STATISTICAL METHOD
Time Series Analysis and Forecasting
Statistical Consulting for Temporal Data
We apply time series analysis within your study design, examining stationarity, autocorrelation and seasonality, specifying and validating the model, and reporting estimates or forecasts with prediction intervals and out-of-sample accuracy.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Time Series Analysis?
Time series analysis models one outcome recorded at ordered, regularly spaced time points, such as monthly admissions or daily temperatures, to describe its structure or forecast it. Neighboring values are usually correlated, so the analysis examines trend, seasonality and autocorrelation, and fits models such as ARIMA once the series is made stationary, often by differencing. The aim may be forecasting, estimating the role of an exogenous variable or understanding dynamics. Ordinary regression on such data gives unreliable standard errors. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides time series analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is a Time Series Model Appropriate?
The method fits one outcome observed repeatedly at regular intervals over a long span, and these are the research situations in which researchers most often ask us to apply or confirm it.
Forecasting Demand or Incidence A long series of monthly or weekly values exists, and predictions with honest uncertainty are needed, such as admissions, case counts or sales next quarter.
Seasonality and Trend Questions The question is how an outcome moves over time, including cycles, seasonal peaks and long-run trend, in a series observed at regular intervals.
Regression With Time-Ordered Data An outcome and an exposure series, such as air pollution and daily visits, must be related while allowing for autocorrelation, trend and seasonal confounding.
Reviewing a Completed Series Model An ARIMA model is done, and a reviewer has questioned stationarity or forecast validation. Independent Statistical Review re-examines the differencing and the hold-out.
ANALYTICAL APPROACH
How We Apply Time Series Models
Within the family of Longitudinal & Multilevel Analysis, the series is examined for its structure first, because dependence over time decides which models are valid.
Stationarity and Differencing We judge trend and changing variance from plots, then difference or transform only as far as needed, reading unit root tests as supporting evidence of limited power.
Autocorrelation and Order Autocorrelation and partial autocorrelation plots guide candidate ARIMA orders, seasonal terms handle periodic patterns, and candidates are compared by information criteria.
Residual Checks and Breaks We check residuals for remaining autocorrelation with the Ljung-Box test and plots, and look for outliers and structural breaks that one model would otherwise average over.
Out-of-Sample Validation Forecasts are judged on held-out later periods, never a random split, with MAE, RMSE or MASE, and are reported with prediction intervals that are checked for coverage.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the model and its forecasts come with the diagnostics and files needed to report and defend them.
Data & Variable Review The time index, regular spacing, missing periods, outliers, changes in how the series is recorded and the number of observations are reviewed before any model is fitted.
Method-Specific Checks Stationarity, seasonality and structural breaks are examined, with autocorrelation analysis of the series and the residuals and sensitivity to the chosen model order.
Statistical Results The fitted model with parameter estimates and 95% confidence intervals, information criteria, and forecasts with prediction intervals and accuracy on held-out periods.
Publication-Ready Tables & Figures Series plots, correlograms, decomposition and forecast figures with prediction bands, formatted to the journal's requirements, ready to insert.
Interpretation Findings are written in terms of the pattern, the estimates and the forecast uncertainty, without presenting a forecast as certain or a shared trend as a relationship.
Reproducible Analysis Files R scripts, Stata do-files, SAS programs or Python code for the models and forecasts are provided where applicable, so results can be rerun when new observations arrive.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
The method follows the question, the series length and the design. These methods fit when an intervention is evaluated, when many units are followed or when subjects each contribute short series.
01
Interrupted Time Series
When the question is whether a change at a known date shifted the series, the model is built around that date, with level and slope terms fixed in advance.
02
Difference-in-Differences (DiD)
When only some units were exposed, comparing their change with unexposed units removes shared shocks, which one aggregate series cannot separate from the effect.
03
Linear Mixed Models (Multilevel Modeling)
When many subjects each contribute a short run of repeated measures, random effects describe individual trajectories better than a single pooled series model.
04
Cross-Lagged Panel Models
When two variables are measured in many people over a few waves, cross-lagged paths describe how each predicts the other, where a time series needs one long run of points.
CASE EXAMPLE
How We Work in Practice
An illustration of how a forecasting analysis moves from a fixed validation plan to a reportable, defensible model.
ILLUSTRATIVE EXAMPLE · EMERGENCY DEPARTMENT OPERATIONS · UNITED STATES
A hospital emergency department wanted to forecast daily visit counts for the next quarter to plan staffing, and to report how accurate the forecasts were likely to be.
Before any model was fit, the plan held out the last quarter of four years of daily data and compared models by held-out MASE and RMSE and by the coverage of 95% prediction intervals. The counts showed weekly and annual seasonality, so we compared seasonal ARIMA with Fourier terms and a calendar regression with ARIMA errors. A change in how visits were recorded produced a structural break, which we modeled explicitly and checked by starting the series after it. Residual autocorrelation was examined with the Ljung-Box test and correlograms, and the chosen model was refitted on all data only after the held-out comparison.
Outcome: The department received the chosen model with its forecasts and prediction intervals, held-out accuracy and interval coverage, the residual diagnostics, a methods summary and the code.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Time Series Models
ARIMA models, diagnostics and forecasts are run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Series Modeling Across Research Fields
Time series methods appear across research fields, each with its own series, seasonal patterns and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a public health researcher who needed stationarity, autocorrelation and the series specification confirmed.
“I had already started the Time Series Analysis, but I was not confident about stationarity, autocorrelation, and the right time-series specification. The team checked the setup against our study design, explained the decisions in plain language, and returned results we could actually use. The final output was concise, clearly interpreted, and ready to use in our research reporting.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your series analysis, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your series modeling, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The research question, how any forecast is used and your conclusions remain with you, and our interpretation stays within what the estimates and the data support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Time Series Modeling
Short answers to what researchers ask before modeling a series, from stationarity and validation to confidentiality and the assessment process.
Should I use ARIMA or an interrupted time series model?
It depends on the question. ARIMA and related models describe a series’ dependence and forecast it, while interrupted time series evaluates a change at a known date through its level and slope. ARIMA can carry an intervention term, but the date must then be prespecified and enough observations are needed on both sides. With many units, a mixed or panel model may fit better.
Is a random train and test split valid for forecasting?
No, a random split lets the model learn from the future and breaks the time order, so accuracy looks better than it will be. Forecasts are judged on held-out later periods, ideally with rolling-origin evaluation, using MAE, RMSE or MASE, and prediction interval coverage is checked. The test period must follow the training period in time.
Do I need a stationarity test before fitting ARIMA?
Stationarity must be addressed, but one unit root test does not settle it. ADF and KPSS tests have limited power and can disagree, so we read them with plots and the autocorrelation function. Differencing is applied as far as needed, since overdifferencing adds noise. The order is then checked with residual diagnostics, and short series support only simple models.
Can you review an analysis that has already been completed?
Yes, we can review a completed series analysis before submission or a response to reviewers. We check the stationarity decisions, the model order and seasonal terms, the residual diagnostics, how forecasts were validated and the reporting, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With
Time Series Analysis?
Share your research question, the series and its time span. We assess which modeling approach fits and confirm the plan before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014