because they contain trend or seasonality. The analyst must therefore test for stationarity and, when it is absent, transform the series.

Differencing is the standard transformation. A first difference, \(y_t - y_{t-1}\), removes a linear trend. A seasonal difference, \(y_t - y_{t-12}\), removes a fixed annual pattern. The order of differencing is a modeling decision, not a mechanical rule. Overdifferencing introduces spurious autocorrelation and inflates variance.

The autocorrelation function (ACF) plots the correlation between the series and its lagged versions against the lag. It is the primary diagnostic tool. A slowly decaying ACF suggests nonstationarity. A sharp peak at lag 12 in monthly data indicates annual seasonality. The partial autocorrelation function (PACF) shows the correlation at each lag after removing the contributions of shorter lags, it helps identify the order of autoregressive terms.

An early application in veterinary medicine illustrates the approach. Cortisol concentrations measured every 30 minutes in seven bulls over 24 to 48 hours were analyzed with time series methods to distinguish episodic secretion from circadian rhythm. The analysis revealed a distinct pattern: depressed secretory activity in the evening and peak concentrations near the onset of daylight twenty-four-hour secretory pattern of cortisol in the bull. The study demonstrates that time series analysis can resolve periodic structure even when individual observations are highly variable, a situation common in surveillance data.

Trend Detection

The simplest approach to trend detection is linear regression of the outcome on time. The method is straightforward and interpretable: the slope estimates the average change per unit time. But the method assumes independent errors, and surveillance data rarely satisfy that assumption. Autocorrelated errors bias the standard errors and can produce spurious significance.

Two remedies are common. The first is to include lagged values of the outcome as predictors, creating an autoregressive model. The second is to model the error structure explicitly, as in generalized least squares or ARIMA. Both approaches correct the standard errors and yield valid inference about the trend.

The choice of trend model depends on the question. A linear trend answers whether the average level is changing at a constant rate. A nonlinear trend, fitted with splines or polynomial terms, answers whether the rate of change itself varies over time. Nonlinear trends are often more realistic for infectious diseases, where control programs, immunity, and management changes alter the trajectory.

A study of endoparasitic infections in dogs and cats presented to a veterinary teaching hospital illustrates both the value and the limits of trend analysis. Monthly prevalence data from 1984 to 1991 showed a significant downward trend in canine hookworms and heartworms and a significant upward trend in feline tapeworms, while other parasites showed no significant long-term change time series analysis of the prevalence of endoparasitic infections. The study also illustrates a common difficulty: the same data that support trend detection may fail to provide conclusive evidence of seasonality, and the analyst must report that uncertainty honestly.

Seasonal Patterns

Seasonality in veterinary surveillance arises from multiple mechanisms. Climate drives vector populations and pathogen survival. Management practices follow the calendar, with calving seasons, housing changes, and pasture access. Host physiology varies seasonally, as the cortisol study demonstrates. Distinguishing these mechanisms requires more than detecting a seasonal pattern, it requires relating the pattern to candidate drivers.

The classical approach is to estimate seasonal indices, the average deviation from the overall mean for each month or week. The indices describe the shape of the seasonal pattern and can be tested for significance. A more flexible approach fits harmonic terms, sine and cosine functions at the seasonal frequency, within a regression framework. Harmonics are parsimonious and can capture smooth seasonal patterns with few parameters.

Autocorrelation analysis provides a complementary view. The ACF of a seasonal series shows peaks at the seasonal lag and its multiples. In the endoparasite study, repeated peaks at lags of 6, 12, and 24 months suggested a 12-month cycle with a December peak in ascarid infections, though the evidence did not reach statistical significance time series analysis of the prevalence of endoparasitic infections. The example is instructive: suggestive autocorrelation patterns require confirmation with formal tests before they are reported as seasonality.

Relating Seasonality to Environmental Drivers

Detecting seasonality is often a means to an end. The analytical goal is to identify the environmental or management factors that drive the seasonal pattern, because those factors may be modifiable or predictive. Rainfall is the most studied driver in veterinary surveillance, particularly for diseases with environmental transmission.

