Service overview
Statistical analysis, designed experiments, regression, reliability and measurement analytics. This service is part of that division and is scoped individually around what you need to learn, decide or publish.
Time-series data have memory. Today's temperature, load or flow depends on yesterday's, and ordinary statistical methods that assume independent observations can produce overconfident or simply wrong conclusions. Time-series analysis treats the order of observations as essential information, decomposing signals into trend, seasonality and irregular components and building models that exploit temporal dependence for description and forecasting.
Engineering applications are everywhere: energy demand, river flow, vibration trends in rotating machinery, production rates, sensor drift. The challenge is that real series are messy, with gaps, regime changes, outliers and sensor faults. A forecast is only valuable if it has been tested honestly on periods the model has never seen, and if its uncertainty is communicated alongside its central estimate.
If you plan to publish the outcome, see manuscript & publication support, for example computational & simulation manuscripts or original research article writing.
What this service covers
Problems this service can address
- Non-stationary data that violate standard assumptions
- Forecasts evaluated on data that leak future information
- Missing samples and irregular sampling
Methods and analytical approaches
- Trend, seasonality and decomposition analysis
- ARIMA-family and state-space models
- Stationarity testing and differencing
- Rolling-origin forecast validation
Applications
- Energy demand and generation forecasting
- Hydrological and environmental series
- Machine condition monitoring trends
Relevant engineering disciplines
Scope, inputs and deliverables
Scope of work
- Review of your objectives, constraints and the evidence already available
- Selection of methods suited to the question and the data
- Analysis or synthesis with documented, repeatable steps
- Written outputs you can reuse in a thesis, proposal or report
- Feasibility check on: timestamped data with sampling description
Typical inputs required from you
- Timestamped data with sampling description
- Known events or interventions
- Forecast horizon needed
Deliverables
- Cleaned series and diagnostics
- Forecast with prediction intervals
- Validation report and method description
Highly specialised requests are first checked for feasibility from this information. Please do not send confidential data through the public form; describe it first and agree secure transfer afterwards.
Project workflow and method
- 01Enquiry and requirement assessment
- 02Technical scoping and proposal
- 03Execution
- 04Quality review and delivery, with an agreed round of revisions
Read the full project workflow.
In depth: how the work is done
Exploring and decomposing the series
Plots of the raw series, its autocorrelation function and spectral content reveal trends, seasonal patterns at multiple scales, outliers and level shifts. Decomposition separates a slowly varying trend, repeating seasonal effects and a residual. Understanding sampling intervals, missing data and sensor behaviour comes first, since imputing gaps naively can distort dynamics. Domain knowledge, such as known operating schedules or weather effects, is combined with the statistical analysis to decide which patterns are real and which are artefacts.
Stationarity and model families
Many classical models require stationarity, meaning stable statistical properties over time. Tests and visual checks guide differencing or transformation to achieve it. ARIMA-family models capture autocorrelation structure, seasonal variants handle repeating patterns and exogenous regressors bring in weather or operating variables. State-space formulations offer flexible handling of trends, missing values and time-varying parameters. For nonlinear or multivariate problems, regression on lagged features or other machine-learning approaches can be considered and compared with these baselines.
Validating forecasts correctly
Random train and test splits are invalid for time series because they allow the model to see the future. Rolling-origin evaluation repeatedly fits on past data and forecasts the next period, giving a realistic estimate of accuracy across different times and conditions. Forecast errors are summarised with measures suited to the application, and comparisons include simple baselines such as persistence or seasonal naive forecasts. A complex model must beat these to justify its existence.
Uncertainty, anomalies and operational use
A point forecast without an interval is incomplete. Prediction intervals, checked for calibration on held-out data, show the range of plausible outcomes. For monitoring tasks, residuals from the model can be used to flag unusual behaviour. We also discuss how models should be updated as conditions change and how to detect when a model's performance degrades, because structural changes, such as new equipment, can invalidate historical relationships.