A study of canine leptospirosis in the United States and Canada illustrates the analytical strategy. Monthly case counts from 22 veterinary teaching hospitals were analyzed with time series regression. The best-fitting model, selected by Akaike's corrected information criterion, included cases from the previous month and 12 months previously, plus rainfall recorded 3 months earlier. The correlation between cases and prior rainfall was significant, and the seasonal peak from August to November was explained in part by the rainfall pattern seasonality of canine leptospirosis in the United States and Canada. The design is a template for environmental association studies: lag the environmental variable, compare candidate models with information criteria, and report the selected model with its diagnostics.

The lag between rainfall and cases reflects the biology of transmission. Leptospires persist in moist soil and water, and exposure follows contact with contaminated environments. A 3-month lag is biologically plausible and statistically identifiable. The analyst should always ask whether an estimated lag is consistent with the known biology of the pathogen, because spurious correlations can arise when both the disease and the environmental variable share a common seasonal trend.

Decomposing the Series in Practice

Decomposition separates a time series into components: trend, seasonal, cyclic, and residual (irregular) variation. For veterinary surveillance data, the practical goal is to isolate each component so that the residual series can be examined for aberrations that warrant investigation. The additive model expresses the observed value as the sum of components, the multiplicative model expresses it as their product. The choice between them depends on whether the amplitude of seasonal fluctuations scales with the level of the series. Counts of infectious disease cases often follow the multiplicative form, because transmission amplifies both trend and seasonal effects proportionally. Prevalence proportions from large passive surveillance systems, such as the endoparasite data reported by Nolan and Smith, may be handled with either form, but multiplicative decomposition is usually safer when the series spans several orders of magnitude.

The classical decomposition procedure is straightforward. First, estimate the trend-cycle component with a moving average whose window length equals the seasonal period. For monthly data with an annual cycle, a 12-month centerd moving average smooths out seasonal fluctuations. Second, subtract or divide the trend from the original series to obtain the detrended series. Third, average the detrended values for each season (for example, each calendar month) across all years to obtain the seasonal component. Fourth, subtract both trend and seasonal components from the original series to obtain the residual series. The residuals should appear random, any remaining pattern indicates model misspecification.

A worked example clarifies the procedure. Ward's analysis of canine leptospirosis diagnoses in the United States and Canada used monthly case counts from 22 veterinary teaching hospitals over 16 years. The series showed a pronounced late summer to autumn peak. Decomposition would reveal this seasonal component directly, and the residual series would then be examined for years in which case counts deviated from the expected seasonal pattern. Such deviations might correspond to unusual rainfall events or changes in diagnostic practices.

Selecting the Seasonal Period

The seasonal period must be specified before decomposition. For most veterinary surveillance data, the natural period is one year. Monthly data have a period of 12, weekly data have a period of 52. Quarterly data have a period of 4. The choice is dictated by the data collection interval, not by the biology of the pathogen. A series collected at irregular intervals cannot be decomposed without first resampling to a regular grid, a step that introduces its own assumptions.

Shorter periods can also be biologically meaningful. The circadian rhythm in bovine cortisol secretion documented by Thun and colleagues provides an example at the opposite end of the temporal scale. Blood samples collected every 30 minutes over 24 to 48 hours revealed episodic secretion with a distinct day-night pattern. For such high-frequency data, the seasonal period is 24 hours, and the decomposition would separate the circadian component from the episodic pulses. This illustrates that the same analytical machinery applies across temporal scales, from hours to years.

The choice of period should be justified by the biology of the condition and the sampling frame. For vector-borne diseases, the relevant seasonal period may correspond to vector activity, which itself follows an annual cycle in temperate regions. For production diseases, management cycles such as calving seasons or batch housing may impose periodicities that are not strictly annual. The autocorrelation function, described in the previous section, provides empirical guidance: peaks at lags corresponding to the suspected period support the choice.

Method Selection Checklist

The following checklist guides method selection for a given surveillance series. The correct choice depends on the data structure, the question being asked, and the resources available for analysis.

The distinction between description and prediction matters. Decomposition and autocorrelation analysis describe the structure of a series. ARIMA models can do both, but they require more data and more assumptions. For surveillance purposes, the descriptive tools are usually sufficient to detect anomalies and generate hypotheses. Forecasting, which is excluded from this article's scope, would require additional model validation steps.