Handling messy real-world signals
Sensor data often include spikes, flat-lined segments, unit changes and timestamp problems. Before modelling, we document the data pipeline, flag suspicious segments and decide with you whether to repair, down-weight or exclude them. Resampling to a common interval is done in a way that avoids introducing artefacts, and outliers are treated according to whether they are errors or genuine events. Clear handling rules prevent a model from learning sensor faults as if they were physical behaviour.
Quality control and good practice
Quality-control approach
- Search, selection or analysis steps are documented so another researcher can repeat them.
- Assumptions, exclusions and limitations are stated rather than implied.
- Numbers in text, tables and figures are cross-checked for consistency.
- Conclusions are limited to what the evidence supports.
Common pitfalls this service helps avoid
- Random cross-validation. Shuffling time-ordered data leaks future information into training and exaggerates accuracy.
- Ignoring structural breaks. Level or regime changes make older data unrepresentative and can mislead parameter estimates.
- Over-fitting seasonal patterns. Flexible models can memorise a few seasons and then fail when patterns shift.
- Reporting forecasts without baselines. Without a simple benchmark, it is impossible to know whether a model adds value.
What good reporting looks like
A time-series report describes the data source, sampling, cleaning and treatment of gaps, exploratory findings, the models compared and their assumptions, the validation scheme with horizon and rolling-origin details, forecast accuracy against baselines, prediction intervals and their calibration, and the limitations including structural change risk. Code and parameter settings are documented to allow the forecasts to be reproduced and updated.
An illustrative scenario
Hypothetical example written for explanation. It is not a client case, a result or a testimonial.
Imagine an engineer forecasting daily electricity demand for a campus. The series shows weekly and annual seasonality and a drop during a holiday period. A seasonal model with temperature as an external input is compared with a seasonal naive baseline using rolling-origin evaluation over two years. The model improves on the baseline except during unusual events such as closures, so the report recommends adding a calendar indicator and shows interval coverage for each month. It also notes that a major building addition will change the relationship and the model must be re-estimated.
Questions to settle before you begin
- What is the forecast horizon and how often will forecasts be made?
- How long is my history, and does it cover the conditions I care about?
- What simple baseline must any model beat?
- How will I handle gaps, sensor faults and structural changes?
- What decision depends on the forecast, and how much error can it tolerate?
Key terms
- Stationarity
- Stability of mean, variance and autocorrelation over time.
- Autocorrelation
- Correlation between a series and a lagged copy of itself.
- ARIMA
- A model class combining autoregression, differencing and moving average terms.
- Rolling-origin evaluation
- Repeated forecasting from successive cut-off times to test accuracy.
- Prediction interval
- A range expected to contain future observations with a stated probability.
Working together on Engineering Data Analysis & Statistics projects
Data analysis engagements start with a data description before any modelling: what was measured, how, under what conditions, with which instruments and with what known problems. Sharing a small sample or a data dictionary first is usually enough to scope the work. Analyses are documented step by step so that every figure and table can be reproduced from the supplied data, and code or workflow files can be provided on request. Please avoid sending confidential or personal data through the public form; secure transfer can be arranged after scoping. Conclusions are phrased with the uncertainty the data justify, not stronger.
Frequently asked questions
Do you use deep learning for forecasting?
Only when the data volume and the problem justify it. Classical models are often competitive and easier to interpret, and we compare them fairly.
How much history do I need?
Enough to cover the patterns you want to model, typically several seasonal cycles, and enough variety in operating conditions. Short histories limit what can be reliably learned.
Can you forecast with missing data?
Yes, within limits. Methods handle gaps, but the cause and pattern of missingness should be understood.
Should I use deep learning for forecasting?
Sometimes, but simpler models often perform comparably on small datasets and are easier to validate and explain. Comparison with baselines settles the question.
Can the model detect anomalies?
Residual-based detection is possible. Whether flagged events are faults depends on the process, so thresholds should be set with domain input.
How is this service scoped and priced?
After your enquiry we review what you need, ask for missing information and send a written scope and quotation. Price depends on complexity, deliverables and timeline. See the project workflow.