Documenting the Analysis

Surveillance analyzes should be documented with the same rigour as laboratory procedures. The documentation should record the data source, the inclusion and exclusion criteria for cases, the time interval and aggregation level, the decomposition method and seasonal period, and the software and parameter settings used. This allows the analysis to be reproduced and updated as new data accrue.

The World Organization for Animal Health surveillance standards emphasize the importance of transparent, documented methods for animal health surveillance. WOAH animal health surveillance standards describe the expectations for surveillance systems, including the need for clear descriptions of data collection and analysis procedures. Similarly, the CDC principles of epidemiology in public health practice provide a framework for describing surveillance data and interpreting temporal patterns. These references support the practice of maintaining an analysis log that records decisions and their rationale.

The analysis log should also record the date on which each analysis was run. Surveillance data are updated continuously, and a time series analysis performed in January will differ from the same analysis performed in July once additional months of data are included. Version control for analyzes is as important as version control for laboratory protocols.

Species and System Considerations

The correct analytical approach varies with the species and production system under surveillance. Companion animal data from teaching hospitals, such as the endoparasite prevalence series reported by Nolan and Smith, are subject to referral bias. The population presenting to a teaching hospital is not representative of the general pet population, and trends in the series may reflect changes in referral patterns instead of changes in parasite prevalence. This limitation should be stated whenever such data are analyzed.

Livestock surveillance data have different constraints. Production records are often collected at the herd level, and the unit of analysis may be the herd instead of the individual animal. Automated monitoring systems, such as the GAITWISE pressure-sensitive walkway described by Maertens and colleagues, generate high-frequency individual-level data that require different handling. The authors noted that their gait variables would be stored for time series analysis to detect changes in individual cow walking behavior over time. Such data are autocorrelated at short lags, and the analysis must account for the repeated measures structure.

Wildlife surveillance data are typically sparse and irregular. Decomposition methods that require complete regular grids are often inapplicable, and the analyst must rely on methods that accommodate missing data. The choice of method should be guided by the data quality and the question, not by the availability of software.

The MSD Veterinary Manual provides species-specific guidance on disease patterns and diagnostic approaches, which can inform the interpretation of temporal analyzes. The AVMA practice resources offer additional context on surveillance and reporting expectations in the United States. Neither source prescribes specific time series methods, but both help the analyst understand the clinical and regulatory context in which the analysis will be used.

Recognized Complications and Failure Modes

Time series analyzes of surveillance data fail in characteriztic ways. The most common failure is over-interpreting noise as signal. Autocorrelation functions will always show some peaks, and a peak at lag 12 in a short series can arise by chance. Nolan and Smith, analyzing seven years of endoparasite prevalence data, found repeated peaks at 6, 12, and 24 month lags for feline ascarids that suggested December seasonality, yet the result did not reach statistical significance at the 5% level. Their caution is the correct default: treat suggestive autocorrelation as a hypothesis to test with longer series or external validation, not as a finding.

A second failure mode is ignoring non-stationarity in the variance. Surveillance counts often show variance that scales with the mean, so raw counts violate the assumptions of ordinary least squares regression. A log or square-root transformation, or a model with an explicit variance structure, is usually required before trend estimation. Detecting this early requires plotting residuals against fitted values after any preliminary model fit, a funnel-shaped spread indicates the variance problem persists.

A third failure is mis-specifying the seasonal period. Using a 12-month period when the biologically relevant cycle is shorter, such as a 6-month cycle driven by biannual calving or two transmission seasons per year, will smear the seasonal signal across adjacent harmonics. The discriminating check is to compare models fit with different seasonal periods using an information criterion. Ward, modeling canine leptospirosis diagnoses, selected the best-fitting regression using Akaike's corrected information criterion, a practice that should be routine instead of exceptional.

A fourth failure is confusing correlation with causation when environmental covariates are included. Rainfall, temperature, and humidity are collinear, and a model that includes all three will produce unstable coefficient estimates. Ward found a significant correlation between leptospirosis cases and rainfall recorded three months prior, but the biological pathway from rainfall to exposure is indirect and the lag may vary by region and serovar. Sensitivity analysis, fitting the model with and without each covariate, is the appropriate check.

Common Errors in Application

Less experienced analysts frequently begin by fitting an ARIMA model before examining the raw series. The correct sequence is descriptive first: plot the series, compute a moving average, and inspect the autocorrelation function. A model fitted to a series with an unexamined structural break, such as a change in diagnostic test or reporting protocol, will attribute the break to trend or seasonality. The corrective action is to annotate the series with known events and to fit separate models or include an intervention term.

A second error is using calendar month as the only temporal unit when the surveillance system records events at irregular intervals. Aggregating to a fixed unit discards information and can create artificial zeros. If the data are event-based, consider whether the analysis should model time-to-event or incidence density instead of monthly counts.

A third error is failing to account for population at risk. Prevalence and incidence require a denominator. A rising count of diagnosed cases may reflect an increasing tested population instead of increasing disease frequency. Nolan and Smith reported apparent prevalence, the proportion of submitted samples positive, which is a defensible measure but one that is sensitive to changes in submission patterns. When denominators are available, use them.

Limitations of the Current Evidence

The published veterinary literature contains relatively few rigorous time series analyzes of surveillance data. Many studies, including the endoparasite prevalence work of Nolan and Smith, are based on single institutions and convenience samples, which limits generalizability. The leptospirosis study by Ward used teaching hospital data from the Veterinary Medical Database, a source that over-represents referral populations and may miss cases diagnosed in private practice. Neither study could fully separate diagnostic effort from disease occurrence.

Expert opinion still differs on how much complexity is warranted. Some analysts advocate for hierarchical or state-space models that can accommodate multiple sources of variation. Others argue that simpler decomposition methods, applied carefully, capture the features that matter for surveillance decisions. The choice depends on the question. For detecting a change in seasonal amplitude, a straightforward seasonal decomposition may suffice. For generating a signal that triggers an automated alert, a more flexible model may be justified. The evidence base does not yet resolve this debate.

There is also genuine uncertainty about the optimal temporal resolution for surveillance data. Daily data can reveal short-term clustering but are noisy and require more complex models. Monthly data are stable but can obscure within-month dynamics. The correct resolution depends on the disease's incubation period, the reporting lag, and the speed of the response that the surveillance system can mount.

When to Escalate

Referral to a specialist biostatistician or epidemiologist is warranted when the series is short, when the data contain missing periods or structural breaks, or when the analysis will inform a regulatory decision. A veterinary researcher who finds a significant trend should not report it without checking whether the result is robust to the choice of method. If two reasonable methods give different conclusions, that disagreement should be reported and explained.

Laboratory involvement is indicated when the surveillance metric depends on diagnostic test performance. Changes in test sensitivity or specificity over time can masquerade as trends in disease frequency. A clinical pathologist or diagnostic laboratory can document test characteriztics and flag changes in reagents or protocols.

Regulatory reporting obligations are defined by international standards. The World Organization for Animal Health maintains surveillance standards and reporting frameworks for notifiable diseases, and its terrestrial animal health code specifies the obligations of member countries. When a time series analysis reveals an unusual cluster or an unexpected increase in a notifiable disease, the responsible authority should be contacted promptly. The decision to report is not the analyst's alone, but the analyst has a duty to communicate findings that meet the reporting threshold. The Centers for Disease Control and Prevention's principles of epidemiology provide a general framework for outbreak detection and response that applies across species, even though the specific reporting pathways differ by jurisdiction.

Frequently Asked Questions

How much historical data do I need before I can detect a meaningful seasonal pattern?

A practical rule is to have at least four to five full seasonal cycles, so 48 to 60 months for an annual pattern. Shorter series can still be examined with descriptive methods, but formal tests for seasonality will lack power. The autocorrelation approach used in the canine leptospirosis study relied on 16 years of monthly teaching hospital records to identify a late summer to fall peak. If you have fewer cycles, restrict claims to trend description and avoid asserting that an absent seasonal signal means no seasonality exists. Consider aggregating to a coarser time unit, such as quarters, to stabilize sparse counts.

What can I do when my surveillance data are collected irregularly or have gaps?

First, determine whether gaps are missing at random or tied to reporting effort. If gaps are sparse, interpolation may be acceptable for exploratory plots, but formal inference should use methods that accommodate uneven spacing. Aggregating irregular events into fixed time bins, such as weekly or monthly counts, is often the simplest fix. For hospital-based data, adjust for changes in patient throughput by modeling rates instead of raw counts, as was done in the teaching hospital endoparasite prevalence series. If gaps reflect holidays or laboratory closures, include an indicator variable for those periods. Do not impute long runs of missing months and then test for seasonality, the results will be artefactual.

How should I analyze time series from a single herd or farm instead of a regional population?

Single-farm series are noisier and more vulnerable to management changes, so interpret them as descriptive monitoring instead of population inference. Focus on abrupt changes that coincide with known interventions, such as vaccination or housing changes. The automated cow gait monitoring system was designed to store individual cow variables specifically for later time series analysis of walking behavior, which illustrates the value of repeated measures on the same animals. For herd-level counts, use control chart methods instead of formal seasonal decomposition when the series is short. Compare the herd pattern against regional reference data if available, but remember that regional seasonality may not hold for a single premises with unique management.

What level of record keeping is needed to support future time series analysis?

Record the denominator alongside every numerator. A case count without the population at risk, or without the number of samples tested, cannot be converted into a rate later. Store the date of sample collection, also the date of laboratory accession, because diagnostic delays distort seasonality. The WOAH animal health surveillance standards emphasize consistent case definitions and reporting protocols across time. Keep a log of changes in diagnostic tests, laboratory personnel, and submission criteria, since these create artificial shifts in the series. Archive raw data in a non-proprietary format and document any cleaning steps. If you cannot guarantee consistent denominators, state that limitation in any report.

How do I explain a seasonal pattern to a producer or practice owner without overstating the evidence?

Describe the pattern in practical terms, such as cases rising in late summer, and connect it to plausible mechanisms like rainfall or vector activity. Distinguish between a consistent seasonal peak and a single year's spike. The leptospirosis rainfall association provides a useful template: cases were most common from August to November, and rainfall three months earlier was correlated with case numbers. Explain that prediction is probabilistic, not certain, and that management adjustments should be evaluated over several seasons. Avoid claiming that a statistical association proves causation. Offer concrete monitoring actions, such as increasing sampling during the high-risk period, and agree on how you will review the data together at the end of the season.

Which software options are realistic for a clinician without a dedicated bioinformatics unit?

Spreadsheet software can handle moving averages, simple linear trends, and basic seasonal plots, and is adequate for descriptive work. For formal decomposition and autocorrelation, free statistical environments such as R provide established time series packages with extensive documentation. The CDC epidemiology self-study course covers the underlying analytic concepts and is a reasonable starting point for clinicians who want to strengthen their quantitative skills. Commercial statistical packages are also suitable if already licensed. Choose software based on the complexity of the question, not on fashion. For a single seasonal decomposition, a spreadsheet with careful documentation is defensible. For multi-site or multi-year analyzes with covariates, move to a scripting environment where every step is reproducible.

Related Clinical & Scientific Guides

• Evaluating Veterinary Surveillance System Attributes
• Network Analysis for Infectious Disease Spread in Animal Populations
• Randomized Controlled Trials in Veterinary Field Settings

References and Further Reading

• Time series analysis of the prevalence of endoparasitic infections in cats and dogs presented to a veterinary teaching hospital.. 1995.
• Rates and time trends in the consumption of breastmilk, formula, and animal milk by children younger than 2 years from 2000 to 2019: analysis of 113 countries.. 2021.
• Twenty-four-hour secretory pattern of cortisol in the bull: evidence of episodic secretion and circadian rhythm.. 1981.
• Seasonality of canine leptospirosis in the United States and Canada and its association with rainfall.. 2002.
• Development of a real time cow gait tracking and analyzing tool to assess lameness using a pressure sensitive walkway: The GAITWISE system. 2011.
• WOAH Animal Health Surveillance Standards. WOAH.
• CDC Principles of Epidemiology in Public Health Practice. CDC.
• MSD Veterinary Manual, Professional Edition. MSD Veterinary Manual.
• American Veterinary Medical Association Practice Resources. American Veterinary Medical Association.

Related Articles

• Sensitivity Analysis in Veterinary Disease Models
• Risk Factor Analysis for Disease in Animal Populations
• Designing and Implementing Animal Disease Surveillance Systems
• Designing Participatory Disease Surveillance in Livestock Systems
• Network Analysis for Infectious Disease Spread in Animal Populations

This article is educational professional reference material for veterinary audiences. It is not a substitute for veterinary diagnosis, individual clinical judgment, current product labeling, or applicable regulatory requirements.